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A rational method for analysis and design of geosynthetic reinforced soil foundations

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Title:
A rational method for analysis and design of geosynthetic reinforced soil foundations
Creator:
Barreire, William J
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Language:
English
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x, 110 leaves : ill. ; 28 cm.

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Geosynthetics ( lcsh )
Soil mechanics ( lcsh )
Soil-structure interaction ( lcsh )
Foundations ( lcsh )
Foundations ( fast )
Geosynthetics ( fast )
Soil mechanics ( fast )
Soil-structure interaction ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (M.S.)--University of Colorado at Denver, 2001.
Bibliography:
Includes bibliographical references (leaves 109-110).
General Note:
Department of Civil Engineering
Statement of Responsibility:
by William J. Barreire.

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University of Colorado Denver
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All applicable rights reserved by the source institution and holding location.
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50727477 ( OCLC )
ocm50727477

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A RATIONAL METHOD FOR ANALYSIS AND DESIGN OF GEOSYNTHETIC REINFORCED SOIL FOUNDATIONS by William J. Barre ire B.S., Colorado State University, 1992 A thesis submitted to the University of Colorado at Denver in partial fulfilhnent of the requirements for the degree of Master of Science Civil Engineering 2001

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This thesis for the Master of Science degree by William J. Barreire has been approved by 1,. Bnan Brady Sarosh Khan I 1 Date

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Barreire, William 1. (M.S., Civil Engineering) A Rational Method for Analysis and Design of Geosynthetic Reinforced Soil Foundations Thesis directed by Professor Jonathan Wu ABSTRACT Geosynthetic Reinforced Soil Foundation (GRSF) systems provide designers with a foundation alternative to use in lieu of some of the more common ground improvement techniques, or deep foundation alternatives. For sites where poor ground conditions exist, and more common mitigation alternatives prove to be cost prohibitive, GSRF systems can provide a good and economical foundation alternative. While the GRSF system is a relatively new concept, existing research, field and laboratory experiments, as well as documented practical applications indicate this type of system can provide a reliable foundation alternative when properly designed and constructed. This study was undertaken to review and summarize previous studies on GRSF systems. Based on the literature review, and the author's experience, a rational method for analysis and design ofGRSF systems was proposed. The design method includes applying the concept of a "deep footing" to the GRSF system and utilizing the general bearing capacity equation to estimate the increase in bearing capacity. Additionally, a method for evaluating the settlement of a GRSF system includes combining the deep footing concept with an "apparent footing" that is significantly wider than the actual footing, then utilizing classical settlement analysis methods. The apparent footing has dimensions that are defined by a stress distribution angle within the GRSF system that is significantly larger than that ofunreinforced soils. The results of employing these concepts for estimation of the bearing capacity and settlement of GRSF systems shows good correlation with the measured results of large-scale experimental testing. This abstract accurately represents the contents of the candidate's thesis. I recommend its publication. Ill

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CONTENTS Figures .................................................................................................................... vii Tables ...................................................................................................................... x Chapter 1. Introduction ........................................................................................................... I 1.1 Problem Statement ............................................................................................... l 1.2 Objectives ......................................................................................................... 2 1.3 Method of Research ............................................................................................ 3 1.4 Report Overview .................................................................................................. 3 2. Literature Review .................................................................................................. 4 2.1 Literature Review Sununaries ............................................................................... 5 3. Sythesis ofthe Literature ...................................................................................... 51 3.1 Vertical Reinforcement Layer Spacing (Su, Sr, Sb) .............................................. 53 3.2 Nwnber of Reinforcement Layers (Nr) ................................................................ 54 3.3 Depth of Reinforced Zone (Dr) ........................................................................... 54 3.4 Width (b) and Length (I) of Reinforcement ......................................................... 55 3.5 Type and Strength/Sti.ffuess of Reinforcement .................................................... 55 3.6 Soil/Aggregate Fill Type and Density Within the Reinforced Zone ...................... 57 IV

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3.7 Summary ........................................................................................................ 58 4. Proposed Model for Estimating Bearing Capacity and Settlement of a GRSF ....... 60 4.1 Bearing Capacity ............................................................................................... 60 4.1.1 General Concepts ........................................................................................... 60 4.1.2 Bearing Capacity Failure Modes ...................................................................... 67 4.1.3 Proposed Model for Bearing Capacity Analysis ............................................... 68 4.2 Settlement. ...................................................................................................... 71 4.2.1 General Concepts ........................................................................................... 71 4.2.2 Proposed Model for Settlement Analysis ......................................................... 73 5. Design of a GRSF System .................................................................................... 78 5.1 Appropriate Applications ofa GRSF System ...................................................... 78 5.2 Typical GRSF Design Parameters ....................................................................... 79 5.3 Estiinating Bearing Capacity .............................................................................. 81 5.4 Estiinating Settlement ........................................................................................ 82 5.5 Design Exan1ple ................................................................................................ 82 6. Construction Considerations ................................................................................ 86 6.1 Subgrade Preparation ......................................................................................... 86 6.2 Utilities ........................................................................................................... 87 6.3 Fill Type and Compaction .................................................................................. 88 6.4 Providing GRSF Parameters for Construction .................................................... 88 6.5 Other Considerations .......................................................................................... 89 v

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7. Concluding Remarks ............................................................................................ 90 Appendix A. Bearing Capacity Calculations ............................................................................. 91 B. SettleiTlent Calculations ....................................................................................... 96 References ............................................................................................................. 1 09 VI

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FIGURES Figure 2.1 Typical GRSF Configuration. ....................................................... 5 2.2 Test-Pit Footing Layout .............................................................. 6 2.3 Bearing Pressure vs. Settlement Curves for 0.46 m Footing, Series 1-3 ....... 9 2.4 Bearing Pressure vs. Settlement Curves for 0.61 m Footing, Series l-3 ....... 9 2.5 Bearing Pressure vs. Settlement Curves for 0.91 m Footing, Series 1-3 ...... lO 2.6 Bearing Pressure vs. Settlement Curves for All Footings for Series 1 ......... 1 0 2.7 Bearing Pressure vs. Settlement Curves for All Footings for Series 2 ......... 11 2.8 Bearing Pressure vs. Settlement Curves for All Footings for Series 3 ......... 11 2.9 Test Series 2-Bearing Capacity Ratio Based on 0.5, 1.0, and 3.0% Settlements ............................................................................ 12 2.10 Bearing Pressure vs. Settlement Curves for 0.46 m Footing, Series 4 ......... 14 2.11 Bearing Pressure vs. Settlement Curves for 0.61 m, Footing Series 5 ......... 15 2.12 Bearing Pressure vs. Settlement Curves for 0.61 m, Footing Series 6 ......... 15 2.13 Geometry ofthe Test Model.. ...................................................... 18 2.14 Load-Settlement Curves For M/B=0.25, N=3 and b/B=3 ...................... 19 2.15 BCR Variation with Depth of Top Layer, .::\z/B=0.25, N=3 and b/B=3 ....... 19 2.16 BCR Variation with Vertical Spacing ofReinforcement, u/B=0.25, N=2 and b!B=3 .............................................................................. 20 2.17 BCR Variation with Number of Reinforcing Layers, u!B=0.50, .::\:zJB=0/25 and b/B=3 .............................................................................. 21 2.18 BCR Variation with Width Ratio, ul8=0.50, .::\z/B=0.25 and N=3 ............ 22 2.19 Geometric Parameters of Reinforced Foundation ................................ 24 2.20 Variation of BCR with Depth Ratio in Single-Layer Reinforced Sand (s/B=s/D= 2%, B/B= D/0= 4.5) ........................................... 26 2.21 Variation ofBCR with Depth Ratio in Multi-Layer Reinforced Sand (s!B=s/D= 2%, N=4, :z!B= zJD = 0.30, B..IB= D,/D= 4.5) ...................... 27 Vll

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2.22 Typical Variation ofBCR with Vertical Spacing of Reinforcement Layers (s/B=s/D= 2%, N=4, u!B= uiD = 0.30, BJB= DJD= 4.5) ............. 28 2.23 Variation ofBCR with Number ofReinforcement Layers (s/B=s/D= 2%, u!B= u!D=z!B= z/D = 0.30, B/B= D!D= 4.5) ................................... 29 2.24 Variation ofBCR with Reinforcement Size (s!B=s/D=2%, N=4, u!B=u!D=z/B=z!D = 0.30) ................................................... 30 2.25 Variation ofBCR with Reinforcement Stiffuess ( N=3, u!D=z!D= 0.30, D!D= 4.5) ............................................................................. 31 2.26 Rectangular Surfuce Foundation on Sand Reinforced with Layers of Geogrid ................................................................................. 33 2.27 Variation of Ultimate Bearing Capacity qu with BIL (Test Series A; Tests with Unreinforced Sand) .............................................................. 34 2.28 Typical Plots of Load per Unit Area Versus Settlement for Strip Foundation on Geogrid-reinforced Sand (Test Series B-1) .................................... 35 2.29 Variation ofBCR with Nand diB (Test series B-1, B-2, B-3, and B-4) ...... 37 2.30 Variation ofBCR with biB (Test Series C-1, C-2, C-3, and C-4) ............. 38 2.31 Variation ofbc/B with BIL ......................................................... 39 2.32 Variation ofBCR with VB (Test Series D-1, D-2, and C-4) .................... 40 2.33 Model Test Arrangement ............................................................. 42 2.34 Footing Load-displacement Relations for Group-a .............................. 44 2.35 Footing Load-displacement Relations for Group-b ................................ 45 2.36 Footing Load-displacement Relations for Group-c ................................ 46 2.37 Footing Load-displacement Relations for Group-d ................................ 47 2.38 Footing Load-displacement Relations for Group-e ................................ 48 2.39 Geometry of System: (a) Transverse Cross Section; and (b) Longitudinal Cross Section (SectionX-X) ........................................................ 49 3.1 Typical GRSF Configuration ....................................................... 52 3.2 Variation ofBCR with Reinforcement Stiffuess ( N=3, u!D=z/D= 0.30, DJD= 4.5) ............................................................................. 56 4.1 "Apparent Confinement" ............................................................ 62 4.2 "Apparent Cohesion" ................................................................ 62 4.3 "Deep-Footing Effect" ............................................................... 63 Vlll

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4.4 Load (N)/Settlement (SIB) Curves, Illustrating the "Deep-Footing Effect"; Huang & Tatsuoka (1990) ................................................ 64 4.5 Anchoring Resistance of Extended Portion of Reinforcement.. ................ 65 4.6 Tensile Forces in Reinforcement up to Peak. Test No. 17(L/B=6, n=3, CR=18%) (Huang & Tatsuoka, 1990) ...................................... 66 4.7 Failure Above Upper Reinforcement Layer (Upper Failure) .................... 67 4.8 Failure Between Reinforcement (Inter-layer Failure) ............................ 67 4.9 Punching Failure Through Reinforcement (GSRF Failure) ..................... 67 4.10 Punching Failure of Entire GSRF (Deep-footing Failure) ....................... 67 4.11 "Deep-footing Effect" ............................................................... 69 4.12 Stress Distribution Angle ............................................................ 71 4.13 Stress Distribution .................................................................... 76 5.1 Typical GRSF Configuration ....................................................... 80 IX

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TABLES Table 2.1 Phase I Test Summary ............................................................... 8 2.2 Phase II Test Summary .............................................................. 14 2.3 Summary ofSome Test Results for Reinforced and Unreinforced Sand ...... 25 2.4 Details of Laboratory Model Tests ................................................ 33 2.5 Summary of Results from Test Series B-1, B-2, B-3, and B-4 ................. 36 2.6 Summary of Results from Test Series C-1, C-2, C-3, and C-4 ................. 38 2.7 Summary ofResults from Test Series D-1 and D-2 .............................. 40 2.8 Summary of Test Results ............................................................ 50 4.1 Bearing Capacity Comparison Results ............................................. 70 4.2 Elastic Modulus for Cohesionless Soil, Es (kst) .................................. 73 4.3 Typical Range of Elastic Parameters for Various Soil Types (Das, 1995) .... 74 4.4 Increase in Elastic Modulus due to Geogrid ...................................... 74 4.5 Settlement Comparison Results .................................................... 77 5.1 Typical GRSF Design Parameters .................................................. 81 X

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1. Introduction l.l Problem Statement Geosynthetics have recently become a widely accepted engineering material used by practitioners to design reinforced soil structures including retaining walls, embankments, dams, slopes, etc. Additionally, geosynthetic reinforcement has been used to increase support capabilities of foundation soils, which is commonly referred to as base reinforcement. Geosynthetic reinforcement is also commonly used beneath roadways where additional support is required to improve the performance of poor subgrade soils. Research, experimentation, and practical application have proven that this technology can provide a reliable and economical alternative to more classical stabilization and reinforcement techniques. With the successful use of geosynthetics for the purposes described above, it naturally follows that they might also be used to improve the support characteristics of poor subgrade soils located beneath structure foundations. This type of application is conunonly referred to as a Geosynthetic Reinforced Soil Foundation (GRSF) system, and is the main focus of this report. There are various classical methods of mitigation on sites with poor subgrade soil conditions, which include: construction of deep foundations, replacement of all or a portion of the poor subgrade soils with stronger material, densification through consolidation or compaction, use of chemical admixtures to strengthen existing soils, and, to a lesser extent, the use of thermal, or biological stabilization techniques. The purpose of aU of these approaches is to increase the load carrying capability of the resulting foundations and reduce settlement. Many of these approaches are used everyday and are successful in achieving the desired performance characteristics. However, most of the above systems add significant expense to a project and can be cost prohibitive.

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Therefore, the purpose of introducing the GRSF system is to provide a reliable foundation alternative to the more classical approaches. While there is no "cheap and reliable" method to mitigate sites with poor foundation soils, it is the authors opinion that GRSF systems can provide an economically viable and reliable alternative to the previously mentioned approaches to ground improvement. However, this requires that these systems are used in appropriate situations and are properly designed and constructed. In general terms, the GRSF system can be thought of as an additional ground improvement alternative. A GRSF system is an extension of a "remove and replace" ground improvement approach, in that a portion of the poor soils are removed and generally replaced with stronger soil or aggregate material. However, the difference is that the material is reinforced with the inclusion of geosynthetic reinforcement. 1.2 Objectives A significant amount of research and experimentation has been performed in the area of "reinforced soil foundations". The vast majority of the published information provides the results of numerous smaller scale laboratory experiments as well as various large-scale field experiments. In general, the majority of the experiments evaluated the effect that the inclusion of various types of reinforcement (geosynthetics and otherwise) had on the bearing capacity of a soil mass, as compared to the bearing capacity of the same soil mass without reinforcement. Additionally, many of the experiments also evaluated the effect of reinforcement on reducing settlement. At this time, only a few of the published reports have attempted to include a design methodology as part of their results. The objectives of this report were two-fold. The first objective was to review the results of some of the existing research on GRSF systems. The second objective was to propose a rational approach for the analysis and design of reinforced soil foundations. 2

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Due to the widely accepted use of geos)1lthetics in the area of soil reinforcement, the large amount of technical data that is available on these types of products, and significant amount of recent research that has been performed using geosynthetics for reinforcement of soil foundations, this report will focus only on the use of geosynthetics for reinforcement. Presently, stiff geogrids are generally used for this purpose due to their strength, relatively high modulus as compared to most other geosynthetic reinforcement, as well as their durability. 1.3 Method of Research Research was performed by reviewing published material found in numerous technical papers as well as some text books. The research included evaluating the results of the numerous experiments as well as reviewing existing design related data in order to compile a reasonable approach for the analysis and design of Geosynthetic Reinforced Soil Foundation systems. Data obtained from large-scale experiments was used to verifY the analysis and design method presented in this report. 1.4 Report Ovenriew This report provides an extensive summary of the literature review (Chapter 2), as well as conclusions regarding the results from the various reviewed experiments, in order to determine various parameters or range of parameters that appear to be useful from a design and construction standpoint (Chapter 3). Existing concepts related to the analysis and design of GRSF systems are also discussed (Chapter 4). Using the existing experimental data, and design and analysis concepts, a rational method for analysis and design of GRSF systems is proposed (Chapters 4 & 5). The method includes a range of recommended parameters regarding the extent of the reinforced zone, vertical spacing of the reinforcement, appropriate soil and reinforcement materials, etc. A design example is provided to illustrate the proposed design method (Chapter 5). Additionally, various considerations regarding construction of this '"not so conventional" type of foundation system are discussed (Chapter 6), as well as the limitations of its use. 3

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2. Literature Review The following section presents a swnmary of selected published papers that present various studies on reinforced soil foundations. While the type of reinforcement used in the numerous published studies that exist can vary significantly from metal strips to rope or geosynthetics, etc., the majority of the studies summarized in this section concentrate on the use of geosynthetics as reinforcement with a few variations. This is mainly because geosynthetics have become a popular tool for engineers due to the fact that it is a relatively well researched and widely practiced technology that has proven to be beneficial for many applications. Additionally, specific types of geosynthetics (namely geogrid) appear to provide a good balance of availability, economics, and the desired properties that make it well suited for use in reinforced soil foundations. The following summaries, as well as many of the other studies of reinforced soil foundations that exist, have had similar goals. While each may present somewhat different approaches and purposes, the majority of the studies included an evaluation of the effects of the type, size, and configuration of the reinforcement, as well as the type of soil used on the bearing capacity of different types of shallow foundations. With this, there are various parameters and associated acronyms that will be discussed and used frequently in the following sections. While the parameters including the spacing between reinforcement layers, the size of the reinforcement, the total depth of reinforcement, etc., will be labeled somewhat differently for each study (e.g. s,u,or a may be used to designate reinforcement layer spacing), most, if not all of the studies present these parameters as a ratio of the footing width. For example, the vertical spacing (s) between each reinforcement layer will be presented as Spacing/Footing Width, (siB). While spacing may or may not be labeled "s", the footing width is almost always labeled "B" with a few exceptions where ''D" is used to represent the diameter of a circular footing. However, the use of "B" will be used frequently throughout this section to represent the footing width. Settlement due to loading is presented as a ratio ofthe footing width as well. Additionally, the increase in bearing 4

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capacity due to the inclusion of reinforcement in the foundation soils is presented as the Bearing Capacity Ratio (BCR) where the BCR = bearing capacity (reinforced)lbearing capacity (unreinforced). The following figure presents a typical configuration of a reinforced soil foundation. Excavation Limits 8 (footing width) Footing Reinforcement Structural Fit Typical GRSF Configuration Figure 2.1 Lastly, because settlement typically controls foundation design rather than ultimate bearing capacity. attention is brought to test results that include settlement data in conjunction with the bearing capacity data. 2.1 Literature Review Summaries Adams and Collin (1997) This research included performing 34 large-scale load tests to evaluate the effect of using single and multiple layers of geosynthetics to reinforce the soil below square footing pads. The tests were performed in a relatively large test pit that was constructed ofreinforced concrete and had plan dimensions of approximately 5.5 by 7 5

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m and a depth of approximately 6 m. Due to the size of the test pit, multiple tests could be set up at one time. The footings were constructed of reinforced concrete and ranged in size from 0.3 to 0.91 m (12 to 36 inches) square in plan dimension. The soil consisted of a poorly graded sand with inclusion of a stiff biaxial geogrid as well as a geocell. The ultimate strength of the geogrid per ASTM 04595 was 34 kN/m. At 5% strain, the strength was 20kN/m in the machine direction and 25 kN/m in the cross machine direction. The aperture size for the geogrid was 25 by 30 nun. The geoceU consisted of high density polyethylene sheets that were 1.25 mm thick. The sheets were cut into strips 200 mm wide and welded together in a honeycomb pattern. The cell dimensions were 200 by 244 mm The tested parameters included the number of reinforcing layers, vertical spacing of the layers, depth to the first layer, plan area of reinforcement, type of reinforcement (geogrid vs. geocell), and soil density. The primary objective of the study was to evaluate the above parameters with respect to bearing capacity and settlement. Figure 2.2, below, shows a typical test layout. !i I I II II e-o-&oTest-Pit Footing Layout Figure 2.2 6 1: co .... trol -------1 I Cross-Section

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The study included two phases, with three series of testing in each phase. The following descnbes the different series within each phase, as well as the primary purpose of each of the two phases: PHASE I (all footing sizes and both reinforcement types were used; soil density was 14.8 kN/m3 ) Purpose ofPhase I Testing Evaluate the effect of vertical spacing of the reinforcement of the Bearing Capacity Ratio (BCR) Quantify the difference in performance between the geogrid versus the geocell reinforcement Series Description Series I -All footing sizes tested on unreinforced sand (control tests) Series 2 -Same as series 1 except all footings were founded on three layers of geogrid Series 3 Same as series 2 except one layer of geocell was used as reinforcement PHASE II (Only 0.61-m footing and geogrid reinforcement were used for this phase) Purpose ofPhase II Testing Evaluate the effect of one versus two layers of reinforcement on the BCR Evaluate the effect of the depth of the first layer of reinforcement below the bottom of the footing on the BCR Evaluate the effect ofthe size (plan area) ofthe reinforcement on the BCR Evaluate the effect of the density of the reinforced soil on the BCR Series Description Series 4 One layer of reinforcement was used at varying depths and widths; soil density was 14.7 kN/m3 Series 5 -Three tests included two layers of geogrid, one test included one layer, one test was unreinforced; soil density was 14.5 kN/m3 Series 6 Same as series 5 except soil density was reduced to 14.2 kN/m3 7

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It srou1d be noted that the BCR at 0.5. I, ani 3% settlenrnt, where the sett.Ierrent (s) is defuxrl as a ratio ofthe footing width B (e.g., Settlerrent Ratio, siB= 0.5, I, or 3%). 1k "uhimate" BCR was also measured However, fur the purpose of this testing the uhirnate BCR was conservatively defined as the intersection between the two straight portions of the settlenalt curve shown in Figure 2.3, following. While there is typical1y a relatively distinct break in the settlement curve where rearing failure takes place without the ctDVes where the geogrid was used were relatively smJOth and the typical phmging fui1ure was not reached Therefore, where the use of geogrid resuhed in a relatively smooth load curve, the procedure presented in the figure below was used as an estimation of the uhirnate bearing capacity. With this it should be noted that values in the column termed '"Tangent intersect" in the data tables provided are the approximated uhimate BCRs. Also, note that the load-settlement curve resulting from the use of geocell reinforcement was similar in shape to that of the tmreinforced (control) case. The following table and seven figures present the resuhs of the Phase I testing, as presented by Adarm and Coll:im (I 997). Test Identification B n=l (m) (I) Z,!B (2) (3) 1195 0.31 15395 0.46 2295 0.61 3195 0.91 1194T 0.31 0.5 1294T 0.31 o.s 15194T 0.46 0.33 15295T 0.46 0.33 2194T 0.61 0.25 2294T 0.61 0.25 3194T 0.91 0.17 1295G O.JI 0.66 15195G 0.46 0.44 15295G 0.46 0.44 2295G 0.61 0.32 2395G 0.61 0.32 3195G 0.91 0.22 Reinforcement n=2 l2IB (4) --I I 0.66 0.66 0.5 0.5 0.34 -n=3 Area Qab Tangent (ml) (kPa) Z,!B (5) (6) (7) (8) (a) Y(drvl = 14.8 kN/m3 --247 I --245 I --269 I --283 I (b) Yrdrvl = 14.8 kN/m3 1.5 Continuous 554 2.24 1.5 Continuous 528 2.13 I Continuous 558 2.28 I Continuous 639 2.61 0.75 Continuous -0.75 Continuous 664 2.47 0.5 Continuous 542 1.92 (c) Y
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0 100 0 ..................... -5 -10 -15 'E i -20 -25 -30 -35 -40 200 ----------,\ ' ' ' ' ' ' ' ' ' ' ' Bearing Pre99ure (kPo) JOO 400 500 600 700 Bearing Pressure vs. Settlement Curves for 0.46 m Footing, Series 1-3 Figure 2.3 800 900 ---------(Control} --<>--o--(Geocoll) ,295C (Ceoc .. l) (Goo9rW!) ----1,2!141 (Goo9rld) ___ J_I_) --J ..... la-r-) ----12'to01 (a...p..) Bearing Pressure vs. Settlement Curves For 0.61 m Footing, Series 1-3 Figure 2.4 9 '

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0 100 0 -10 -20 -30 'E -40 < j -50 "' -60 -70 -80 -90 0 0 -10 -20 ,....... E -30 E "-' -40 c Q) -50 E .!!! -60 a; V1 -70 -80 -90 Bearing Pressure (kPo) 200 300 ---<>--J194T (Geo.gri
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0 0 -5 -o _,. I -20 l l -lO _,. ....., 0 0 -10 -20 -30 E' s -40 c ., -50 E .!! v -60 Vl -70 -soi -90 S.O,..,.. Pr.-...e (IIPo) 000 000 ------22tlf \ \ Bearing Pressure vs. Settlement Curves for AU Footings for Series 2 Figure 2.7 Beoring Pressure (kPo) 100 200 300 400 500 Bearing Pressure vs. Settlement Curves for All Footings for Series 3 Figure 2.8 11 600 ------1295G ---<>----1 5195G 15295G -o--2195G ---2295G ----2395G 3195G

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.3.00 2.50 2.00 .. a i< .!>0 ... "" 1.00 0.50 0.00 1 1294T 2194T !ll1i BCROO.""' BCRC>T.O"' D BCRCI>3.0"' 2294T 31Si14T Test Series 2-Bearing Capacity Ratio Based On 0.5, 1.0, and 3.0% Settlements Figure 2.9 As discussed above, the primary purpose of the Phase I testing was to evaluate the effect of vertical spacing of the reinforcement on the BCR as well as to evaluate the effectiveness of using geogrid reinforcement versus a geocell. When evaluating the resuhs presented in Table 2.1 (for the series two testing), it can be seen that at low settlements, close spacing of the geogrid reinforcement resulted in the highest BCRs. However, where the footing pressure and therefore settlement was higher, better resuhs were generally obtained with a deeper total depth of reinforcement (in this case, total depth= footing width = 1B) in conjunction with a reasonable vertical spacing (spacing = 0.33B in this case). Therefore the trend of this data would appear to indicate that a close vertical spacing of approximately 0.3B or less in conjunction with a total depth of reinforcement of 1 to 1.5 B likely provides desirable if not optimal results regarding the BCR at lower settlements. 12

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It appears that a general conclusion could be that it is more important to have the first layer closer to the bottom ofthe footing and closer spacing for subsequent reinforcing layers, where lower footing pressures and settlements are concerned; compared to having a deeper total depth of reinforcement beneath the footing. On the other hand, for higher footing pressures and larger settlements, the total depth of reinforcement becomes an important factor. Therefore, for practical applications, an engineer must balance foundation widths and expected pressures with the vertical spacing and total depth of reinforcement, while keeping economics and construction considerations in mind. Tests performed using the geocell reinforcement resulted in lower BCRs than those using a geogrid reinforcement. It should be noted that the results in Table 2.1 indicate that only one layer of geocell was used. The ultimate BCRs for the geocell were erratic, and generally ranged from approximately 1 to 1.25, with one higher BCR of 1.62, whereas the BCRs for the geogrid were typically more consistent, and for one layer of geogrid reinforcement, were in the range of approximately 1.5 to 1.9. Therefore, the use of geocell to reinforce foundation soils does not appear to provide consistent or effective resuhs. 13

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The following table and three figures present the results of the Phase II testing. Test B Ideotific:ation n=l (m) (I) Z1/B (2) (3) SDill-ll 0.61 TLI46 0.61 025 TL149 0.61 0.38 TLI66 0.61 025 TL169 0.61 0.38 TL186 0.61 025 TL20(..,_1) 0.61 -TL286 0.61 0.25 TL2461 0.61 025 TL2661 0.61 025 TL2861 0.61 0.25 TL301..-, 0.61 -TL386 0.61 0.25 TL3461 0.61 025 TL3661 0.61 025 TL3861 0.61 025 0 0 -o -20 _,., _.., I 1 _.., :; -00 -70 -eo -00 Rcinfurccmcnt Z2/B (4) --0.5 0.5 0.5 --0.5 0.5 0.5 Q.., Area Tangent (m2) (kPa) Zv'B Intersect (5) (6) (7) (8) a) = 14.7 kN/m3 -160 1.00 -12X 12 250 1.56 12XI.2 260 1.63 -1.8 X 1.8 253 1.58 -1.8 X 1.8 302 1.89 -2.4 X2.4 249 1.56 (b) r(dly) = 14.5 kN/m3 --180 1.00 -2.4 X2.4 208 1.16 -1.2 X 12 264 1.47 -1.8X1.8 195 1.08 -2.4X2.4 215 1.19 c) = 14.2 kN/m3 --93 1.00 -2.4 X2.4 127 1.37 12XI2 157 1.69 -1.8XI.8 117 1.26 -2.4X2.4 112 120 Phase H Test Summary Table 2.2 Bearing Capacity Ratio siB 1% (9) (10) 1.00 I 1.08 1.29 1.19 1.36 0.95 1.22 0.92 1.23 1.09 1.40 1.00 I 1.30 1.26 1.42 1.43 1.42 1.23 1.20 1.15 1.00 I 1.38 1.42 0.67 0.75 1.07 1.05 0.76 0.86 oOOO .., ------mn (c.t-1) -'I\.1U --'1\.lal Bearing Pressure vs. Settlement Curves for 0.46 m Footing, Series 4 Figure 2.10 14 3% (II) I 1.63 1.63 1.53 1.71 1.61 I 1.25 1.51 1.13 1.15 I 1.45 1.05 1.14 1.01

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0 50 0 -10 -20 e -5. -JO ] J j -40 -50 -60 -70 l 0 50 0 -10 -20 -30 E' E -40 c: -50 ., E -60 Q) "' -70 -80 -90 -100 Beori"9 Prenure {kPa) 100 150 200 250 300 350 " ' 400 450 ------1L.20 (Conlol) -TL.21K1 ---a---1L2N1 ---1L.21!181 Bearing Pressure vs. Settlement Curves for 0.61 m, Footing Series 5 Figure 2.11 Bearing Pressure (kPo) 100 ...... ...... ...... 150 ...... ' ' ...... ' ' ' ' ' ...... 200 ' 250 300 ------lL30 (Con1rol) --<>--ll386 lL3461 ----o--lL3661 ---ll)861 ' ' Bearing Pressure vs. Settlement Curves for 0.61 m, Footing Series 6 Figure 2.12 15

PAGE 26

The pressure-settlement curves shown in Figure 2.1 0 above clearly show that the use of one layer of geogrid reinforcement can substantially increase the ultimate BCR. This testing also indicated that the BCR was not significantly sensitive to the depth of reinforcement that was varied from 0.25 to 0.388 below the bottom of the footing. However, the increase in the BCR for one reinforcement layer was small to insignificant for small settlements in the range of 0.5 to 1%8, and only became significant at 0.3%8 or greater. Similarly, the single reinforcement testing showed that the BCR was not sensitive to the width of the reinforcement. The BCRs for the Series 5 tests were generally less than those for Series 4, which had a higher soil density. This was believed to be due to the reduction in soil density. This is plausible, as less dense soil requires more movement or settlement to mobilize the strength of the reinforcement. This was also evident in the lower settlement range for the Series 6 tests. However, the ultimate BCRs for the less dense soil used in test Series 6 were actually higher than those for Series 5. It was suggested that this could very well be the result of the approximation of ultimate BCR using the ''tangent intersect" method. Therefore, the study indicated that perhaps a different method of determining the ultimate BCR where a distinct failure is not achieved may be more desirable. While an additional focus of the phase II portion of this study was to evaluate the use of one versus two layers of reinforcement, this goal was not achieved. This was likely due to the variation of two parameters at the same time, namely the number of layers as well as the soil density. It is likely that the change in soil density masked the effect of changing from one layer of reinforcement to two. ConclusionsAdams and Collin, (1997): The test results indicated that the Bearing Capacity Ratio (BCR) for three geogrid layers can be substantial; BCR > 2.6 for the optimal conditions in this study. Three layers of grid reinforcement substantially out-performed one or two layers for which BCR ratios up to approximately 1.6 were achieved. It is noted that the increase in the 16

PAGE 27

BCR is probably a function of the overall thickness of the reinforced mass beneath the foundations, not just the number of layers. The BCR using geogrid at smaller settlements also increased steadily when the top layer of reinforcement was within 0.5B of the base of the footing. However, the maximum improvement at small settlements was realized when the upper layer of geogrid reinforcement was within 0.25B of the base of the footing. Where one layer of reinforcement was tested, there appeared to an improvement in performance where the sand within the reinforced soil mass was compacted to a higher density such that stress transfer to the reinforcement resuhed before large strains occurred in the soil. Also, footings tested were less likely to experience general shear, (plunging failure) when the upper layer of reinforcement was located within 0.4B of the bottom of the footing. The improvement in bearing capacity and settlement reduction observed in this study was attributed to an increase in the shear strength of the reinforced soil mass. Additionally, the reinforced mass inhibits the development of a soil failure wedge. It should also be noted that the use of geogrid in the tests performed for this study substantially outperfonned the geocell. Guido, Chang, & Sweeney et aL (1985) This study included 70 laboratory bearing tests to evaluate the effects of geogrid and geotextile reinforced "earth slabs." The footing was a 305-mm, square plate consisting of 25-mm thick plywood, stiffened by a 3-mm thick steel plate on top and bottom. The foundation soil consisted of a uniformly-graded sand, which was reinforced with a biaxially oriented Tensar SS1 Geogrid or a Dupont Typar 3401 Geotextile. The parameters studied included the depth of the first layer of reinforcement below the bottom of the footing, the vertical spacing and number of layers of reinforcement, the width (size) of reinforcement, the tensile strength of the 17

PAGE 28

reinforcement, and the effect that each of the parameters had on the bearing capacity of the system. The typical reinforced soil foundation system configuration as presented by Guido ,e t al. (1985) is shown in Figure 2.13, below. I. E "' 0'> 0 EDGE OF BOX '----+EDGE OF REINFORCEMENT I f-+--+--EDGE OF FOOTING 1 __ 1 1.22 m .I Geometry of the Test Model Figure 2.13 Resuhs of tre plate bearing tests, as shown by Guido et al., (1985) in Figure 2.14 below, iidicates that tre BCR irueases Imst significantly at relatively small settienms wmt tre first layer of reinforcem:D placed at a depth of 0.25B or less below tre bottom of tre footing plate. The increase was even rmre dramatic fur large settlements. Parameters hekl constant fur this testing ft:luded tre number of reinfOrcing ]ayers (3), tre spacing oftre layers at 0.25B, am tre wilthofreinforcing at 3B. Ultimate BCRs up to 2.5 (see Figure 2.15) were ol:tairrd where the depth to tre first layer of reinfol'Cell'alt was equal to 0.25B. Additionally, tre results of this testing indicate that pJacing the first layer of reinforceJrellt beyom 1 B (below the bottom of the footing) 1m little effect on tre BCR It was noted that the ultimate BCR values ol:tairrd with the geotextile were only 5 to 10 percent less that that ofthe geogrn 18

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BEARING PRESSURE. q0 & q (kPo) 0 50 100 150 200 250 0 0.01 TENSAR SSI GRID 0.02 0.03 (D 0.04 ';;;-0.05 0.06 0.07 0.06 Load-Settlement Curves For Az/B=0.25, N=3 and b/B=3 Figure 2.14 1 .00 0 0.25 0.50 0.75 1.00 1.25 DEPTH OF TOP LAYER. u/B BCR Variation with Depth of Top Layer, Az/B=0.25, N=3 and b/B=3 Figure 2.15 19 1.50

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Similar to the placement of the first layer, the results of the testing shown below in Figure 2.16, as presented by Guido et al. ( 1985), indicate the most effective vertical spacing appears to be approximately 0.25B or less. Parameters held constant for this test included: the depth of the first layer of reinforcement at 0.25B, the nwnber of reinforcing layers at 2, and the width of the reinforcement at 3B. While testing of both the geogrid and geotextile showed similar results, the geotextile showed slightly lower BCR values than that of the geogrid. 0:: 0 m 3.00 2.50 2.00 t I 1.50 + i.- TENSAR SSI GRID 1.00 +---+---+---+------+---+---+-------0 0.25 0.50 0.75 1.00 1.25 1.50 VERTICAL SPACING OF LAYERS OF REINFORCEMENT, 6z/8 BCR Variation with Vertical Spacing of Reinforcement, u/B=0.25, N=2 and b/B=J Figure 2.16 The effect of the number of layers of reinforcement was tested using both the geogrid and geosynthetic reinforcement. For this portion of the testing, the parameters held constant included the depth of the first layer of reinforcement at 0.5B, the reinforcement spacing at 0.25B, and the width of the reinforcement at 3B. The testing indicated that the optimal nwnber of layers was 3 for both the geogrid and geotextile reinforcement in this case. Where the number of layers was increased to 4, the depth 20

PAGE 31

to the bottom layer of reinforcement below the bottom of the footing plate was 1.258, again suggesting that all layers of reinforcement should be placed within a depth of approximately 1 8 below the bottom of the footing. The increase in the 8CR with increase in the number of layers of reinforcement was more rapid for the geogrid than the geotextile. This is attnbuted to a "stiffer system" with the geogrid in comparison to that using the geotextile for one or two layers of reinforcement. Where three layers were used, the 8CR was only slightly less for the geotextile, indicating that as the number of layers of reinforcement increases, the rigidity of the reinforcement becomes less important. Figure 2.17 below (Guido et al., 1985) presents the results of the testing described above. n:: u m io) TENSAR SSI GR'O Cb) DuPONT TYPAR 3401 2 N 3 4 BCR Variation with Number of Reinforcing Layers, u/B=0.50, .tir/B=0/25 and b/B=3 Figure 2.17 The width of the reinforcement was evaluated using both the geogrid and geotextile. The parameters held constant for this testing included the depth to the first layer of reinforcement at 0.58, the vertical spacing of the reinforcement at 0.258, and the number of layers of reinforcement at 3. The results for this testing indicate that an effective width for the geogrid reinforcement was reached at a width of approximately 28 after which the increase in 8CR leveled off. The effective width using the geotextile reinforcement was approximately 38. This indicates the geogrid required a 21

PAGE 32

smaller plan area than that of the geotextile to achieve a similar BCR The fundamental difference in the results is attributed to the difference in the mechanism of reinforcement for the geogrid versus the geotextile. For the geogrid, the tensile strength of the reinforcement is mobilized mainly through the interface of the soil to the geogrid mesh cross-bar, while the geotextile relies on the area of reinforcement over which friction can develop between the soil and the geotextile. Figure 2.18 (Guido et al., 1985) below presents the results of this testing. I I 2 00 I 0 0" 1 .75 ""' cr a:u 1.50 m 1 25 iOO 0 ( o) TEN5AR 551 GRID (b) DuPONT TYPAR 3401 / if / 2 3 WIDTH RATIO, b/8 4 BCR Variation with W"ulth Ratio, u/B=0.50, .1:/B=0.15 and N=3 Figure 2.18 Testing performed as part of this study to evaluate the effect of the tensile strength of the reinforcement included the use of multiple geosynthetic fabrics with variable strengths. It was found that the strength was an important parameter as the BCR values increased significantly (25 to 30 percent) with an increase in tensile strength for the fabrics used in this evaluation. Additionally, three different types of geogrid with tensile strengths varymg approximately 30% were tested. Based on the results ofthis testing it was concluded that the tensile strength of geogrid alone was not sufficient in determining its effect on 22

PAGE 33

the BCR. However, it was noted that the aperture size of the grid must also be considered in conjunction with the tensile strength. It was noted that prior testing performed by Guido, et al (1985) indicated that the tensile strength ofthe geosynthetic fabrics used had a considerable effect on the BCR Additionally, testing performed by Akinmusuru and Akimbo lade (1981) indicated that the BCR increased as the density of reinforcement (LDR) increased. Therefore, it was concluded that there are various factors that must be considered with the strength of the reinforcement such as the aperture size of a grid or "density" of the reinforcement in order to evaluate the effect on the BCR It was concluded that more testing is required in this area to better quantify the effects of these parameters. Yetimoglu and Wu (1994) This study was performed to evaluate the bearing capacity of rectangular footings on geogrid reinforced sand. This study included testing the bearing capacity in a laboratory environment as well as performing a finite-element comparison analysis. The reinforced soil system was constructed within a 70 by 70-cm steel tank that was 1 00-cm deep. The sand consisted of a uniform, cohesionless, quartz, river sand with an angle of internal friction of 40 degrees. The reinforcement consisted of a uniaxial geogrid (Terragrid GS 1000). The test footing was a rectangular steel plate 12.5-mm thick by 101.5-mm wide and 127-mm long. The parameters evaluated during this study included the depth of the first layer of reinforcement, the vertical spacing of subsequent layers, the number of layers used, the size of the reinforcing layers, and the stiffhess of the reinforcement. 23

PAGE 34

Figure 2.19, shown below as presented Yetimoglu & Wu (1994), shows the typical reinforced foundation configuration. 8 or 0 _''-@_'ii!F_' _-"_""_' ---------------""_' .. 'ill _=,,_=l_l;tn-:t ___ ---------------------J ,_________--------"----"'---"---------Geometric Parameters of Reinforced Foundation Figure 2.19 One of the major variations in three groups of tests performed as part of this study, as show in Table 2.3 below, was the difference in the depth to the first layer of reinforcement, which was 0.38 in Group 1 (the "control" group) and 0.458 in Group 2, with all other factors the same. As can be seen from the values shown in the table, the decrease in depth to the first layer of reinforcement in Group 1 as compared to that of Group 2, had a relatively small effect on increasing the 8CR where one or two reinforcing layers were present. However, the increase was more significant where three to four layers of reinforcement were utilized. This would suggest that the effectiveness of the deeper layers of reinforcement is somewhat dependent on the position of the first layer of reinforcement. As is typically the case, the 8CR was significantly increased with the first layer of reinforcement closer to the bottom of the 24

PAGE 35

footing (depth of 0.38 for this test), where more than two layers of reinforcement were used. Additionally, the size of the reinforcement was increased from 4.58 for Group I to 68 for Group 3, with all of the other factors remaining the same. The increase in the size of the reinforcement shows nil to very little increase in 8CR where one to two layers of reinforcement were used. However, a moderate increase in 8CR resulted where three and four reinforcing layers were used. While this testing shows an increase in the 8CR with an increase in the area of reinforcement, the increase was small enough that in practice it may not warrant the cost of additional excavation and materials. The 8CRs for the tests shown below are in the range of approximately 1.8 to 2.5 where one or two layers were utilized, and approximately 3.2 to 3.9 where three to four layers were used. An exception to these ranges of 8CR values is Group 2, where the first layer of reinforcement was deeper, resulting in smaller 8CRs. N (I) 0 I 2 3 4 Group I Group 2 Group 3 U/B = 0.30 U/B = 0.45 U/B= 0.30 ZJB = 0.30 ZJB = 0.30 ZJB = 0.30 B,IB=4.5 8,/B = 4.5 B/B = 6.0 stB Quit BCRb siB. Quit BCRb sfB Quit BCRb (percent) (kPa) (4) (percent) (kPa) (7) (percent) (kPa) (10) (2) (3) (5) (6) (8) (9) 2.7 316 2.7 316 2.7 316 3.4 586 1.85 3.1 558 1.77 3.8 579 1.83 4.8 790 2.50 3.1 718 227 3.4 795 2.52 4.8 1002 3.17 3.0 768 2.43 4.9 1081 3.42 3.9 1147 3.63 2.8 766 2.42 4.4 1225 3.88 Ratio of the settlement at failure to the width of footing. b Ratio of the ultimate capacity of reinforced sand to the ultimate bearing capacity of unreinforced sand. Summary of Some Test Results for Reinforced and Unreinforced Sand Table 2.3 1k nnuinJer (lfthe testing per.fonnoo as put of tim study ewhJated the tei:OOtet:llM sizt; depth, and II.II1M of 1ayels in rrme detail. Additi>mlly, the e1h:t of the gjffies of the 25

PAGE 36

reinfurrenm \\m ew1uated ming finire.emm IIDdeling. As incOCated arove, conprion was am }Xrl>mrd with each set oflab tests. 1k data mwn in tir figw"es rehw mn JXOvDe tim data as well. 1k &nlltmit.e tre resuhs of each set of tests. For of teiufi:urenai, tre optimm depth rebw tre oottom oftre Doting appeared to re aprroxirmtely OJB a BCR of arout 1.7 as smwn in FJgUre 2.20, rehw (Y etiimglu & Wu, 1994). This \\m ImSJred at a settbn::ri: of2"/o oftre wiJth, with a teir:tim:mtrt wDth equal to 4.5B. It slnukl re mted tim 2"/o settbmi: is within typi:al tolt:aarn::s JDr wiJths up to appuxirmtely 4 to 5 &t. WJue tre sett1t:atm \\m hig1u (greater tlEn 6%), tir oJXimm depth oftre teinJDnr:rmt \\m am higlrc. However, settlt:an:n of 6% is lE3[' or arow typi:al tOr hJbitable structures comidemg Doting wXJtiE up to 4 or 5 iet 1k BCR was comiiten (at 2"/o sett:lt:arert), \Were tir depth to tir teinfOrcmm was appuximtely 0.15B am 0.5B. W1ue tre depth to tlr reintO:ocenm greater tim 1B, tlr BCR 1 trarly comtmt. FJgUre 2.20 rehw p-es:rts tir BCR \'USUS tlr depth to tre of reininu:uai, as dinJsgOO arow. _....... 0:: u en 0 0:: 2.0 1.5 u TEST 4 ANALYSIS <( ____________ J 0... <( u <..:> 1.0 z 0.5+-------+-------+-------,_ ______ ,_ ______ 0 0.3 0.6 0.9 1.2 1.5 DEPTH RATIO (u/8 or u/D) Variation of BCR with Depth Ratio in Single-Layer Reinforced Sand (s/B=s/D= 2%, B,IB= D,ID= 4.5) Figure 2.20 26

PAGE 37

Where multiple reinforcement layers were considered, test results indicate that the optimum depth to the first layer of reinforcement is approximately 0.25B or slightly less. The BCR versus Depth curve shown in Figure 2.21 below (Y etimoglu & Wu, 1994) differs somewhat from that where only one layer of reinforcement was used. It should be noted that the BCR values obtained were consistently high (BCR 3) for first layer depths up to approximately 0.3B. On the low end of the curve, the BCR approached a value of I for a first layer depth near 0.9B. These resuhs were measured at a settlement of 2% of the footing width, and included 4 layers of reinforcement, vertical reinforcement spacing of0.3B, and a reinforcement width equal to 4.5B. 0 1--1u
PAGE 38

(Yetimoglu & Wu, 1994), indicate the optimum vertical spacing of reinforcement is approximately 0.28 resulting in a 8CR of about 3.4. However, relatively high BCR values resulted with reinforcement spacings in the range of approximately 0.38 or less, above which the 8CR dropped off consistently with increased spacing. It should be noted that testing performed using various numbers of reinforcing layers indicated a wider range of "optimum" spacing from approximately 0.2 to 0.48. Therefore, it can be inferred that an effective spacing should also consider the number of layers used. 4.0 0:: J u o TEST m 4 ANALYSIS 0 I / -1/ ', I <( II. 0 ---0:: ......... ____ ;>-2.0 ll-----1:::: ----.,a u <( 0.. <( u () 1.0 z it <( w m 0.0 0 0.3 0.6 0.9 1.2 1.5 NORMALIZED VERTICAL SPACING OF REINFORCEMENT LAYERS, (z/B or z/0) Typical Varilltion of BCR with Vertical Spacing of Reinforcement Layers (s/B=s/D= 2%, N=4, u/B= uiD = 0.30, B,IB= D,ID= 4.5) Figure 2.22 According to the testing perfonned, the number of layers of reinforcement (assuming a reasonable vertical spacing) has a greater effect on the 8CR than any of the other parameters evaluated for this study. While testing indicated 4 layers of reinforcement was optimum. considering a total reinforcement depth of approximately 1.58, good results are obtained for 3 to 5 layers, beyond which the improvement was negligtole 28

PAGE 39

(see Figure 2.23 below, Yetimoglu & Wu, 1994). It should be noted that these values were measured at settlements of 2% of the footing width and used a depth to the first layer of reinforcement and subsequent vertical reinforcement spacing of 0.3B, as well as a size of reinforcement of 4.5B. The resulting optimum BCR with 4 layers of reinforcement was approximately 3. While the BCR did increase with the number of reinforcement layers (N) to a depth of approximately 3B below the bottom of the footing, little increase in the BCR was realized for reinforcement located at a depth of 1.5B or greater. 4.0 0::: u m 3.0 0 f<( Ct >-2 0 I f-u <( Q_ <( u () 101 z 0:::
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ranged from approximately 2.6 with a reinforcement size of 1.5B to approximately 3 for a size of 4.5 B or more. Again, these BCR values were recorded for settlements of 2% of the foundation width, where four reinforcement layers and a vertical reinforcement spacing was used. The study by Y etimoglu & Wu ( 1994) indicates results from various researchers are highly variable regarding the optimum width of reinforcement, and that the values vary significantly for strip versus square or rectangular footings as well. Some researchers have found that the "effective" size of reinforcement is in the range of 7 to 8B for strip footings and on the order of 2 to 4B for square footings. On the other hand some have found significant increases in BCR with reinforcing widths similar to that of the footing. Some have also found that the optimum reinforcing size increases with a decrease in footing size. Figure 2.24 below presents the results of BCR versus size of reinforcement for this study. 4.0 (J: u i (]J I 0 30 r ;::: -t:: u
PAGE 41

In addition to the parameters associated with the geometry of the reinforced foundation, this study also evaluated the effect ofthe stiffuess ofthe reinforcement on the BCR using finite-element analysis. The reinforcement axial stiffuess that was analyzed ranged between 15kN/m and 4,000 kN/m The axial stifihess is defined as the sti.ffuess per unit area of reinforcement and is equal to the modulus of elasticity (E) and the thickness ofthe reinforcement (t). Figure 2.25 (Yetimoglu & WU, 1994) below presents the BCR versus the reinforcement stifihess. The various curves represent the BCR versus reinforcement stiffuess at various settlement ratios, where the settlement is a ratio of the footing width or diameter (D). As can be seen from the figure, a reinforcement stifihess greater that I 000 kN/m does not resuh in a significant increase in the BCR It should be noted that the typical stifihess of higher quality commercially available geogrids falls in the range of approximately 200 to 500 kN/m, which would still result in relatively high BCR values (BCR l'o::j 2 to 3) for the lower settlement ranges (2 to 4%) for the test resuhs presented below. 8 u CD 7 0 ;:::: <( 0:: >-5 1--u <( Q_ 4 <( u 0 z 2 ii <( w CD 0 1000 2000 3000 STIFFNESS OF REINFORCEMENT. kN/m 4000 s/D = 10% s/D = 8% o s/D = 6% s/D = 4% s/D = 2% Variation of BCR with Reinforcement Stiffness ( N=J, uiD=1ID= 0.30, D,ID= 4.5) Figure 2.25 31

PAGE 42

Omar, Das, Yen, Purl, and Cook (1993) This study included perfonning multiple small-scale laboratory load tests to evaluate the effect of using geogrid-reinforced sand below square, rectangular, and strip type footings. These tests were performed using only one type of sand compacted on one density and a single type of geogrid. Bearing capacity testing of the strip footing was perfonned in a box with dimensions of approximately 1.1 m long, by 0.305 m wide, by 0.914 m deep. Testing for square and rectangular footings were performed in a box measuring 0.91 m square, by 0.91 m deep. The insides of the boxes were polished to reduce friction and braced around the perimeters to reduce lateral flex during testing. A total of four model footings were used to represent the square, rectangular, and strip type footings. The dimensions of the footings were 76.2 by 76.2 mm (square footing), 76.2 by 152.4 mm and 76.2 by 228.6 mm (rectangular footings), and 76.2 by 304.8 mm (strip footing). The soil consisted of a fine, rounded, silica sand that was compacted to an average relative density of 70% resulting in an angle of internal friction of approximately 41 degrees. The reinforcement consisted of a Tensar BXIOOO(SSO) biaxial geogrid. The primary objective of this testing was to determining the critical depth ( da/B), critical width (ba!B) and critical length (lcJB) of reinforcement required to obtain the maximum BCRs. Figure 2.26 (Omar et al., 1993) presented below, shows a typical layout of a footing on geogrid-reinforced sand. 32

PAGE 43

I I I' ,s-o.. ._. .... r---------------I J -I I I fi I I I I I I I L ---_j Rectangular Surface Foundation on Sand Reinforced with Layers of Geogrid Figure 2.26 The tests \\a'e diviJed no i>ur seers (Series A, B, C, ard D) in order to de:ternD: tre desired JH3IlEleiS aOO\e. The fOibwmg table (Onm et al, 1993) swutmia:s tre each series, as \\dlas tre comtart arxl Series A B-1 B-2 8-3 84 C-1 C-2 C-3 C4 D-1 D-2 Variable Parameter Constant Parameter N N N N BIB biB biB b/8=1/B LIB liB B/L=();u!B--biB=().333;1J/B-1 0;1/B=co 8/L=().333;u/B=b/B=0.333;b18=8;VB=B BIL=().5;u/B=b/B=0.333;bi8-=8;1/B=B BIL=1;u/B=bl8=().333;bi8=6;1/B=6 8/L=();u/B=h/B=0.333 ;N-=6;1/B==> BIL=().333;u/B=bi8=().333;N=6;1/B=B BIL=0.5;u!B--biB=().333;N=5;1/B=B BIL=1;u/B=bi8=().333;N=4 BIL=0.333;u/B=b/B=0.333;N=6;bl8=7 BIL=0.5;u!B--b/8=0.333;N=5;bl8=6 Details of Laboratory Model Tests Table 2.4 33 Remarks Tesls on uoreinfun:ed soil For delamination of d../8 For determination ofb,./8 For delamination

PAGE 44

Series A: Test Series A (unreinforced case) was performed using all four footing configurations, the results ofwhich are shown in Figure 2.27 (Omar et al., 1993) below. The actual tests are represented by the four solid dots connected by the curved, dotted line. The straight, line represents the calculated ultimate bearing capacity using the bearing capacity equation and factors suggested by Vesic ( 1973 ). 90 E z 80 -'< v 0 Q. 70 0 u Cl' c 0 rn 60 0 E 3 Eq 4 Exper1rnem; Series A 50 0 0.2 0.4 0.6 0.8 1.0 B/L Variation of Ultimate Bearing Capacity q, with BIL (Test Series A; Tests with Unreinforced Sand) Figure 2.27 34

PAGE 45

Series B: The results of Series B testing performed to determine the critical, total depth of reinforcement required to maximize the BCR are presented in the Figures 2.28 & 2.29, and Table 2.5, (Omar et al., 1993) below. As can be seen from data presented, the critical depth of reinforcement increases from slightly over I B for the square footing to approximately 2B for the strip footing. 'E ..s ., ... c: u E u c: a =s ..., "' ::J 0 0 5 10 15 20 LDad per unit area, q (kN/m2 ) 100 200 300 400 450 Ultimate bearing capacity, q..(JI) -B = = 0.333 10 4 7 Typical Plots of Load per Unit Area versus Settlement for Strip Foundation on Geogrid-reinforced Sand (Test Series B-1) Figure 2.28 35

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Test Series N 1 2 3 B-1 4 5 6 7 1 2 B-2 3 4 5 6 1 2 B-3 3 4 5 1 2 B-4 3 4 5 6 Uhimate Bearing Capacity, Settlement at ql(R), Ultimate Load, kN/m2 Mm 132.6 7.61 197.2 12.71 289.8 14.22 317.4 15.24 346.5 14.61 369.2 16.51 374.7 15.99 126.3 4.94 188.9 5.72 269.1 6.16 306.9 7.49 324.0 7.86 326.4 8.23 125.3 4.88 182.9 5.69 255.3 5.97 291.9 7.23 293.9 7.75 90.5 4.08 136.6 3.23 161.5 3.96 179.4 4.19 185.5 4.09 187.1 4.10 SumiiUlry of Results from Test Series Table 2.5 36 Comments 8/L=() u/B=h/B=Q.333 b/8=10 1/B=co BIL=Q.333 u!B=h/B=Q.333 biB=8 VB=8 B/L=Q.5 u!B=h/IH).3 33 b/8=8 VB=8 BIL=1 u/B=h/B=0.333 biB9i VB=6

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d/B 0 0.5 1.0 1.5 2 0 2 5 N Variation of BCR with Nand d/B (Test series B-1, B-2, B-3, and B-4) Figure 2.29 Series C: The resuhs of Series C testing, pe1funred to tre critical widtm of reinfui'CeiDD required to maximize tre BCR, are presented in tre Figures 2.30 & 2.31, and Table 2.6, (Omar et al, 1993) below. As can be seen from Figure 2.30, tre critical wi1th of reinfurcemn increases from slightly over 4B for tre square footing to approximately 8B for tre strip footing. It should be mted however, that the critical widths detenniil:d during tim testing provided a ''maximum'' BCR value, and that relatively good BCR resuhs could be obtained using gmfier reinforcetrent sizes. For example, for the strip footings, a reinfOrcing width of only 2B resulted in a BCR of slightly above 3, and width of 4B resulted in a BCR of approximately 3.6, as compared to tre ''maximum'' BCR of sligbtly above 4 resuhiog from a wi1th of8B. Similarly, a reinforcemm width of2B for square footings resulted in a BCR of slightly over 2, wrereas the critical width of 4B resulted in a BCR of approximately 2. 7. '11m difference in wi1th (especially for strip or rectangular footings) can make a significant diffurence in the cost of constructing fouOOatiom lh:refore, evaluation of these pararn.ms should be done with care, as specifYing rmre width than can resuh in significant economic irq>lications. 37

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a:: u (I] 5 4 .3 2 0 4 6 8 b/B Variation of BCR with biB (Test Series C-1, C-2, C-3, and C-4) Figure 2.30 Ultimate Bearing Capacity, Settlement at ql(R), Ultimate Load, 10 Test Series biB kN/m2 Mm Comments 2 4 C-1 6 8 10 2 4 C-2 6 7 8 2 C-3 4 6 8 I 2 C-4 3 4 5 6 255.3 9.23 303.6 10.25 324.3 11.81 357.8 13.46 369.2 17.29 238.7 5.70 277.5 5.89 311.7 6.91 324.0 7.65 325.0 8.23 226.2 4.95 255.3 5.79 288.3 6.79 294.4 7.75 87.4 2.79 134.6 3.81 156.6 4.45 170.2 4.61 177.9 4.57 179.4 4.19 Summary of Results from Test Series C-1, C-2, C-3, and C-4 Table 2.6 38 B/L=O u/B=h!B=0.333 N=6 liB= BIL=0.333 u/B=h/B=0.333 N=6 IIB=8 B!L=0.5 u!B--h!B=0.333 N=S IIB=8 B!L=I u/B=h/B=0.333 N=4 IJB=biB

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CD "-.D Series D: 10 8 I I 4 0 0.2 Experiment. from Figure 7 Eq 9 I 0.4 8/L 0.6 Variation of bc/B with BIL Figure 2.31 0.8 1.0 The results of Series D testing performed to determine the critical lengths of reinforcement required to maximize the BCR are presented in Figure 2.32 and Table 2.7, below (Omar et al., 1993). As would be expected, the critical length of reinforcement for the square footing is slightly greater than 4B, equal to that of the width as observed in Series C. The critical length for both the rectangular and strip footings is also approximately 4B. However, similar to that for the evaluation of the critical width as discussed previously, the BCR can still be significant at lesser reinforcement lengths. Generally speaking, the data indicated that good BCR values (on the order of 2 or higher) can be achieved with a reinforcement length of 2B or more for square footings, and lengths of approximately 1 B to 1.5B can result in BCR values of about 2.2 to 3 for rectangular and strip footings. 39

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5 5 3 (I) Test Series D-1 D-2 / / /, I / liB 2 3 4 8 2 3 4 8 -------------------1 .0 2 8 1/8 Variation of BCR with VB (Test Series D-1, D-2, and C-4) Figure 2.32 Uhimate Bearing Capacity, Settlement at ql(R), Ultimate Load, kN/m2 Mm 276.2 6.34 306.9 6.54 321.5 6.79 324.0 7.65 242.2 5.42 269.8 5.59 285.5 6.24 288.3 6.67 Summary of Results from Test Series D-1 andD-2 Table 2.7 40 10 Comments BIL=0.333 u/B=h/8=0.333 N=6 b/8=7 BIL=0.5 u/B=h/8=0.333 N=S b/8=6

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Conclusions-Omar et al., (1993): The data presented in this study indicates that the critical depth of reinforcement, defined as that required to maximize the ultimate BCR, increases as the width-to length (BIL) ratio of the foundation decreases. This study indicates the critical depth is approximately 2B for strip footings and 1.2B for square footings, resulting in BCR values of approximately 4.4 to 2.7, respectively. However, relatively good BCR values on the order of 2.5 to above 3 were obtained for a reinforcement depth of 1 B for all footings. The critical width of reinforcement also increases as the BIL ratio decreases, varying from slightly over 4B for a square footing to approximately 8B for a strip footing resulting in BCRs of approximately 2.8 to above 4. However, widths of approximately 2B for both square and strip footings resulted in relatively good BCR values of slightly above 2 and 3, respectively. The critical lengths of reinforcement for square and strip footings were all near 4B resuhing in BCR values of nearly 2. 7 to 3.8 respectively. As would be expected, the resuhs for rectangular footings were somewhere between the two. However, similar to the width as discussed above, BCR values for lesser length were still relatively good, ranging from approximately 2 (square footing) to nearly 3.4 (strip footing), for reinforcement lengths of2B. Lastly, for a constant reinforcement spacing, and critical depth, width, and length, the uhimate BCR decreases with and increase in the BIL ratio. In other words, square footings typically resuh in smaller increases in ultimate bearing capacities than do strip footings. HUilng & Tatsuoka (1990) This study included a series of plain strain model tests to evaluate the bearing capacity of reinforced sand. The testing was performed in a reinforced, transparent, acrylic box 41

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(3cm thick walls) with plan dimensions of 40 by 183 em, and 74 em deep. The purpose of the acrylic box was to enable the researchers to view the mode and geometry of the bearing failures. A 1 Ocm wide rigid footing was used for load testing. The soil consisted of air dried ''Toyoura" sand. The reinforcement was metal strips consisting of Phosphor bronze and aluminum foil that ranged in thickness from 0.05 em for the bronze to 0.005 em for the aluminum foil. All of the reinforcing strips were 0.3 em wide and ranged in length from 1 to 6B, depending on the test being performed. To reduce the effects of friction at the interface of the sand and box, the sides of the box were lubricated with a layer of silicon grease placed between sides of the acrylic box and a rubber membrane that was in contact with the sand. Figure 2.33 (Huang & Tatsuoka, 1990) below shows the general layout of the testing apparatus. Model Test A"angement Figure2.33 Part of the purpose of this study was to perform an experimental examination of the effect of the length of the reinforcing layers, the number and the horizontal spacing of the reinforcement layers, as well as the stiffiless and rupture strength of the 42

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reinforcement on the bearing capacity. The results of each are discussed on the following sections. The tests were divided into five separate groups as follows: Group a) The purpose of this group of tests was to evaluate the effectiveness of a reinforced width equal to the width of the footing (1 B), in conjunction with evaluating the variation in the number of layers and therefore the total depth of reinforcement below the footing. Group b) The purpose of this group was to evaluate the effect of the length of reinforcement, which was varied from 1 to 68 using 3 layers of reinforcement on the bearing capacity. Group c) The purpose of this group was to study the effect of the number of layers of reinforcement which were varied from 1 to 3 layers and using a reinforcement width of 68 on the bearing capacity. Group d) The purpose of this group was to evaluate the covering ratio ( CR) or horizontal spacing ofthe reinforcement where the width ofthe reinforcement was held at 28 and the number oflayers at 3. Group e) The purpose of this group was to study the effect of the rigidity and strength ofthe reinforcement on the bearing capacity. The width of reinforcement was held at 28 and the number oflayers at 3. Group a Test Results: As shown in Figure 2.34 (Huang & Tatsuoka, 1990) below, the ultimate bearing capacity is increased by approximately 2.5 to 2.8 times the "unreinforced" case where the total depth ofreinforcement is equal to 0.9 to 1.58. Additionally, tests performed using a rigid footing that was equal to the depth and the width of the reinforced 43

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foundation indicated nearly the same results. This data would indicate that a good approximation of the bearing capacity of a reinforced foundation could be made by analyzing the system as a rigid footing of the same size, and at the depth of the lowest layer of reinforcement. This is generally referred to as the "deep footing effect." oo (0. /B) 300 e a 200 "' 5/B Footing Load-displacement Relations for Group-a Figure2.34 Group b Test Results: The results of this testing indicate that while a reinforcement width is equal to the width of the footing can result in a significant increase in the 8CR, increasing the width of the reinforcing beyond the edge of the footing can result in an additional increase (see Figure 2.35, below). For this particular study, increasing the size ofthe reinforcement from 18, to 28 and 3.58, resulted in sizable increases in the 8CR. However, the increase in size from 3.58 to 68 produced only a slight increase in the 8CR indicating that an increase in the size of reinforcement beyond approximately 3.58 was not effective. 44

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" <00,-------,--------.--------. S/8 Footing Load-displacement Relations for Group-h Figure 2.35 Group c Test Results: Figure 2.36 (Huang & Tatsuoka, 1990) below shows the load settlement curves for the group c testing. This testing varies the nwnber of layers of reinforcement from 1 to 3 using a large reinforcement width of 6B. The data are similar to that of the group a tests which indicated that the "deep footing effect" is the dominant factor in increasing the BCR. whether the size or width of the reinforcement is small or large. However, this data, in comparison to that of group a, would indicate that the width does have some effect on increasing the BCR even if it is not as significant as that of the depth of reinforcement. 45

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JOO 5/B Footing Load-displacement Relations for Group-e Figure 2.36 Group d Test Results: This testing entailed varying the spacing between the reinforcing elements in order to increase or reduce the "density" of the reinforcement, which is referred to the covering ratio (CR) in this study. The results presented in Figure 2.37 (Huang & Tatsuoka, 1990) below indicate that increasing the density of the reinforcement, from 0 to 18% coverage in this particular case, can result in a significant increase in the BCR A maximum increase in the BCR of nearly 3 times that of the unreinforced was realized. 46

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400,------,------,----------, -ti<>lnQ Sllot. . ., JOO a. S/B Footing Load-displacement Relations for Group-d Figure 2.37 Groupe Test Resuhs: The purpose of this test group was to evaluate the effect of the tensile strength of the reinforcement on the BCR As mentioned previously the reinforcement used for this study consisted of several grades of phosphor bronze strips in addition to aluminum foil. Observation of the data presented in Figure 2.38 (Huang & Tatsuoka, 1990) below indicates that the three grades of bronze reinforcement resuked in very similar results, while the resuks obtained using the significantly weaker aluminum foil showed a moderate decrease in bearing capacity. This data suggests that the strength of the reinforcement materials used for this study was a minor factor in changing the BCR 47

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300 S/B Footing Load-displacement Relations for Group-e Figure 2.38 Samtani and Sonpal, 1989 This study included perfonning multiple small-scale laboratory load tests to evaluate the effect of using metal strips to reinforce a cohesive soil below a strip footing. These tests were performed using a clayey sand soil containing 39 percent clay fines (% passing the No. 200 sieve) with a liquid limit of 55.5%, and a plastic limit of 27%. The angle of internal friction was 16.5 degrees based on undrained triaxial testing that was performed on samples compacted at optimum moisture content. The reinforcing strips consisted of 0.05 mm thick aluminum foil that was cut into strips measuring 20 mm in width. Bearing capacity testing of the strip footing was performed in a box with plan dimensions of914.4 mm by 914.4 nun. and 762 mm deep. The strip footing consisted of a stiff cast-iron strip 495.3 mm long by 76.2 mm wide. Figure 2.39 (Samtani & Sonpal, 1989) shows the general test layout. 48

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(o) c> r-----------< I (b) Geometry of System: (a) Transverse Cross Section; and (b) Longitudinal Cross Section (SectionX-X) Figure 2.39 Table 2.8 (Samtani & Sonpal, 1989) below presents a sununary of the test results for this study. As the data indicates, reinforcement of cohesive soil can result in significant increases in the BCR. The study indicated that the "density" of the reinforcement was likely the biggest factor in increasing the BCR. Increasing the length of the reinforcement only provided a minimal increase. It should be noted that the number of reinforcement layers and depth of reinforcement, as well as the vertical spacing were fixed parameters. Therefore, the variance of these was not evaluated as part of this study. 49

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Test Type LDR(%) L(m) q (kPa) BCR BCR* Average BCR & BCR (1) (2) (3) (4) (5) (6) (7) (8) I UR --578.8 --2 UR -559.2 --3 R 40 0.6096 1294.9 2.28 2.28 -4 R 40 0.4572 1274.5 2.24 2.12 For LDR=40%,BCR= 5 R 40 0.3048 1250.8 2.20 1.99 2.24,BCR *=2.13 6 R 36 0.4572 1172.3 2.06 1.91 For LDR=36%,BCR= 7 R 36 0.3048 1079.1 1.90 1.65 1.98.BCR*=I.78 8 R 32 0.4512 1064.4 1.87 1.72 For LDR=32%,BCR= 9 R 32 0.3048 1035.0 1.82 1.76 1.8S,BCR *=I. 74 10 R 28 0.3048 1020.2 1.79 1.60 BCR=I.79,BCR*=1.6 Note: UR = unreinforced; R = reinforced; L = length of ties; q = q. for unreinforced soil; q = q, for reinforced soil; for BCR an average q. = 569.0 kPa for unreinforced soil is used; and in all tests on reinforced soil, four layers of ties were used. Summary of Test Results Table 2.8 50

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3. Sytbesis of the Literature Due to the variable materials and testing approaches used, the various ways the data were presented, as well as the variation in the scale of the test models, the studies summarized in Chapter 2 provide a good cross-section of the type of published research that exists in the area of reinforced soil foundations. There is a multitude of published data that exists related to the topic of reinforced soil foundations, therefore the following observations are not based solely on the studies summarized previously in this report. Additionally, the following observations not only consider the results of published testing but also general economics versus the desired improvements in bearing capacity and settlement, the benefits that can be realized using this type of system to support typical modem structures, construction issues, as well as the availability of soil/aggregate and reinforcing materials. Based on the available literature, and practical experience, the following sections present the author's opinion of the "'effective" ranges of each of the individual reinforced soil foundation design parameters that will be required for design of such systems. It should be noted that the studies from which these observations were made included foundation sizes up to approximately 3 feet in width. Therefore, care should be taken when applying these parameters to significantly larger footings as the optimwn design parameters could change. Additionally, the soils used in these studies were all granular in nature. Application of these parameters to conditions that are significantly different than those which were studied should be done only with caution. To provide a better understanding of the following sections of this report, the designation of each parameter as shown in the following figure is proposed. 51

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Excavation Limits 8 = footing width B ,.., Footing Reinforcement b Typical GRSF Configuration Figure 3.1 L = footing length (into page, not shown) Su = spacing between the base of the footing and upper layer of reinforcement Sr = vertical spacing between reinforcement layers Sb = spacing between the base of the excavation and lowest reinforcement layer Dr= total depth ofreinforced fill zone b = width of reinforced fill zone I= length of the reinforced fill zone for strip or rectangular footings (into page, not shown) .11 = length of reinforcement beyond end of strip or rectangular footings Nr = number of reinforcement layers 52

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3.1 Vertical Reinforcement Layer Spacing (S.., Sb) .sl! The literature indicate that reinforcement below footings can produce a sizable increase in the ultimate BCR when the uppermost layer is within approximately 0.58 ofthe bottom of the footing. However, optimum BCR values were typically obtained where the spacing between the uppermost reinforcement layer and the base of the footing (Su) was approximately 0.48 or less for single layers and approximately 0.38 or less where multiple layers were utilized. The highest 8CRs at low settlements were generally obtained when the first layer of reinforcement was within 0.258 to 0.158, where multiple layers were used. Therefore, where single layers are used the optimum spacing between the base of the footing and the reinforcement appears to be in the range of0.3B to 0.48. For multiple layers of reinforcement, the optimum Su spacing is between approximately 0.158 to 0.38. .Sr The literature indicate that when multiple layers of reinforcement are utilized, closer spacings typically result in higher BCR values and lower settlements when the appropriate total depth of reinforcement Dr is used. Generally speaking, where fewer layers of reinforcement are used, optimum vertical spacing will be larger (increasing Dr), and where more reinforcement layers are used, optimum vertical spacing will be smaller. The vertical spacing between reinforcement layers (Sr) that results in optimal BCR values at lower settlements is typically between approximately 0.158 and 0.38 where an appropriate Dr is used .St! None of the literature reviewed evaluated the spacing between the base of the reinforced fill zone and the deepest layer of reinforcement as shown in the above Figure 3 .I. However, it is typically wise to provide a layer of properly compacted fill 53

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beneath the lowest layer of reinforcement to achieve good interaction between the reinforcement and the fill soils. A good rule ofthumb would be 6 or more inches. 3.2 Number of Layers (Nr) Research indicates that the number of layers of reinforcement likely has the greatest influence on the BCR and settlements than any of the other parameters when considered alone. However, the optimal number of layers is really a function of the optimal spacing and optimal total depth of reinforcement, and visa versa. In other words, the effect that each of these three parameters has on the BCR is function ofthe other two. With this in mind, the literature indicate that the optimal number of layers is typically in the range of 3 to 4 for most footings. However, some increase in the BCR has resulted with the number of layers as low as 2 and as high as 5. Various studies indicate that the optimal total depth of reinforcement, and therefore optimal number of layers of reinforcement is generally somewhat higher for strip footings than for square footings, asswning an appropriate spacing is utilized. 3.3 Depth of Reinforced Zone (Dr) As indicated above, the depth of the reinforced zone is a function of the spacing and number of reinforcement layers. Its effect on increasing the BCR and reducing the settlement depend on the appropriate selection of the other parameters as well. The literature indicate that a depth of reinforcement of as little as 0.5B can result in a significant increase in the BCR. However, optimal results in both the BCR and settlement appear to result with a depth of reinforcement between approximately 0. 75B and 1.5B. As discussed above, the optimal depth of reinforcement appears to increase somewhat for strip footings (up to approximately 2B in some cases). 54

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3.4 Width (b) and Length (I) of Reinforcement The literature indicate that the width of the reinforcement can also effect the 8CR and settlement but is secondary to the proper choices of the three above discussed parameters. In genera4 optimal BCR values for square footings were obtained with reinforcement widths (b) in the range of 2B to 48. For strip footings, increases in BCR values were obtained with widths up to 88, however, good values were obtained at widths as low as 28. The length of the reinforcement is best described in tenns of the length of reinforcement extending beyond the end of the footing (.L\1) as shown in the above figure. GeneraUy speaking, for rectangular or strip footings with an LIB ratio greater than 3, a .L\1 length of 0.5B to 1.5B is generally appropriate. Where the footing LIB ratio is less than 3, .L\llengths should generally equalt\b. 3.5 Type and Strength/Stiffness of Reinforcement While previous studies have performed testing using a variety of types of reinforcement, it appears geosynthetics lend themselves the best to this type of application because of their availability, reasonable cost, and well-researched and documented engineering properties. Generally speaking, geogrid type reinforcement appears to be the choice of geosynthetics for use as reinforcement in GRSF systems. Studies indicate that a lesser amount of geogrid (nwnber of layers and width) versus a geosynthetic fabric is typically required to achieve similar results. Additionally, where less settlement is desired, geogrid appears to perform better than an equal amount of geotextile. However, it should be noted that some woven geotextiles have strength and sti.ffitess properties that are comparable to geogrids and therefore may also produce desirable results when properly designed. It should be noted that while ultimate strength and stiffuess are two different measures, the two are typically related for geosynthetic materials. 55

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One study by Yetimoglu and Wu ( 1994) evaluated the effect of reinforcement stiffitess on bearing capacity. In order to properly evaluate the effect of reinforcement stiffitess on the BCR, a finite element analysis was performed. The results of the study are presented in Figure 3.2. u < u 0 1000 2000 3000 -"000 3TIFFNESS 0' REINFORCEMENT. "N /m A s I c: I s c; :-"; s 5 J .. 0 s -"" -' Variation of BCR with Reinfon:emeot Stiffness ( N=3, uJD=zJD= 0.30, D/0= 4.5) Figure 3.2 One conclusion of this study was that there was minimal improvement in the BCR above a stiffuess of approximately I OOOkN/m. The sti.ffuess is defined as axial stiffuess per unit width of reinforcement and is equal to the product of the modulus of elasticity (E) and the thickness of the reinforcement (t). The stiffuess of commercially available geogrid reinforcement is generally in the range of200 to 500 kN/m The hatched woe in Figure 3.2 represents this range. The BCR results obtained within this hatched woe are comparable to the BCR results obtained during actual testing, where the configuration of the reinforcement and settlements were the same (compare to Table 2.3, Yetimoglu and Wu, 1994). 56

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3.6 Soil/ Aggregate FiU Type and Density Within the Reinforced Zone In the type of fill material desired within the reinforced zone is that which will provide good, long-tenn, soil-reinforcement interaction such that the stresses of the overlaying footing are transferred to the reinforcement even at minimal strains or settlement. This typically requires a granular material whose strength properties will not reduce significantly with time or the addition of moisture. Because the strength of cohesive soils can be significantly reduced over time due to increases in moisture as well as other factors, these types of soils are not recommended. An additional consideration in determining the proper type of fill material is whether or not additional water reaching the existing subgrade soils will result in additional settlement or further ''weakening" of the ground. Where the existing subgrade soils are already soft and wet, water penetrating the reinforced fill zone and wetting the existing subgrade at the base of the excavated zone will not likely cause significant additional problems related to support capability or settlement. Therefore, a relatively well-draining granular material, is likely suitable. However, where it is desired to at least hinder the amount of water that may penetrate the reinforced zone and wet the underlying subgrade, a material with more "fines" (% passing the No. 200 Sieve) is desirable. Lastly, the maximum particle size and amount of larger particles within the fill material should be such that they will not damage the reinforcement. With the above considerations in mind, the following preferred fill properties are provided as a general guideline: The fill should consist of materials that classify as a well-graded sand or gravel. Materials of uniform size (poorly-graded) should be avoided where possible as compaction ofthese types of materials can be problematic. Material consisting of crushed rock, resulting in angular particles are preferred when available. The maximum particle size of the fill should be less than approximately 1 Y2 inches. 57

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The amoWit of"fines" (material passing the No. 200 Sieve) should be between about 5 and 25 percent by weight. This range can vary somewhat based on the plasticity of the fines. Less fines should be used when possible. The Liquid Limit and Plasticity Index should be less than 30 and 8 respectively, where lesser fines (i.e. 15% to 20% passing the No.200 Sieve or less) exist. However, where the percent passing the No. 200 Sieve exceeds 20 percent, it is generaUy desirable to have very low plasticity (say, PI::=: 4) or non-plastic fines. The literature indicate that the density of the fill material will also effect the ultimate BCR but more importantly the BCR at low settlements. Where lower fill density is utilized, higher settlements are required to mobilize the strength of the reinforcement required to increase the BCR. Higher fill density results in a ''tighter" reinforced soil foundation system where the soil-reinforcement interaction is mobilized at lower settlements. Therefore, a compaction specification in the range of 90 to 95 percent of the maximum modified Proctor dry density (ASTM D 1557) is preferable. 3.7 Summary In general, where the configuration, conditions and materials used are optimal, the existing literature indicates that BCRs on the order of 1.2 to 1.9 can be achieved with only one layer of reinforcement. Additionally, available settlement data indicate a settlement reduction of up to approximately 20 to 30 percent is common. Where two layers of reinforcement area were utilized the BCR values increase to a range on the order of 1.5 to 2.5 with settlement reductions on the order of 20 to 40%. Where three to four layers are used, BCR values on the of2 to 3 are common with some values up to approximately 3.5, and settlements reductions of up to 40 to 60 percent. Higher BCR values have been observed for strip footings with more than four layers of reinforcement and total reinforcement depths of up to approximately 2B. A summary of typical ranges of the parameters discussed above that have resulted in significant increases in the BCR as well as significant decreases in settlement are presented in Chapter 5 ofthis report. 58

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It should be noted that the above results were obtained for testing of mainly geosynthetic reinforced soil foundations (GRSF), using sand soils within the reinforced zone as weU as the same soils below the reinforced zone. The above BCR values and settlement reductions may or may not be as significant in practical applications where the subgrade soils are poor and differ from the materials that would be used within the reinforced zone. Therefore, in order to estimate the ultimate BCR and more importantly the resulting settlement of a GRSF in for variable field conditions, each situation must be evaluated individually. The next chapter of this report will discuss some of the design and analysis concepts for GRSF systems and propose a rational design procedure. 59

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4 Proposed Model for Estimating Bearing Capacity and Settlement of a GRSF As previously mentioned, the purpose of the GRSF system, similar to that of the more classical approaches to ground improvement, is to increase the bearing capacity of the foundation soils, and limit the amount of total and differential settlement that will occur as a result of applied load. Other associated advantages include the ability ofthe system to increase the margin of safety for unforeseen problematic soil conditions by improving the ability of the foundations soils to "bridge" small, localized soft zones or other zones that may be more prone to settlement. Additionally, the use of reinforcement can reduce the amount of material that may need to be removed when compared to an unreinforced replacement zone, which may result in a significant economic benefit. Shallower excavation and replacement can also be beneficial in areas where shallow groundwater conditions or contaminated soils may exist. This chapter discusses some of the theoretically based concepts of GRSF systems that result in achieving the above advantages, and presents a rational method for estimating bearing capacity and settlement. 4.1 Bearing Capacity 4.1.1 General Concepts As previously discussed, the bearing capacity for GRSF systems is generally described in terms of the Bearing Capacity Ratio (BCR), which is equal to the ratio of the ultimate bearing capacity for the reinforced condition to that of the non-reinforced condition. Because this involves "ultimate" bearing capacities, the ratio is based on the "failure" condition. As we know from classical foundation design, a relatively large amount of settlement will generally occur before bearing capacity failure takes place. These settlements are typically well above those generally considered acceptable for modern, rigid structures. Therefore, as was presented in some of the literature reviews, a similar Bearing Capacity Ratio can be obtained in terms of an 60

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allowable settlement and, in most cases, is more appropriate for design of structures that are sensitive to settlement. The bearing capacity of GRSF systems can show significant increases over a non reinforced foundation system. One of the reasons for the increase in bearing capacity is that a portion of the poor soils is typically removed from beneath the proposed foundation and replaced with stronger soil, generally consisting of granular fill. More importantly, however, the inclusion of geosynthetic reinforcement within the replaced zone can result in significant increases in bearing capacity. Concepts explaining the increase in strength of soil reinforced with geosynthetics include: I) apparent confinement, and 2) apparent cohesion. The inclusion of geosynthetics in a soil mass hinders lateral movement of the soil, causing what is termed "apparent confinement." Basic soil mechanics indicates that as confinement of a soil mass is increased, so is its shear strength. Results of triaxial strength testing perfonned on reinforced soil samples show an "apparent cohesion" that results in an increase in shear strength. While the increase in shear strength appears graphically as an increase in cohesion, this increase is explained as an internal confinement, or the "apparent confinement" due to the inclusion of reinforcement. Figures 4.1 and 4.2 present these concepts graphically. 61

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F oot in g "Confining" tensile resistance in "ll ....... ...... + ... Shear Stress ('t) "Apparent Confinement" Figure 4.1 Unreinfon:ed Sand Normal Stress (a') "Apparent Cohesion" Figure 4.2 (Wu, 1994) 62

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Lastly, vanous studies have determined that construction of a GRSF foWldation exhibits a "deep-footing effect," where the bearing capacity of a GRSF system is similar to that of a conventional footing constructed at a depth equal to that of the bottom ofthe GRSF reinforced zone. Figure 4.3 presents this concept. '-I ___ Foo_tm_' 8 __ ____..1 ..... ..... ... ... ... moo .m .. .......... m ....... Reinforcement "GRSF System" "Deep-Footing Effect" Figure 4.3 Footing "Equivalent Foundation" Figure 4.4 from the study performed by Huang & Tatsuoka (1990), compares load test results on GRSF systems with varying depths of reinforcement that have the same width as the overlying footing, with load tests performed on a rigid footing of the same size at the same depth as the base of the reinforced zone. As is shown in Figure 4.4, the results obtained using the ofthe GRSF system were very similar to that of the footing of the same depth. This would indicate that analyzing a GRSF system using the classical bearing capacity equation, and assuming the deep footing effect, would provide a reasonable estimate ofthe bearing capacity. In this study, the reinforcement width was approximately the same size as the footing. 63

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I I 2001-:o. '6) 005 5/6 Load (N)/Settlement (SIB) Curves, Illustrating the "Deep-Footing Effect"; Huang & Tatsuoka (1990) Figure 4.4 Based on the data above, it appears that analyzing the bearing capacity of a GRSF system with use of the classical bearing capacity equation and assuming the theory of the deep-footing effect is a reasonable approach. However, the review of existing studies indicates that increasing the width of the reinforcement from that of the overlying footing size to something larger (typically on the order of 2B to 4B) can result in an additional increase in the bearing capacity as well as an additional reduction in settlement. It should be noted that most research also indicates that the effect of increasing the width of the reinforcement is secondary to having the proper spacing and depth of reinforcement. Therefore, the most significant benefit from increasing the reinforcement width results when optimal spacing and depth of reinforcement and good compaction were used. Huang & Tatsuoka ( 1990) found that increasing the width of reinforcement can increase the overall BCR, but the increases were variable between approximately 1 0 to 50%, depending on the reinforcement spacing and total depth of reinforcement. 64

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While the mechanics of GRSF systems are not fully understood, it is believe that the increase in the width of reinforcement provides additional reinforcement "anchorage" beyond the footing width or failure zone. This in tum increases the resistance of the reinforcement to the overlying load. Figure 4.5 presents this concept. Resisting tension forces in extended portion of reinforcement Footing I I I I 1 I I I I I I I 1 I I I I I _._ _____ Anchoring Resistance of Extended Portion of Reinforcement Figure 4.5 Furthermore, Figure 4.6 below presents the tension forces that were measured within three reinforcement layers of a GRSF system at various settlements during testing performed by Huang & Tatsuoka (1990). The data indicate that the forces were the highest in the lowest reinforcement layer at the footing centerline. The tensile forces were most significant within a reinforcement width of 28, however smaU tension forces within a width of 48 were measured below this rectangular footing as weU. 65

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.2 . .... ;;; D z "' !! . .... c: 0 c: .... 3rd layer Depth 0 .98 I ---j Tensile Forces in Reinforcement Up to Peak. Test No. 17(UB=6, n=l, CR=JB%) (Huang & Tatsuoka, 1990) Figure 4.6 While the increase in bearing capacity resulting from increasing the width of reinforcement can be significant, review of various studies indicates the benefit of extending the reinforcement beyond the edge ofthe footing is of secondary importance and can be somewhat variable and difficult to predict. Therefore, as will be presented below, for analysis purposes it is proposed to estimate the bearing capacity using the deep footing concept only, ignoring the reinforcement beyond the edge ofthe footing. While it is likely that this approach is somewhat conservative, calculations of bearing capacity using the bearing capacity equation and assuming the deep-footing effect result in similar values as those obtained from large-scale model tests when directly compared. Further discussion of this analysis approach and comparison calculations will be presented later in the next section. 66

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4.1.2 Bearing Capacity Failure Modes It is generally beneficial to consider possible modes of failure before a method to estimate the ultimate bearing capacity can be proposed. While various potential failure modes for GRSF systems have been proposed, Wayne et al. (1998) proposed four failure modes as shown in Figures 4. 7 through 4.1 0. Footing .... Failure above Upper Reinforcement Layer (Upper Failure) Figure 4.7 Footing ------------------------. ........ .. ..... .... .. Punching Failure through Reinforcement (GRSF Failure) Figure 4.9 Footing ------------:-; .... --------. :>":. Failure between Reinforcement (Inter-layer Failure) Figure 4.8 I FoOOIJg I .......... / Punching Failure of Entire GRSF (Deep-footing Failure) Figure 4.10 .. Recent studies of load tests on reinforced soils would indicate that failures above or within the reinforced soil mass (Figures 4. 7 and 4.8 above) are unlikely where proper 67

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spacing of the reinforcing layers is utilized. Therefore, the more plausible failures would be those depicted in Figures 4.9 and 4.10 where failure occurs as a punching type failure through the reinforced system, or a punching of the entire reinforced mass into the subgrade soils. These types offailures are likely the more common where the subgrade soils are soft. Wayne et al. ( 1998) indicates punching failure through the reinforced zone is more likely where the width of the reinforced zone is relatively wide and the underlying soils are only moderately soft. A punching failure of the entire reinforced mass (deep footing failure) into the subgrade would be the more likely mode of failure where the width of the reinforced zone is approximately equal to the width ofthe footing, and the underlying soils are very soft. 4.1.3 Proposed Model for Bearing Capacity Analysis In all of the studies reviewed, none indicated failure of the reinforcement. Additionally, in order to rupture the reinforcement, it is expected that large settlements would occur prior to rupture, which would likely result in settlements much larger than that tolerable by many structures. Therefore, while likely a conservative approach, it is recommended the bearing capacity be analyzed assuming a deep-footing failure. In the case of the failure mode shown in Figure 4.10 where the entire reinforced zone punches into the underlying soils, the bearing capacity can be analyzed using the general bearing capacity equation and the concept of the "deep-footing effect." For calculation purposes, the General Bearing Capacity Equation can be utilized by assuming the pressure at the base of the footing is transmitted to the bottom of the reinforced zone as shown in Figure 4.11. An appropriate model ofthe general bearing capacity equation (such as Vesic's, 1973) should be used to account for the deep footing effect. It should be noted that the Terzaghi, 1943 model is only applicable to foundations placed on or near the ground surface and should not be used for the proposed application. 68

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I Actual Footing I Ground Surface ...._____ Reinforcement Deep Footing "GRSF System" "Equivalent Deep Footing" "Deep-footing Effect" Figure 4.11 Figure 4.11 indicates the reinforcement width is equal to that ofthe overlying footing. It should be noted that where the reinforcement is extended beyond the footing as is typically recommended, analysis using the deep footing concept should consider the "deep footing" is the same width and the actual footing. It is proposed that the following generalized bearing capacity equation be used to evaluate the bearing capacity of a GRSF (ASCE. 1993): quit= (c)(Nc)(Sc) + (l/2)(B')(y'H)( Ny)(s1 ) + Where, quit = ultimate bearing capacity c = soil cohesion B' = width or "effective" width of foundation y' o = effective soil or surcharge pressure at the foundation depth D = depth of footing base below the ground surface Nc. Ny, Nq =dimensionless bearing capacity factors Sc. Sy, Sq = dimensionless correction factors 69

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The accuracy of this approach was examined by comparing ultimate bearing capacities obtained from large-scale load tests (namely, Adams and 1997) to those obtained using the above equation (with Vesic s, 1973 bearing capacity and correction factors). These comparison studies show good agreement between the estimated bearing capacity using the equation and the model test results. The results are presented in Table 4.1. Bearing Capacity Comparison Results (3 layers of Geogrid) Footing First Layer Reinforcement Total Reinf. Measured1 Predicted2 Pred./Meas Width Depth Ratio Spacing Ratio Depth Ratio B(m) SufB S,IB D,IB quit (kPa) quh (kPa) 0.31 0.5 0.5 1.5 541 554 1.02 0.46 0.33 0.33 1.0 599 580 0.97 0.61 0.25 0.25 0.75 664 589 0.89 0.91 0.17 0.17 0.5 542 630 1.16 1 The measured bearing cap!citics wen: obtained from a study performed by Adams and Collin ( 1997). 1 The angle of internal fiiction <+>of the soil used in the Adams and Collin study was c:stimatcd through back-calculation and tables of values based on gradation and density. Bearing Capacity Comparison Results Table 4.1 As with the above analysis, evaluating the bearing capacity of a footing or GRSF system requires estimating soil properties such as the angle of internal friction through correlation with common field tests or more sophisticated laboratory testing. It is cautioned that estimation of these properties be done with care and a proper degree of conservatism. 70

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4.2 Settlement 4.2.1 Genenl Concepts Besides increasing the bearing capacity of a foundation system, the other major benefit of using GRSF systems is the reduction in total and differential settlement. More than the increase in bearing capacity, the reduction in settlement is usually the controlling design factor because the magnitude of settlement that occurs prior to bearing capacity failure is typically much larger than is tolerable or desirable for most structures. Settlement of a GRSF system, like any other settlement problem, is caused by an increase in vertical stress (due to the application of a foundation load) within the reinforced zone as well as within the underlying soils. The reduction in settlement with a GRSF system is partially due to the fact that the reinforced zone typically consists of stronger, granular fill material with inclusion of geosynthetic reinforcement, and therefore has a significantly stiffer response (i.e. a higher elastic modulus) to load than the weaker soils which were removed. Secondly, the stronger "'composite" material with in the reinforced zone has the capability of spreading the loads over a wider area (by increasing the Stress Distribution Angle), resulting in a reduction of the contact pressure at the interface of the reinforced zone and underlying weaker soils. With this in mind, one must consider the proper width of the reinforced zone to ensure it is sufficiently wide to take full advantage of the stress distribution if the full reduction in settlement is desired. Figure 4.12 provides illustrations ofthese concepts. Stress Distribution Angle Figure 4.12 71

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Once the reinforced soil properties have been estimated, the proper tests have been performed on the underlying weaker soils to determine their settlement/consolidation characteristics, and the stress distribution has been estimated, settlement analysis can be performed using classical procedures. While judgement might indicate that larger settlement would be required in order to gain any strength due to the reinforcement, experimentation has indicated that a significant effect can be realized even at settlements within the generally accepted building standards. Settlement is most significantly reduced when the spacing of the reinforcement is close, the width of reinforcement is adequate to take full advantage of the stress distribution angle, and the reinforced fill soil is compacted to a sufficiently high density such resistance within the reinforcement can be mobilized at small settlements. Data indicate that settlement reductions on the order of 40 to 60 percent are possible where GRSF systems are properly constructed. It should be noted that these reductions were obtained under controlled conditions where the fill within the reinforced zone and the underlying soils were the same, generally consisting of granular material. Based on the fact that GRSF systems are typically used where the site soils are less than desirable for shallow foundation systems, settlement reductions may be somewhat less than those listed above, and will depend on the foundation sizes and loads. A method for estimating the settlement for a GRSF system is presented in the following section. It assumes the reader has some knowledge elastic and consolidation settlement. By estimating the settlement of a foundation placed directly on the less desirable existing soils and comparing it to the estimated settlement using a GSRF system, the reduction in settlement, or benefit of the GRSF system can be evaluated. 72

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4.2.2 Proposed Model for Settlement Analysis a) Settlement Analysis within the Reinforced Zone Because the fill within the reinforced zore is typically a granular material with inclusion of reinforccrrent, ard is of a limited depth, settlement within this zone is generally relatively small for a properly constructed GRSF system Additionally, where the subgrade soils are poor, the annunt of sett1ement that will occur within this zone is generally minor as compared to the total settlerrent irduding that of the tmlerlying poor soils. Regardless, an estirmte of the settlerrent within this zore shoukl be performed to completely analyze the benefit of the GRSF system Estimation of settlenrnt within this zore may be best perfonred ming available rn=tlnds that are OOsed on elastic theory. These types of rn=tlnds required estimation of the Elastic Modu.l\5 (Es) of the soil within the reinforced zone. There are scores of correlations that can be used to estimate Es for sand soils that are based on comrrnn field tests such as the SPT (N-value) ard Cone Penetration Test (cone resistaoce value, 'lc)Since these tests are generally not perfonned on the reinforced fill zone, no correlation can be made unless some asswnptions are made. Wayne et al., (1998) suggested assuming an SPT N-value of25 to 40 for granular compacted soils ard ming the correlatiom for the "N" value provided in Table 4.2. Soil Type UB= 1 Silts, sandy silts, slightly cohesive silt-sand mixtures ION Clean, fine to medium sands, & slightly silty sands 17.5N Coarse sands, & sands with little gravel 25N Sandy gravels & gravel JON After Schmemnann ( 1970) and Schmertmann. Hartman, and Brown ( 1978) Notes: I) N = SPT "N" value 2) UB = footing length/footing width Elastic Modulus for Cohesionless Soil, Es (ksj) Table 4.2 73 VB= 10 14N 24.5N 35N 42N

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An additional method of estirmtion, or comparison to the rrethod suggested above can include assuming an Es value in the ranges provided in Table 4.3 that are !Sed by soil type. Modulus of Elasticity, Type of Soil lb/in. 1 MN!m2 Poisson's ratio, f.ls Loose sand 1,500-3,500 10.35 24.15 0.20-0.40 Medium dense sand 2,500 4,000 17.25 27.60 0.25-0.40 Dense sand 5,000 8,000 34.5055.20 0.30-0.45 Silty sand I ,500 2,500 10.35 17.25 0.20-0.40 Sand & gravel 10, 000 25,000 69.00-172.50 0.15-0.35 Typical Range of Elastic Parameters for Various Soil Types (Das, 1995) Table 4.3 As the estimations of the elastic mxlulus Es suggested arove are for soil only, neither of the above rretlxxis take into account the increase in stiffuess of the soil mass due to the inclusion of reinforcement. Wayne et al, ( 1998) indicates the following iocreases in the elastic mxlulus have resuhed from the use of geogrid reinfurcerrent in granular soil as listed below. Geogrid Properties Measured increase in Elastic Modulus, E, True I% Junction tensile Modulus in Use= 17 kilt M D. 20 kilt XMD True 2%Junction tensile Modulus in Use= 11.75 kilt MD. 15 k/ft XMD True Junction tensile Strength In Usc @ I% Sin! in = 0.170 klft MD. 0.2 150% (2 grid layers) kilt XMD 400% ( 3 grid layers) True Junction tensile Strength In Use @ 2% Slnlin = 0.235 klft MD. 0.3 kiltXMD True I% Junction tensile Modulus in Use= 22 kilt MD. 30 kilt XMD True 2% Junction tensile Modulus in Usc= 18.2 klft MD. 25 klft XMD True Junction tensile Strength In Use@ 1% Slnlin = 0.220 k!ft MD, 0.3 350% (2 grid layers) k/ltXMD 800% (3 grid layers) True Junction tensile Strength In Usc @ 2% stnlin = 0.365 klft MD, 0.5 k/ltXMD Increase in Elastic Modulus due to Geogrid Table 4.4 74

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Therefore, once the Es values for soil only have been estimated from the table or correlations provided above, an appropriate increase should be added to achieve an estimated Es value for the "composite" GSRF system. Once the modulus of elasticity Es for the reinforced zone has been estimated, the settlement within this zone can be evaluated using the Schmertmann method (Das, 1995) for calculating immediate settlement in cohesionless soils as: Where: S = settlement C1 & C2 are correction factors for foundation embedment and soil creep, respectively Iz = strain influence factor q = stress at the level of the foundation q = yDr = existing effective stress at the proposed foundation depth Es = soil elastic modulus value llz = layer thickness b) Settlement Analysis Below the Reinforced Zone As discussed above, the reinforcement within the replacement zone effectively spreads the overlying foundation load over a wider area by increasing the stress distribution angle. Where classically it has been suggested that a stress distribution of 2:1 (vertical:horizontal) can be assumed to estimate stresses in soil beneath a foundation, various studies including Wayne, 1998 have suggested that a stress distribution of I: 1 (vertical:horizontal) can be achieved for reinforced granular soils. Therefore, it is suggested that settlement analysis be performed assuming an "apparent footing" at the depth of the deepest reinforcement layer. However, as opposed to that 75

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suggested for analysis of the bearing capacity above, the apparent footing will increase in size based on the stress distribution assumed for the reinforced zone. The stresses at the base of the actual footing will therefore be reduced when they are applied over the larger area ofthe apparent footing. Figure 4.13 presents this concept. prrssurr = IOOOpsf t lfl t 2: I stress distribution angle for unreinfurcal soil Stronger fill w!Reinfurcement -------. t ---------------Apparrut footiug Prrssurr = Ill psf apparent footing width-3 ft. Stress Distribution Figure 4.13 Based on the analysis conducted in this study, it is believed that the approach discussed above and use of a I: I ( 45) stress distribution angle will provide an adequate estimation of settlement for GRSF systems. The accuracy of this approach was evaluated by comparing settlements resulting for various footings and loads obtained from large-scale load tests (namely, Adams and Collin, I997) to those obtained using the above approach to analyzing settlement. Because the soil used for this study consisted of a non-cohesive sand, a method for evaluating immediate settlement by Schmertmann and Hartman ( 1978) was utilized. For the most part, these comparison studies show good agreement between the estimated settlement and the model test results with better agreement for the larger footings. The results are presented in the Table 4.5. 76

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Settlement Comparison Results (3 layers ofGeogrid) Footing First Layer Reinforcement Total Reinf. Footing Measured1 Predicted2 Width Depth Ratio Spacing Ratio Depth Ratio Pressure (kN/mz) S(mm) S(mm) B(m) S./B S,./B D,IB 100 2.0 2.0 0.91 0.17 0.17 0.5 150 4.0 3.9 200 6.0 6.3 100 1.0 0.6 150 2.0 1.6 0.61 0.25 0.25 0.75 200 3.0 3.1 250 5.0 5.8 100 1.0 0.3 150 2.0 0.8 0.46 0.33 0.33 1.0 200 3.0 2.0 250 4.0 5.1 1 The measural settlcmcniS were oblained from a study performed by Adams and Collin ( 1997). 1 The clastic paramder5 of !he soil used in the Adams and Collin study 'h"ae estimated through back-calculation using daiB from their unn:infura:d (control) tests. Settlement Comparison Results Table 4.5 As with the above analysis, evaluating the expected settlements of a GRSF system requires estimating soil parameters through corre]ation with common field tests or more sophisticated laboratory testing. It is cautioned that estimation of these properties be done with care and a proper degree of conservatism 77

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S. Design of a GRSF System This chapter provides a general procedural guideline that may be used to evaluate if a GRSF system is a viable alternative for a project, and to provide an approach to estimating the benefits that can be realized through use of the system. 5.1 Appropriate Applications of a GRSF System Prior to performing an analysis, one must understand the appropriate applications of a GRSF system as well as its limitations. The following provides some guidance that may be helpful in evaluating whether or not this system is appropriate for a specific project and site conditions. Typical applications for a GRSF system include: Light to moderately loaded, generally one to two story structures (bearing pressures of approximately 4000 psf or less) Conventional shallow footing foundations on the order of2 to 6 feet in width Relatively uniform subsurface conditions Loose sand or soft clay foundation soils lffill is encountered at a site, adequate investigation and analysis should be performed to evaluate the variable nature of the material. In general, on sites with large area fills or highly variable fill or native soil conditions that will result in significant differential settlement, a GRSF system may not be a viable foundation alternative. GRSF systems may also be applicable to projects somewhat outside the range of parameters provided above, however each situation must be evaluated on a case by case basis and with caution. 78

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The geotechnical issues that need to be addressed must be weU defined also. For example, is the major issue the need to reduce settlement or increase the bearing capacity? Are there any other site or structure issues that may impact the decision to use this type of foundation system? Can a traditional overexcavation and replacement of reasonable depth without the use of reinforcement be used? Structural information such as the maximum total and differential settlement that the structure will tolerate must also be known. Additionally. since the geometry of the GRSF system is dependent on footing width, configuration, and contact pressures, this information must be known as well. 5.2 Typical GRSF Design Parameters If it is detennined that a GRSF system is or may be a viable foundation alternative, the next step is to choose an appropriate set of design parameters depending on the type and amount of improvement that is desired. Figure 5.1 and Table 5.1 can be used as general guidelines for selection of the design parameters. 79

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Excavation Limits I 14-4:--Footing Reinforcement (SECTION VIEW) 4-----------------b Jl' "' ,. L Footing -i .... "''If B ,. (PLAN VIEW) Typical GRSF Configuration Figure 5.1 80 limits of reinforcement

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TYPICAL GRSF DESIGN PARAMETERS PARAMETER DESCRIPTION TYPICAL RANGE B fuoring "'idth :::::: 2.0 to 6.0 ft. ll L Footing length Unlimited Su Spacing between the base of the tOOting and upper layer of 0.158 to 0.38 2 l reinforcement s. Vertical spacing between reinforcement layers 0.158 to 0.358 sb Spacing betl.l.l:CII the base of the excavation and lowest reinforcement > 6" layer o. Total depth of reinforced fill mnc 0.758 to 1.5B 3 l b width of reinforced fill zone 2.08 to 4.08 4 l I Length of the reinforced fill zone for strip tOOting See d) below dl (for LIB < 3) Length of reinforcement beyond edge of strip fOoting Same as db dl for (LIB 3) Length of reinforcement beyond edge of strip tOOting 0.58 to 1.58 N, Number of reinforcement layers 2 to 5 Stiffness Stiflilcs<; (tensile moduli) of the reinforcement > 200 kN/m Notes: I) Benefits ofGRSF systems will apply to fOOtings beyond these limits, however, rrm1 of the large-scale test data is within or ncar die ""typical range" provided in this table. 2) This spacing is typically slightly larger where a single reinfun:ement layers is used. 3) Optimal D, is generally near die upper end of this range. Strip fuorings may be slightly higher (max 2.08). 4) Optimal values as low as 1.58 have been found for square footings. and as high as 8.08 for strip. Typical GRSF Design Parameters Table 5.1 5.3 Estimating Bearing Capacity Once the foundation size and configuration are known and the appropriate parameters as provided above are chosen, the improvement in bearing capacity can be evaluated using the proposed model presented in Section 4.1.3 of this report. If more 81

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improvement is needed the GRSF parameters may be adjusted and the bearing capacity re-evaluated until the desired result is achieved. 5.4 Estimating Settlement Knowing the foundation size, configuration, and contact pressure, as well as the appropriate soil parameters, settlement analysis can be perfonned by using the proposed model described in Section 4.2.2 of this report. As with the bearing capacity, if more improvement is needed, the GRSF parameters may be adjusted and the settlement re-evaluated until the desired result is achieved. 5.5 Design Example A geotechnical investigation performed on the proposed site of a new commercial development found an eolian deposit consisting of loose sand soil. No bedrock was encountered to the drill termination depth of I 00 feet. The development is to include construction of various one and two story structures of "tilt-up" concrete construction. Due to the expected foundation loads, settlements beyond the structural tolerance criteria would result. The cost of installing deep foundations is cost prohibitive and the client is requesting other foundation alternatives. Therefore, a Geosynthetic Reinforced Soil Foundation (GRSF) system is being considered as the first alternative. The specific soil and structural data are as follows: Soil Properties: Soil Classification : Silty Sand (SM) Blow Counts (NsPT) range from 3 to 12 with an average of6 cj)' = 28 Moist Density Ym = 115 pounds per cubic foot (pet) 82

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Foundations: Square footing pads ranging from 3 to 5 feet in width Foundation contact pressures based on estimated structural loads are expected to range from 2000 to 5000 pounds per square foot (psf) for the 3 foot footings, and 2000 to 4000 psf for the 5 foot footings Footings will be constructed at a depth of 30 inches beneath the ground surface, which is the local maximum frost depth. Building Settlement Tolerances: Building specifications indicate the proposed structures can tolerate up to 1.5 inches of total settlement and 1 inch of differential settlement between footing pads. Proposed GRSF Configurations: For the 3 foot footing pads, the following GRSF configuration is proposed: I+3 ft. sq. ----.! G.S. r 2.5 ft. ,, I I 8" -lf---------------' 12" 4ft. 12" j 12" 'f --------------------------------------------------------0 4" 83

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For the 5 foot footing pads, the following GRSF configuration is proposed: f+--5 ft. sq.--.! G.S. t 2.5 ft. i Jl' 1.5' '"' -----------------------------------------------------------JI' 1.5' 6ft -------------------------------------------1.5' l ----------------------------------1.5' -,lr--------------------------------------.. ----, ... 17ft *All of the above parameters are within those recommended in Section 5.2. The reinforcement is a high modulus biaxial geogrid (tensile modulus of 400 kN/m). The GRSF parameters shown above were selected based on the "Typical GRSF Design Parameters" presented in Figure 5.1 and Table 5.1 of this report, and the author's experience. 84

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UrreiniDrcOO, 3 ft. !11 fuoting: Alhw.d* Bearing Capacity= 3,256 psf (Fa:tor ofSafety = 3), less thm tre 5000 psf required Settbrert at 200) psf = 0.63 ird"IS, within structural to hal us Settbnrt at SOX) psf = 1.66 ird"lS, arove structural toletmus ReinfOrced, 3ft. !11 Bearing Cap3city = 8,109 pst: (Foctor of Safety= 3), greater fum tre 5 psf required Settbrent at 200) psf = 1.04 ird"lS, slighly arove stroctural toltnn.es Settbrent at 4 psf = 2.18 ird"lS, awrooching stru:tlB'al tolercn res ReinfOrced, 5 ft. !11 footing: Alk>Wcll* Beamg Cap3city = I 0,592 ps( (Factor of Safety = 3), greater fum tre 4 psf required Settlerrent at 200) psf = 0.66 irrhs, within structural tolerarus Sett1e:rrent at SOX) psf = 1.44 ird"lS, within structural to let aJU'S *'Ire results presemrl irdi:ate tre proJX>SOO oonfigurali:>ffi res.lll in settk::mrts tim are wihin stn.x:turai tolernn::e criterB am axeptable capacitis lli lxaring caprity ani settbnn cabJlafum fOr each of tre urreinfurced am reinforced fO\.IOOafun oonfiguratiom are presemrl in Apptnh:es A & B, It slDuld re rnted tim tre settbnrt within tre reinfOrced zon:; ani tb1t rehw tre teirdOrced zore, are amlyzed sqmately. lb:rerore, tre t\W rru;t re added together to cab date tre 85

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6. Construction Considerations The purpose of this chapter is to provide some of the more common construction related considerations that should be addressed when a GRSF system is utilized. These considerations, along with the manufactures specifications and procedures should provide a good basis for evaluating the issues that will impact the construction ofthe system. 6.1 Subgrade Preparation In general, no special steps or techniques, other than typical subgrade preparation recommendations, are required for preparation of existing subgrade soils prior to construction of a GRSF system. However, it is probably most common to construct GRSF type systems over less than desirable subgrade soils. Therefore, the potential for encountering conditions that may prove difficult from a construction standpoint is higher, and should be given appropriate consideration. While it is typically the mentality that subgrade soils be "'stabilized" prior to placement of additional fill, it should be remembered that the purpose of a GRSF system is to stabilize the existing subgrade to an extent that results in the desired performance for the overlying structure(s) over their expected design life. Therefore, stabilization is actually being performed as the GRSF system is being constructed. Due to the typical applications for a GRSF system, it is common to encounter some difficulty when constructing the lower portion of the reinforced fill where poor subgrade conditions generally exist. In general, the subgrade should be prepared only to the extent that difficulties with placement and compaction of the overlying GRSF system are minimized. Typically, as the thickness of the reinforced fill section increases as construction ofthe GRSF system progresses, the reinforced fill begins to "bridge" the underlying poor subgrade, making placement and compaction easier. 86

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Heavier equipment and vibratory equipment can make the subgrade conditions worse especially where shallow groundwater conditions exist. Where placement and compaction of the fill is difficult in the lower portions of the reinforced fill zone, the use of lighter equipment, or compaction techniques that do not require vibratory equipment can help. Where local areas of very poor subgrade conditions exist, it may be required to stabilize the subgrade using common techniques to an extent that allows equipment access and reduces compaction problems. However, if possible, this type of stabilization should be limited as it may be very costly to stabilize large areas, reducing the cost effectiveness of the system. In some cases, it may also be beneficial to place a layer of geotextile on top of the subgrade prior to placement of the reinforced fill as this can provide "separation" between the poor subgrade soils and overlying reinforced fill. Where a high modulus woven geotextile is used, this layer can provide separation as well as add to the overall effectiveness of the GRSF system. Therefore, if very poor subgrade conditions are expected over a large area, this type of technique can be integrated in the design phase, when its added benefit to the overall GRSF system can be evaluated and incorporated in a more cost effective way. Use of geotextiles in this way is a common technique employed for subgrade stabilization for many situations. 6.2 Utilities One of the major considerations when using a GRSF system is construction of utilities that may pass through the system With the typical construction sequence, it is common for contractors to install utilities after construction of foundations, which requires trenching or twmeling beneath the foundation components. Where a GRSF system is utilized, this would result in cutting through the geosynthetic reinforcement, compromising the integrity of the GRSF system. Therefore, it is important to coordinate the construction of the portion of the utilities that will pass beneath or through the GRSF system such that cutting through the geogrid is avoided. 87

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6.3 FiU Type and Compaction As mentioned previously in Chapter 3, the type of fill material desired within the reinforced zone is that which will provide good, long-term, soil-reinforcement interaction such that the stresses of the overlying footing are transferred to the reinforcement even at minimal deformation. Soils that exhibit such characteristics include granular materials with strength properties that will not reduce significantly with time or with the addition of moisture. Because the strength of cohesive (clay) soils can be significantly reduced over time due to increases in moisture as well as other factors, these types of soils are not recommended. Additionally, proper soil compaction is very important for a reinforced soil foundation to work properly. A ''tightly packed" mass of reinforced soil will mobilize the strength within the reinforcement at significantly smaller deformations (footing settlement) than will a loose mass. Section 3.6 of this report should be reviewed for more detailed recommendations and considerations related to the type and compaction of the fill soils. 6.4 Providing GRSF Parameters for Construction As would be expected, most projects involve various foundation sizes, geometry's and loads. Therefore providing parameters that will result in the desired benefits for all of the different types of foundations and loads, and will also be easy to understand and build from a construction standpoint can be a challenge to the designer. If each individual type of foundation has slightly different parameters, the number of parameters and where to apply them can become very confusing and impractical from a construction standpoint. Therefore, rather than providing different parameters for each foundation type, it is recommended to group similar foundation sizes and types such that the same geometric parameters can be applied to all of the foundations in that group, while still providing the desired results for each. 88

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6.5 Other Considerations The manufacturer typically provides construction or installation guidelines that, in addition to the above considerations, may include additional guidelines for placement of the reinforcement layers, and repairing the reinforcement if it is damaged. Placement considerations typically include overlapping, tensioning, and pinning of the reinforcement layers. Repair of damaged sections generally requires placing a new section of reinforcement over the damaged area with a minimum overlap or some type of mechanical connection. The manufacturer's guidelines should be reviewed for these and any other considerations that may be covered in the guidelines. 89

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7. Concluding Remarks A rational method for analysis and design of Geosynthetic Reinforced Soil Foundations (GRSF) was proposed. The method was developed based on the literature review and the author's experience. The proposed design method has been found to be in good agreement with measured results of large-scale experiments of GRSF systems. When utilizing the analysis and design methods proposed in this report it is very important that the designer fully evaluate the appropriateness of using a GRSF system based on the proposed use and site conditions. Section 5.1 in this paper provides guidelines related to appropriate uses of GRSF systems. Additionally, the design engineer must have a good understanding of bearing capacity and settlement analysis and evaluate the site properly such that the parameters used in the analysis are reliable. Conservative estimations are recommended where the parameters are questionable. It is also important to provide a design that is both reliable from an engineering standpoint, as well as one that is not difficult to understand and construct. Chapter 6 ofthis report discusses some of the more significant construction issues. The approach and methods of analysis proposed in this report are based heavily on studies that have included numerous load tests on GRSF systems. While the proposed methods of analysis and design related to bearing capacity and settlement are based mainly on data from large-scale load tests, much of the published studies performed small-scale testing of which only a few addressed scale effects of their results. Therefore, it is suggested that consideration be given to the effect of scale on the results oftesting that is performed on small-scale models. It is believed that the data and proposed methods for analysis and design provided in this paper will provide good results subject to the provisions and limitations stated within the paper. However, more large-scale load testing performed on GRSF systems for various ground conditions and a larger range of foundation types and loadings would greatly enhance the understanding of the behavior of these systems. 90

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Appendix A. Bearing Capacity Calculations 91

PAGE 102

Bearing (Unreinforced, Sq. M B C 0 G H K (B'<=L I 8'=!3.00 e= 0.00 L'= 3.00 0/B= 0.83 Elf Area = 9 00 Nc fed fc' I g ol Q o I 14 0.00 2580 157 1 33 100 amma D NQ fQI 17 115.00 2.50 14 72 1 53 125 1 ooJ I 80991 72891 1 B .nmma Fed fli!i 20 o so I Joo I 115.00 j_ 16 n I o 60 I 100 1.00 1730 15572 ult = 9829 88462 rs= .100 allow= 3276 29487j G.S. 1+3 ft. _l_ ................................................................ ____ ........ t_ .. c----------................................................... .. 215ft. __j + I I Allowable Bearing Pressure (q.) = 3,276 psf 92

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Bearing (Reinforced, 3ft. Sq. Footing) AI B C _1 D E G I H I BEARING CAPACITY 8Y VESIC"S METHOO --:::::Spreadsheet Name : BEARINGlWQl 3/1193 K (B'<=L 1 Ref: Das, 'Principles ol foundation En,<;neerinl!." Section 3 4 ----g Ph( del!)= Em"oo Nc = 25 80 B = 9 Phi(rad) 0 49 Nq = I 14 72 I L = : 10 0,00 = 16 72 Area = e= o.oo L = 3 00 0/B= 2 I 7 E" Area 2 9 00 c Nc Fed I g ol Q ol 14 0 .00 25 80 !.57 146 1.00 amma D Nq fqs fqd fql 17 11s.oo L 6.50 14 72 I 53 I 34 I 00 I I 22596 I 2033651 8 umma N11amma flld ff!i 20 0 so 300 IIS.OO 16 72 060 I 00 I 00 1730 15572 ull= 24326 218937 FS =l 3.00 J allow= 8109 72979 G .S. t"' .. . . ...... ...... .. .. .. . ... .... .. ... ............... ...... . ...... ...................... .. . .. ... 25ft. Jl' 8" I if I I -------1------T--------I' 12" I I if I I -------.. --------. J. .. _________________ _ __ 4ft Ji' 12" : : j -_--_-_ .. "Equivalent Deep Footing" II ft Allowable bearing Pressure ( Qa) = 8, l 09 psf 93

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Bearing (Unreinforced, 5ft. Sq. Footing) A1 8 C 0 E F G H f-:--BEARING CAPACITY BY VESIC"S METHOD Name: BEARING1WQ1 J/1/93 t=: Ref: Oas. 'Principles ol Foundation Section 3.4 K (8'c=L 1 Nc = 25 SO 8 = Ph(rad)= 0.49 Nq = l 14 72_]L = 0.00 Nl!amma = 16 72 Area= 5I e=Em e= 0.00 L'= 5.00 0/8= 0 50 Elf Area = 25.00 :: Nc fcs fed Fe\ I g ol Q ol 14 0.00 2580 1 57 120 1 00 0 Na fas [qd fqo 17 115.00 2.50 14 72 1 53 1 15 100 I 7452 1 186306 1 8 v.omma fl!d Fi!i 20 0 50 5 00 115.00 16.72 060 1 00 100 2884 72091 ull =l 10336 258397 FS =l 3.00 .1 J allow= 3445 86132 j.--s n. sq. I --------.. ------------------------.. -................................................................. .. 2tft. _j + I I Allowable Bearing Pressure (qa) = 3,445 psf 94

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Bearing Capacity (Reinforced, Sft. Sq. Footing) AI B 1 C D L G 1 H I ----:BEARING CAPACITY BY VESIC"S METHOO Soreadsheet Name: BEARING! WQI 3/1/93 = Ref: Oas. "Pnnciples ol Foundation Section 3. 4 1----a Phi(del!l= Nc = 25 80 B = Ph(rad)= 0.49 NQ = 14 72 L = ,......1Q.. beta(dl!l= 0.00 Nl!amma = 16 72 Area = B'=l e= o.oo L'= 0/B= I 70 Ell Area = 0 Nc Fed Fe I g ol Q ol 14 0.00 25 80 I 57 I 42 I 00 D Nq FQd Fq1 17 115.00 a. so 14.72 1.53 131 1.00 I 28894 1 72234o 1 -B l!:amma fl!d Fli!i 20 0 50 5 00 115.00 16.72 060 I 00 I 00 28841 72091 I wt =I 31777 794432 I'S= .100 allow= 10592 264811 G.S 5 ft. sq. __....,, f ........................ ----.................................... --... 25ft. I I I 5ft I I . I I I 5ft I I I I If I I ---------------T-------6ft. "-1 1 K (B'<=L'l s oo I 5 00 J 25 00 j .. =-= =-=-=-=-=-... 1:-::oo-o::::::. -"Equivalent Deep Footing" I7 ft. Allowable Bearing Pressure (qa) = 10,592 psf 95

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B. Settlement Calculations 96

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Unreinforced, 3ft. Sq. Footing, 2000 psf A1 B c I D I E I F I G _( H I _,.,,, ICII"'"' Ul 'UUUIII;: UJ, _,diiU _,'"""'"'' Wldllll" IYit:l IIUU Spreadsheet name: SETLSAND WQl = Ref: Das. "Pnnciples of Foundation Engineerrng." Section 3 12 E/N or gamma= 0.0575 qbar= 1 t(yrs)= I 9 E/qc = D= 2.5 B= 3 C2= 10 81 q= 014375 Q= 9 11 qbar-q= 085625 Settlement 12 C1= 0 9161 I o.os23 1 = gbar*lz(bar)dz Depth Nor qc E z/B lz E sum -17 0.00 6.00 48 0000 0100 0 0 18 1.57 6.00 48 0.523 0.591 00113 0 0113 19 3.14 6.00 48 1047 0381 00159 0.0272 20 4.71 6.00 48 1570 0.172 00090 0.0362 21 6.29 6.00 48 2097 0000 00028 0 0391 22 7.86 6.00 48 2.620 0000 0.0000 0.0391 23 9.42 6.00 48 3140 0000 00000 0.0391 24 11.00 6.00 48 3667 0000 00000 00391 25 12.57 6.00 48 4 190 0000 00000 0.0391 26 14.14 6.00 48 4 713 0000 00000 0 0391 27 15.77 6.00 48 5.237 0000 00000 0 0391 28 17.29 6.00 48 5 763 0000 00000 0 0391 29 18.86 6.00 48 6.287 0000 00000 0 0391 30 20.42 6.00 48 6807 0000 00000 0.0391 31 22.00 6.00 48 7 333 0000 00000 0 0391 G.S. f"" .................... 2 000 psf ( 1 tsf) s = 0.0523 ft. (0.63") 97

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Reinforced, 3ft. Sq. Footing, 2000 psf witbin the reinforced zone) A1 B I C D E F = u uu,mg on :.ana '"'"''""u = Spreadsheet name SETLSAND WQ1 =Ret Das. "Principles of Foundation Engineering," Section 3 .... _12 ___ ..., E/N or gamma= 0.0575 =!bar= t--------'7-f 9 E/qc = D= 2.5 B=t-------'3:-1 G I t(yrs)= I C2= H I _J1 8 q= 0 14375 qbar Settlement I o .0067l -Depth Nor qc 1 7 0.00 40.00 18 0.4J 40.00 19 0.86 40.00 20 1.29 40.00 21 1.71 40.00 22 2.14 40.00 23 2.57 40.00 24 3.00 40.00 25 3.43 40.00 26 3.86 40.00 27 4.00 40.00 28 4.10 1000.00 29 5.14 1000.00 30 5.57 1000.00 31 6.00 1000.00 E z/B 320 0000 320 0 143 320 0.287 320 0430 320 0 570 320 0 713 320 0.857 320 1.000 320 1 143 320 I 287 320 1 333 8000 1367 8000 I 713 8000 1.857 8000 2 .000 lz 0 100 0 243 0 387 0 530 0 572 0 .515 0.457 0 .400 0 343 0 285 0 267 0 .253 0 115 0 .057 0000 E 0 0 .0002 0 .0004 00006 00007 0 .0007 0.0007 0 .0006 0 .0005 00004 0 0001 00000 00000 00000 00000 G.S. J n. .............. ----.... ------..... ... ......... ---. -----. -5 ft. 8 / 2000 psf (1 lsf) ', --------7( _______________________ ___ _ :\--------------12" / / / / / / 12" / ' /1'-149 psf (.0745 1st) I 1 ft. 98 sum 0 00002 0 .0007 0 .0013 00020 0 .0027 0 .0034 0 0040 0 .0045 0 .0049 0 .0050 0 .0050 00050 00050 0 .0050 s = 0.0067ft. (0.08")

PAGE 109

Reinforced, 3ft. Sq. Footing, 2000 psf the reinforced zone) IA1 8 C I D E F b I"'""""'"'"''" 111 u11 ..,auu """"uu I Spreadsheet name: SETLSAND WQ1 = Ref: Das. "Pr1nciples of Foundation Engineering," Section, _3_12--::-::-::-:c=-> 8 E/N or gamma= 0.0575 qbar= 0.0745 9 E/qc = D= 6.5 B= 11 10 8 q= 0 37375 Q= 9 0145 qbar-q= -0 29925 G I t(yrs)= I C2= H I Settlement C1= 1 6245 I o.o2s2 I gbar+lz(bar)dz E Depth Nor qc E z/8 lz 17 0.00 6.00 48 0000 0 100 0 18 1.57 6.00 48 0143 0.243 0.0004 19 3.14 6.00 48 0.285 0.385 0.0008 20 4.71 6.00 48 0428 0.528 0 0011 21 6.29 6.00 48 0 572 0 571 0.0013 22 7.86 6.00 48 0715 0.514 0.0013 23 9.42 6.00 48 0.856 0457 0.0012 24 JJ.OO 6.00 48 1000 0400 00011 25 12.57 6.00 48 1 143 0.343 00009 26 14.14 6.00 48 1.285 0286 0.0008 27 15.71 6.00 48 1428 0229 0.0006 28 17.29 6.00 48 1.572 0 171 0.0005 29 18.86 6.00 48 1715 0.114 00003 30 20.42 6.00 48 1856 0.057 0.0002 31 22.00 6.00 48 2.000 0000 0.0001 G.S. 3 ft. sq. ____.,..,, -------------------15ft. I 8" / 20 psf (I tsf) '\ / ---------------------------------------,-----------------12" / / / -________ /. ________________________________________ -"..!. __________ 12" // / / / 12" / ', L 14-9 psf (.0745 tsO II ft. S = 0.0252 ft. (0.30")settlement below reinforced zone 99 sum 0 00004 0.0012 00023 00036 0.0050 0.0061 00072 00081 0.0089 00095 00100 00103 0.0105 0.0106

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Unreinforced, 3ft. Sq. Footing, 5000 psf IAI 8 c D E F G I H I b l-'l .. lUO:IIJ<:II\ Ul -'ll.fUGI <: uuo Ill!; Qll -"
PAGE 111

Reinforced, 3ft. Sq. Footing, 5000 psr within the reinforced zone) A1 B I C D I E F = 1 ... """''""'"' o ;:,quart: on ::.ana IYietnoo Spreadsheet name SETLSAND WQ1 == Ret Das. 'Principles of Foundation Engineering,' Section 3.12 r-------, I 10 Bj q= 0 143751 G I t(yrs)= I C2= H l ....W. qbar q= 2 35625 Settlement ::::M C I = I o.ol78l gba,...lz(baryodz E Depth Nor qc E z/B lz 17 0.00 40.00 320 0000 0 100 0 18 0.43 40.00 320 0.143 0 243 0 0006 19 0.86 40.00 320 0 287 0387 0.0011 20 1.29 40.00 320 0430 0.530 21 1.71 40.00 320 0 570 0 572 0.0018 22 2.14 40.00 320 0.713 23 2.57 40.00 320 0.857 0.457 24 J.OO 40.00 320 1000 0.400 25 J.4J 40.00 320 1 143 0343 26 J.86 40.00 320 1.287 0 285 0.0011 27 4.00 40.00 320 1333 0.0003 28 4.10 1000.00 8000 1.367 0.253 00000 29 5.14 1000.00 8000 1 713 0 115 0.0001 30 5.57 1000.00 8000 1 857 0.057 00000 31 6.00 1000.00 8000 2.000 0000 00000 G.S. 3ft. r .. .......... ....................... -.. .. ........ .. I I l. 8" / 5000 psf (2.5 tsl) ', / ----------------,-----12" / / ________ 12" / / / / 12" / ', /,.... 372 psf (0.186 tsl) 11 ft. 101 sum 0 00006 00016 0.0032 0.0050 0.0084 00099 0.0122 0.0125 0.0126 0.0126 s = 0.0 178ft. (0.21")

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AI B I Reinforced, 3ft. Sq. Footing, 5000 psf (settlement belov the reinforced zone) c I D I E I F = Ul r uo
PAGE 113

Unreinforced, Sft. Sq. Footing, 2000 psf AI B I C D E F = Ul ;)\jU
PAGE 114

AI = = 8 9 10 -4 12 Reinforced, Sft. Sq. Footing, 2000 psf (settlement the reinforced zone) B I c I D E F I G I u1 u11 ""'"'u -""'"""''"""""""" """"uu Spreadsheet name: SETLSANDWQ1 Ref: Das, "Principles of Foundation Engineering, Section 3.12 E/N or gamma= 0.0575 qbar= 1 t(yrs)= I E/qc = D= 2.5 B= 5 C2= 81 q= 0 14375 Q= 25 qbar-q= 0 85625 C1= 0.9161 I H I Settlement 0.01041 gbar*lz(bar)+dz Depth Nor qc E z/8 lz E = 17 0.00 40.00 320 0000 0100 0 18 0.71 40.00 320 0.142 0.242 0.0004 19 1.43 40.00 320 0286 0.386 0.0007 20 2.14 40.00 320 0428 0.528 0.0010 21 2.86 40.00 320 0.572 0.571 0.0012 22 3.57 40.00 320 0.714 0.514 0.0012 23 4.29 40.00 320 0.858 0.457 0.0011 24 5.00 40.00 320 1.000 0.400 00010 25 6.00 40.00 320 1.200 0320 0.0011 26 6.01 1000.00 8000 1.202 0319 0.0000 27 7.14 1000.00 8000 1.428 0.229 00000 28 7.86 1000.00 8000 1.572 0.171 00000 29 8.57 1000.00 8000 1.714 0.114 00000 30 9.29 1000.00 8000 1.858 0.057 00000 31 1o.oo 1000.00 8000 2.000 0000 00000 G.S. j.-5 ft. sq._----.tllloj 5ft. Uft / 2000 psf (l tst) ', / / -----r-----------"<-----1 "ft / ) / ---'T,--4_5_0_ / t. / 0ft. .-J--------------------\" .. .. / 1 n / .) ' /-------------------------------------------173 psf (0.0865 tsf) 11 n. 104 s:..:m 0 0.0004 0.0011 0.0021 0.0033 00045 0.0056 0.0066 0.0077 0.0077 0.0077 0.0078 0.0078 0.0078 0.0078 s = 0.01 04ft. (0.12")

PAGE 115

Reinforced, Sq. 2000 ps the reinforced zone) A1 B I c D E F I = ;:,e1uemen1 uo ,;,
PAGE 116

Unreinforced, Sft. Sq. Footing, 4000 psf AI 8 c D E F = !"'""'"""'"" uo ""'lua1" rooung un -""'"'"""' '"'aolll 1nemoo Spreadsheet name: SETLSAND WQI = Ref: Das, 'Principles of Foundation Engineering." Section 3 12 r------, 10 8 q= 0 14375 G I t(yrs)= I C2= H I Settlement -4 qbar q-1 85625 12 C 1 = L __ .:::._0.:::._96::..;}:.:::3'-..J I o.1817 I qbar*lz(bar)+dz Depth N or qc E z/8 lz E sum 17 0.00 6.00 48 0 000 0.100 0 0 18 0.71 6.00 48 0 142 0.242 0 0051 0.0051 19 1.43 6.00 48 0.286 0.386 00094 0.0145 20 2.14 6.00 48 0 428 0.528 0 0135 00280 21 2.86 6.00 48 0.572 0.571 0.0165 0.0445 22 3.57 6.00 48 0.714 0.514 0.0161 0.0605 23 4.29 6.00 48 0.858 0.457 0.0146 0.0751 24 5.00 6.00 48 1.000 0.400 0 0127 0.0878 25 6.00 6.00 48 1.200 0320 0.0150 01028 26 6.01 6.00 48 1.202 0319 00001 0.1029 27 7.14 6.00 48 1428 0.229 0.0129 0.1158 28 7.86 6.00 48 1.572 0.171 00060 0.1218 29 8.57 6.00 48 1. 714 0114 0.0042 0.1260 30 9.29 6.00 48 1.858 0.057 0.0026 01286 31 10.00 6.00 48 2.000 0000 00008 0.1295 G.S. I+-5 ft. sq._--.t ... l t""'"" ft t 4000 psf (2 tsO s = 0.1817 ft. (2.18") 106

PAGE 117

[A1 b = 8 9 10 _g -Reinforced, Sft. Sq. Footing, 4000 psf (settlement within the reinforced zone) 8 I c I D E I F I 1 .. "" '"'"'"''" Ul "'4UIIO" "UUlHII; Ull ..,IIIIU .;n.IUII"I lnlllllll" niCliiUU Spreadsheet name: SETLSAND WQ1 Ref: Das, "Prrnciples or Foundat1on Engineerrng,' Section 3 12 EIN or gamma= 0.0575 qbar= 2 E/qc = D= 2.5 8= 5 8 q= 0 14375 Q= 50 qbar q= 1 85625 C1= 0 9613 G I H I t(yrs)= I C2= 146022 Settlement I 0.02191 qbar+lz(bar}"dz -Depth Nor qc E z/8 lz E 17 0.00 40.00 320 0000 0 100 0 18 0.71 40.00 320 0.142 0 242 0.0008 19 1.43 40.00 320 0.286 0.386 0.0014 20 2.14 40.00 320 0.428 0528 0.0020 21 2.86 40.00 320 0.572 0.571 00025 22 3.57 40.00 320 0.714 0.514 00024 23 4.29 40.00 320 0.858 0457 0.0022 24 5.00 40.00 320 1000 0400 00019 25 6.00 40.00 320 1200 0.320 0.0023 26 6.01 1000.00 8000 1202 0319 00000 27 7.14 1000.00 8000 1.428 0.229 00001 28 7.86 1000.00 8000 1572 0.171 00000 29 8.57 1000.00 8000 1714 0.114 00000 30 9.29 1000.00 8000 1858 0057 00000 31 10.00 1000.00 8000 2.000 0000 00000 G.S. 5 ft. r-------------.. -----------------------------------------------------------------------------------------/ r l.5ft. / 4000 psf (2 tsO ', / 1 l. 346 psf (0.173 tsO I 7ft. 107 sum 0 0.0008 0.0022 0.0042 0.0067 00091 0.0113 00132 0.0154 00154 0.0155 00155 0.0156 0.0156 0 0156 s = 0.0219ft (0.26")

PAGE 118

Reinforced, Sft. Sq. Footing, 4000 psf (settlement below the reinforced zone) AI B C I D I E I F '"""""''" ot ;:,quare rootmg on ;:,ana--;:,c;nmenmann s memoa Spreadsheet name: SETLSAND WQl Ref: Das, 'Pnnc1ples of Foundation Engmeenng," Sect1on 3 12 E/N or gamma= 0.0575 qbar= 0.173 9 E/qc = D= 8.5 B= 17 10 81 q= 048875 Q= 49.997 qbar-q= 0 31575 G I t(yrs)= I C2= H I Settlement _g 12 C1= 1 7740 I o.09as I gbar*"lz(bar)*dz Nor qc E z/B lz E = Depth 17 0.00 6.00 48 0 000 0 100 0 18 2.43 6.00 48 0.143 0.243 0 0015 19 4.86 6.00 48 0286 0 386 0.0028 20 7.29 6.00 48 0429 0.529 0.0040 21 9.71 6.00 48 0 571 0 572 0.0048 22 72.14 6.00 48 0.714 0514 0_0048 23 14.57 6.00 48 0.857 0.457 0.0043 24 77.00 6.00 48 1.000 0400 0 0038 25 19.43 6.00 48 1 143 0343 0_0033 26 21.85 6.00 48 1 285 0.286 0.0027 27 24.29 6.00 48 1.429 0.228 0.0023 28 26.72 6.00 48 1.572 0.171 0 0018 29 29.15 6.00 48 1.715 0114 0.0012 30 31.58 6.00 48 1.858 0.057 0.0007 31 34.00 6.00 48 2000 0000 00002 G.S. 5ft.sq. I --------................ --. ....................... 5 ft. L5ft. / 4000 psf (2 tsO ', / / ------------:r-------------------------------',;----------------1.5ft. / '\45o / l. / ', r / / 1.5ft. ' /----------------------------------------------------------346 psf (0.173 tsO 17ft. S = 0.0986 ft. (1.18")-settlement below reinforced zone 108 sum 0 0 0015 00043 0 0083 0 0131 0.0178 0.0221 00258 00291 0 0318 0.0341 0.0358 0.0371 0.0378 0 0381

PAGE 119

References Adams, M.T. and Collin. J.G. (1997) '"Large Model Spread Footing Load Tests on Geosynthetic Reinforced Soil Foundations, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 123, No. I, January 1997, pp. 66-72. American Society of Civil Engineers, Bearing Capacity of Soils, ASCE Press, 1993. Das, B.M., Principles of Foundation Engineering, 3rd ed., Boston: PWS Publishing Company, 1995. Guido, V.A., Chang, O.K., Sweeney, M.A., ( 1985), "Bearing Capacity of Shallow Foundations Reinforced with Geogrids and Geotextiles," Proceedings of the Second Canadian Symposiwn on Geotextiles and Geomembranes, Edmonton, Alberta, pp. 7177. Huang, C.C., and Tatsuoka, F., (1990), "Bearing Capacity ofReinforced Horizontal Sandy Ground," Geotextiles and Geomembranes, 9(1), 51-82. Koerner, R. M., Designing with Geosynthetics, (h ed., Saddle River: Prentice Hall Inc . 1998. Omar, M.T., Das, B.M., Yen, S.C., Puri, V.K., and Cook, E.E., (1993a), ultimate Bearing Capacity ofRectangular Foundations on Geogrid-reinforced Sand," Geotechnical Testing Journal, 16(2), 246-252. Samtani, N.C., and Sonpal, R.C., (1989), "Laboratory Tests of Strip Footings on Reinforced Cohesive Soil," Journal of Geotechnical Engineering, ASCE, 115(9), 1326-1330. Wayne, M.H., Han, J., Akins, K., (1998), "The Design ofGeosynthetic Reinforced Foundations," Accepted for Presentation at ASCE s 1998 Annual Convention & Exposition, Boston, Massachusetts, October 18-21. 109

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Wolff, T.F., Spreadsheet Applications in Geotechnical Engineering, Boston: PWS Publishing Company, 1995. Wu, J. T. H., Designing Construction ofGeosynthetic-Reinforced Soil Retaining Walls, 1997. Yetimoglu, T., Wu, J.T.H., and Saglamer, A (1994). "Bearing Capacity of Rectangular Footings on Geogrid-Reinforced Sand," Journal of Geotechnical Engineering, ASCE, Vol. 120(12), 2083-2099. 110