Citation |

- Permanent Link:
- http://digital.auraria.edu/AA00003195/00001
## Material Information- Title:
- Drilled shafts under combined axial and lateral loads
- Creator:
- Gonzalez, Cesar
- Publication Date:
- 2010
- Language:
- English
- Physical Description:
- xv, 128 leaves : ; 28 cm.
## Subjects- Subjects / Keywords:
- Shafts (Excavations) ( lcsh )
Axial loads ( lcsh ) Lateral loads ( lcsh ) Boring ( lcsh ) Axial loads ( fast ) Boring ( fast ) Lateral loads ( fast ) Shafts (Excavations) ( fast ) - Genre:
- bibliography ( marcgt )
theses ( marcgt ) non-fiction ( marcgt )
## Notes- Thesis:
- Thesis (M.S.)--University of Colorado Denver, 2010.
- Bibliography:
- Includes bibliographical references (leaves 124-128).
- General Note:
- Department of Civil Engineering
- Statement of Responsibility:
- by Cesar Gonzalez.
## Record Information- Source Institution:
- |University of Colorado Denver
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- Auraria Library
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- All applicable rights reserved by the source institution and holding location.
- Resource Identifier:
- 656366336 ( OCLC )
ocn656366336
## Auraria Membership |

Full Text |

DRILLED SHAFTS UNDER COMBINED AXIAL AND LATERAL LOADS
by Cesar Gonzalez B.S., University of Guadalajara, Mexico, 2002 A thesis submitted to the University of Colorado Denver in partial fulfillment of the requirements for the degree of Master of Science Civil Engineering 2010 This thesis for the Master of Science degree by Cesar Gonzalez has been approved by ^ Dale Gonzalez, Cesar (M.S., Civil Engineering) Drilled Shafts under Combined Axial and Lateral Loads Thesis directed by Professor Nien-Yin Chang ABSTRACT This manuscript presents the numerical analyses of a drilled shaft foundation under single and combined axial compressive and lateral loads. In order to evaluate the soil-structure interaction effects on a drilled shaft foundation system, under single or combined static monotonic loads, the analyses were performed using a three- dimensional finite difference numerical code. Construction of drilled shaft foundations for bridge piers, abutments, retaining walls, and buildings are examples of engineering structures than can undergo the combined loading effect during their lifespan. To better understand the behavior of the soil-structure physical system to be modeled, the initial chapters cover an outline of past investigations of deep foundations and more thoroughly the current state of design of drilled shafts under various geologic conditions; such as cohesive and cohesionless soils, and cohesive and cohesionless intermediate geomaterial. This is followed by a summary of the mathematical numerical method utilized, the software application, and an overview on the numerical modeling procedure of a drilled shaft foundation system. The latter chapters include the calibration of the research model and the subject matter of this thesis which is the combined load evaluation. The numerical analysis model was calibrated using actual full-scale field load tests in various foundation materials, such as cohesive and cohesionless soils, and in cohesive intermediate geomaterial. For the combined loads research model a stiff normally consolidated clay was assumed for the geologic profile with a drilled shaft aspect ratio of 10:1. The drilled shaft capacity- under combined loading is dependent on the loading sequence. The results presented in this research document are quantitative estimates of the potential range of axial and lateral load induced displacements in a drilled shaft numerical model. This abstract accurately represents the content of the candidates thesis. I recommend its publication. Signed Nien-Yin Chang DEDICATION I dedicate this thesis to my parents, for their support and patience, and for helping build a strong foundation in my life. ACKNOWLEDGEMENT I would like to give a very special thanks to my friend, professor, academic advisor, and mentor Dr. Nien-Yin Chang. I am grateful for the opportunity of learning from you every weekday for two years in the geotechnical laboratory and for the financial assistance throughout that time. I truly appreciate your words of encouragement and your overall patience with me throughout these many years. I will also like to thank the members of my graduate committee, professors Shing- Chun Trever Wang and Brian T. Brady, and the members of the soil-structure interaction group, Kevin Lee, Russel Cox, Mohammad Abu-Hassan, and Jan Chang, for helping me improve on my knowledge of numerical analysis and become a better geotechnical engineer. CONTENTS Figures..................................................................x Tables..................................................................xv Chapter 1. INTRODUCTION.........................................................1 1.1 Research Overview....................................................1 1.2 Purpose..............................................................2 2. LITERATURE REVIEW....................................................3 2.1 Introduction.........................................................3 2.2 Deep Foundations under Axial Load....................................4 2.3 Deep Foundations under Lateral Load.................................12 2.4 Deep Foundations under Combined Loads...............................19 3. DESIGN PRINCIPLES OF DRILLED SHAFTS.................................21 3.1 Introduction........................................................21 3.2 Drilled Shafts under Axial Load.....................................22 3.2.1 Drilled Shafts in Cohesive Soil..................................27 3.2.1.1 Shaft Resistance in Cohesive Soil...............................27 3.2.1.2 Base Resistance in Cohesive Soil................................31 3.2.2 Drilled Shafts in Cohesionless Soil.............................32 vi 3.2.2.1 Shaft Resistance in Cohesionless Soil...............................32 3.2.2.2 Base Resistance in Cohesionless Soil................................34 3.2.3 Drilled Shafts in Intermediate Geomaterial.............................35 3.2.3.1 Shaft Resistance in Intermediate Geomaterial........................35 3.2.3.2 Base Resistance in Intermediate Geomaterial.........................38 3.2.4 Settlement of Drilled Shafts...........................................38 3.3 Drilled Shafts under Lateral Load........................................40 3.3.1 Soil-Structure Interaction.............................................40 3.3.2 Boundary Conditions....................................................44 3.3.3 Methods for Lateral Load Design........................................45 3.3.3.1 Ultimate Rigid Resistance...........................................46 3.3.3.2 Subgrade Reaction Approach..........................................47 3.3.3.2.1 P-Y Method.........................................................49 3.3.3.2.2 Characteristic Load Method.........................................50 33.3.3 Elastic Continuum Theory............................................56 4. FINITE DIFFERENCE METHOD..................................................57 4.1 Introduction...........................................................57 4.2 Fast Lagrangian Analysis of Continua in Three Dimensions (FLAC 3D)......59 4.2.1 Overview...............................................................59 4.2.2 Mathematical Model.....................................................59 4.2.3 Numerical Formulation..................................................63 vii 4.2.4 Numerical Implementation 64 5. NUMERICAL MODEL OF A DRILLED SHAFT FOUNDATION........................66 5.1 Introduction.......................................................66 5.2 Mesh Generation and Interfaces.....................................66 5.3 Boundary Conditions................................................69 5.4 Initial Static Stress State........................................70 5.5 Loading............................................................72 6. MODEL CALIBRATION WITH FIELD LOAD TESTS..............................74 6.1 Introduction.......................................................74 6.2 Drilled Shafts under Axial Load....................................76 6.2.1 23rd Street Viaduct Field Load Tests, Denver......................78 6.2.1.1 Shaft Wall Resistance Field Load Test (T-l).....................79 6.2.1.2 Base Resistance Field Load Test (T-3)...........................84 6.2.2 1-270 and 1-76 Field Tests, Denver...............................87 6.2.2.1 Base Resistance Field Load Test (T3B)...........................91 6.3 Drilled Shafts under Lateral Load..................................91 6.3.1 1-270 and 1-76 Field Load Test, Denver...........................93 6.3.1.1 Lateral Load Field Test (T3B)...................................93 6.3.2 NGES-UH Field Load Test, Houston..................................95 7. SINGLE AND COMBINED LOADS EVALUATION.................................101 viii 7.1 Introduction 101 7.2 Research Drilled Shaft Numerical Model..............................102 7.3 Single Load Analysis................................................108 7.3.1 Axial Load.........................................................108 7.3.2 Lateral Load.......................................................110 7.3.3 Single Load Results................................................112 7.4 Combined Loads Analysis.............................................112 7.4.1 Axial then Lateral Load............................................113 7.4.2 Lateral then Axial Load............................................115 8. CONCLUSIONS...........................................................117 Appendix A. Constitutive Models in FLAC 3D........................................118 References...............................................................124 IX LIST OF FIGURES Figure 2.1 Drilled shaft..................................................................4 3.1 Axial load resistance of a drilled shaft......................................23 3.2 Axial resistance of a drilled shaft by layers.................................24 3.3 Bearing capacity factors......................................................25 3.4 Measured a values from field tests compared with empirical functions..........28 3.5 Frictional shaft resistance of a drilled shaft in cohesionless soil...........33 3.6 Shaft horizontal stresses and critical depth in cohesionless soils............34 3.7 Values of a\%m as a function of unconfmed compressive strength................36 3.8 Values of Fc as a function of concrete slump and depth........................37 3.9 Behavior of a drilled shaft under lateral load................................41 3.10 Soil reaction due to lateral load, profile and plan section view..............41 3.11 Typical soil resistance as a function of lateral deflection for two types of soil stiffness............................................................42 3.12 Complete soil-structure results for a typical lateral load design.............43 3.13 Soil-structure sign conventions...............................................43 3.14 Top boundary conditions: a) free, and b) fixed................................45 3.15 Free boundary condition for: a) long, and b) short drilled shaft..............46 3.16 Fixed boundary condition for: a) long, b) intermediate, and c) short drilled shaft................................................................47 x 3.17 Drilled shaft model forp-y method.....................................50 3.18 Load-Deflection curves: a) clay, and b) sand..........................52 3.19 Moment-Deflection curves: a) clay, and b) sand........................52 3.20 Lateral load applied above ground surface.............................53 3.21 Load-Moment curves: a) clay, and b) sand..............................54 3.22 Coefficients Am and Bm................................................55 4.1 Approximation of a continuous domain by an array of discrete points....58 4.2 Example of a FLAC 3D numerical model...................................60 4.3 Basic explicit calculation cycle.......................................60 4.4 Sign convention for positive stress components.........................61 4.5 Mechanical pressure: a) positive, b) negative..........................61 4.6 Tetrahedron............................................................64 4.7 An 8-node element with 2 overlays of 5 tetrahedrons in each overlay....65 5.1 Procedure summary for the static load analysis of a drilled shaft...67 5.2 Mesh of a drilled shaft foundation.....................................67 5.3 Types of elements used to shape the model grid.........................68 5.4 Mesh and interfaces for drilled shaft foundation.......................69 5.5 Two dimensional representation of roller boundary conditions........70 5.6 Mohr-Coulomb yield criteria............................................72 5.7 Plane of symmetry for research drilled shaft...........................73 6.1 Calibration process for a numerical model..............................75 xi 6.2 Modified Burland Triangle..................................................76 6.3 Typical axial compressive field load test setup............................77 6.4 Typical axial load-displacement curves.....................................77 6.5 Location for 23rd Street Viaduct test site.................................78 6.6 Construction of a drilled shaft in competent foundation material...........79 6.7 Geologic, construction, and model profile for the shaft wall resistance T-l field test............................................................80 6.8 Numerical model for shaft wall resistance T-l field test...................80 6.9 Shear stress distribution for shaft wall resistance T-l field test at the end of loading............................................................83 6.10 Load-displacement curves for shaft wall resistance T-l field test.........83 6.11 Geologic, construction, and model profile for the base resistance T-3 field test................................................................84 6.12 Numerical model for base resistance T-3 field test........................85 6.13 Vertical normal stress distribution for base resistance T-3 field test at the end of loading........................................................86 6.14 Load-displacement curves for base resistance T-3 field test...............86 6.15 Location for 1-270 and 1-76 test site.....................................87 6.16 Geologic, construction, and model profile for T3B field tests.............88 6.17 Numerical model for T3B field tests.......................................89 6.18 Construction of a drilled shaft in caving soils with temporary casing.....89 6.19 Load-displacement curves for base resistance T3B field test...............91 6.20 Typical lateral field load test setup.....................................92 xii 6.21 Typical lateral load-displacement curves...................................92 6.22 Normal lateral stress distribution for lateral T3B field test at the end of loading.................................................................93 6.23 Contours of x-displacement for lateral T3B field test at the end of loading.94 6.24 Load-displacement curves for lateral T3B field test........................94 6.25 Location for NGES-UH test site.............................................95 6.26 Geologic, construction, and model profile for Shaft 6 field test...........96 6.27 Numerical model for Shaft 6 field test.....................................97 6.28 Construction of a drilled shaft in caving soils............................97 6.29 Contours of x-displacement for Shaft 6 field test at the end of loading....99 6.30 Load-displacement curves for Shaft 6 field test...........................100 7.1 Typical combined axial compressive and lateral field load test setup.......102 7.2 Geologic, construction, and model profile for research drilled shaft.......103 7.3 Research drilled shaft numerical model.....................................103 7.4 Undrained shear strength with depth........................................104 7.5 Contours of undrained shear strength.......................................106 7.6 In-situ vertical normal stress distribution................................106 7.7 In-situ lateral normal stress distribution.................................107 7.8 Shear stress distribution in top 8.0 meters at the end of axial loading....108 7.9 Shear stress distribution in bottom 2.0 meters of shaft at the end of axial loading.............................................................109 7.10 Vertical normal stress distribution at the end of axial loading...........109 xiii 7.11 Contours of vertical displacement at the end of axial loading...........110 7.12 Normal lateral stress distribution at the end of lateral loading........Ill 7.13 Contours of x-displacement at the end of lateral loading................Ill 7.14 Contours of z-displacement at the end of lateral loading................112 7.15 Load-displacement curves for single loads...............................113 7.16 Load-displacement curves for single lateral and combined (axial-lateral) loads...................................................114 7.17 Load-displacement curves for single axial and combined (lateral-axial) loads...................................................116 A.l Mohr-Coulomb and Tresca yield surfaces in principal stress space.........119 A.2 Mohr-Coulomb failure criteria............................................120 A.3 Distribution of representative areas to interface nodes..................121 A.4 Components of the bonded interface constitutive model....................122 xiv LIST OF TABLES Table 3.1 Empirical base coefficients for settlement....................................40 3.2 Minimum length of embedment for Characteristic Load Method....................56 6.1 Material properties for 23rd Street Viaduct Field Tests, Denver...............82 6.2 Material properties for 1-270 and 1-76 Field Tests, Denver....................90 6.3 Material properties for NGES-UH Field Test, Houston...........................98 7.1 Material properties for research drilled shaft model.........................105 xv 1. INTRODUCTION 1.1 Research Overview This thesis presents the numerical analyses of a drilled shaft foundation under combined axial and lateral loads. The behavior of a reinforced concrete drilled shaft under a single type of load is compared to the load-displacement effect caused by the applied combination of two types of loads, axial compressive and lateral. The loads are applied in a static monotonic direction to the top of the drilled shafts. A comprehensive review of research on loading of deep foundations over the past 50 years and the current state of design of drilled shaft foundations under axial or lateral load is presented in early chapters. Since the design of a drilled shaft will vary according to the subsurface profile conditions, the foundation geologic material was divided for design purposes into cohesive and cohesionless soils, and cohesive and cohesionless intermediate geomaterials. This was essential in order to develop a better understanding of this multifaceted soil-structure interaction physical system. The analyses were performed using a three-dimensional finite difference numerical software called FLAC 3D. A summary of the mathematical numerical method utilized and the software application is provided in this thesis. The chosen numerical computer code is considered adequate to analyze the engineering mechanics of geologic material. An outline on the numerical modeling procedure of a drilled shaft foundation system is also included in the literature. The numerical analysis model was calibrated using actual full-scale field load tests in various foundation materials; such as, cohesive and cohesionless soils, and in cohesive intermediate geomaterial. For the combined loads research model, a stiff normally consolidated clay was assumed for the geologic profile with a drilled shaft aspect ratio of 10:1. The evaluation presents approximate values of the potential range of axial and lateral induced displacements due to loading. For this research thesis, all units are presented using the metric system (kilogram, meter, and second) unless otherwise noted in parenthesis. 1 1.2 Purpose It was determined that there is not sufficient research information on the effects caused by the application of combined axial compressive and lateral loads to drilled shafts foundations. A number of new and existing engineering structures that utilize drilled shafts as their construction option are faced with the need to design this type of foundation system considering that combined axial and lateral loads will be applied at some point during the lifespan of the structure. Structures such as buildings, transmission towers, and highway structures like bridge piers, abutments, retaining walls, and overhead signs, can be considered to experience a combined load effect throughout their design lifetime. Therefore, a three-dimensional numerical analysis was considered an acceptable method to enhance the knowledge of the soil-structure interaction behavior of this complex physical foundation system. 2 2. LITERATURE REVIEW 2.1 Introduction The objective of the literature review is to find available information on the general behavior of drilled shafts under combined (axial and lateral) loads. Since the performance is dependent on the combined application of two types of loads, it is also necessary to evaluate the effect of these loads separately. Although a multitude of studies exist on the subject of deep foundations under axial or lateral load, there are only a limited number of published papers on the behavior of deep foundations under combined loads. This chapter will include a summary of reviewed articles that are relevant to the scope of this thesis. Existing literature was also reviewed to establish the current state of knowledge with regard to the design of single drilled shafts under axial or lateral load and will be presented in the following chapter. Foundations are the lowest part of a structure capable of adequately supporting and transmitting the structural loads to the underlying subsurface. The type of foundation to be used will depend on the engineering properties of the soil or rock encountered beneath the structure. Shallow foundations are used when the surficial soil stratum is capable of supporting the structural loads; otherwise, deep foundations are used to transmit the loads at greater depths. Deep foundations can be separated according to their installation method into two main groups: driven piles and drilled shafts. Drilled shafts are concrete column-type elements, constructed by drilling into the earth (soil and/or rock) a hole with a diameter usually greater than 75 centimeters and placing fluid concrete in the excavation with or without steel reinforcement as shown in Figure 2.1. In cohesive soils, drilled shafts may have enlarged bases (bell-shape) by a construction technique known as under-reaming. Drilled shafts are also known as bored piles, drilled piers, caissons, and augered cast-in-place piles. However, drilled shaft is currently the designation with general acceptance for bored foundations. Drilled shafts are greatly used to support buildings, highway structures (overhead signs, retaining walls, bridge piers and abutments), transmission towers, and other engineering structures were large axial loads and lateral resistance are major factors. Drilled shafts are also suitable for loads that result from environmental factors such as 3 wind, ice, waves, water current, scour, earthquakes, and also vessel collision and explosive blasts. Axial Load ntttttt Base Resistance Figure 2.1 Drilled shaft (from Federal Highway Administration website) 2.2 Deep Foundations under Axial Load Meyerhof and Murdock (1953) Presented the results obtained from a series of axial load field tests on bored piles (drilled shafts) and a couple of concrete driven piles in London clay at two different test sites [1]'. Laboratory soil investigations and post-loading pile-soil examinations 1 Numbers in brackets indicate references listed in the last section of this thesis. 4 were also performed. Both sites consisted of hard to stiff fissured London clay, where the undisturbed shear strength of the clay increased rapidly with depth. The shear strength of the clay was reduced by up to one-half of the maximum when the undrained triaxial compression tests were made several days after sampling, even under high lateral pressures exceeding those due to overburden; this was due to gradual opening of the fissures. The residual shear strength on clay tests immediately after sampling were 50 percent less than the maximum strength. Fully remolded clay tests at natural water content resulted in shear strengths slightly higher than tests performed immediately after sampling by eliminating the clays natural fissures. Fully softened clay (in free water for 3 days) with water contents 5 to 8 percent higher than the natural water content resulted in very low, but uniform shear strengths throughout the entire depth at both sites. Adhesion, side resistance between the clay soil and the bored pile concrete, for stiff and hard clays is usually less than the shear strength of the soil itself. Hence, laboratory adhesion tests were performed in a shear box using a coarse stone of similar texture and density as concrete on the lower box frame and undisturbed clay on the upper frame. Adhesion increased with applied normal pressure; for large pressures, adhesion approached the shearing strength of the clay. Also, adhesion was correlated to an equivalent coefficient of friction between the two contacts of approximately 0.8 for a dry stone and 0.4 for a wet stone. Residual adhesion ranged from 0.5 to 0.8 times the maximum adhesion value. Water from a concrete mix tends to migrate towards the clay adjacent to the borehole, causing the clay near the pile to soften (local softening). Two water/cement mix ratios (0.2 and 0.4) were used for the bored piles to evaluate the effect on side resistance. It was found that the water content of clay increased rapidly within 5 centimeters (2 in.) from the shaft for mix ratios of 0.4, while remaining more or less constant at distances 5 centimeters (2 in.) or more away from the shaft. For ratios of 0.2 (crushing failure near surface) the water content of the clay remained the same near or with distance away from the shaft. The top-down loading system consisted of a pile anchored frame, the test piles were loaded using a hydraulic jack. The rate of loading was fast enough to ignore any significant consolidation without increasing the shear strength due to a rapid load rate. The average adhesion for bored piles can be estimated from the fully softened shear strength of the clay. While for driven piles, the average adhesion can be taken from the clays fully remolded shear strength. The undisturbed shear strength of the clay is used when calculating the end bearing resistance. Driven piles carried about double 5 the load of that carried from bored piles, hence the importance of avoiding soil softening in stiff clays. Skempton (1959) Axial load test results on bored piles embedded in London clay from ten different test sites were evaluated [2], The bored piles ranged from 2.44 meters (8 ft) deep and 0.25 meters (10 in.) diameter to 27.43 meters (90 ft) deep and 0.91 meters (36 in.) diameter. An extensive analysis was performed on the relation between the side resistance of the drilled shaft with the clays water content near the borehole wall, as well as the clays increase in strength with depth. The adhesion coefficient (a), which is equal to the ratio of average adhesion strength between the clay and the pile shaft (side resistance) to the average undisturbed shear strength of the clay within the embedded length of the pile, was found to average about 0.45. Values of the adhesion coefficient ranged from 0.6 to 0.3 depending on the workmanship and soil conditions. The adhesion coefficient will always be less than unity. Adhesion should be ignored in the zone of seasonal moisture change. The adhesion strength is less than the strength of the clay due to softening of the clay near the shaft wall, primarily because the clay absorbs water from the concrete and in some cases due to the drilling operations. When drilling below the water table, water will tend to flow out of the clay towards the open borehole. The adhesion strength was found to be about 80 percent of the shear strength of the clay adjacent to the concrete (softened clay). An increase in 1 percent in water content can cause a 20 percent reduction in the adhesion strength. Typical increases in the water content range between 3 to 6 percent, within 5.0 centimeters from the shaft contact surface, which can result in softened strengths 30 percent of the original clays strength. The shear strength of the undisturbed clay was found to increase approximately linearly with depth, while the adhesion coefficient was found to slightly decrease linearly with depth. The side shear resistance which develops in the clay alongside the shaft is essentially restricted to the narrow softened zone. The side resistance is mobilized at an early stage in the loading, and was considered to be fully mobilized after a settlement of 1.0 centimeter. Coyle and Reese (1966) Presented an analytical method to determine the load transfer mechanism of axially loaded driven steel pipe piles embedded in clay soil [3], Reeses (1964) analytical method for predicting load-settlement curves was employed; however, improvement 6 was emphasized on the correlations between soil properties and pile behavior. The pile is divided into various segments to calculate the axial movement of each segment due to the load transferred on to the surrounding soil. Pile load distribution and movement at different depths is obtained by instrumentation of a test pile, while the soil shear strength is acquired by field (vane shear) and laboratory (unconfined compressive strength) tests. Field test data from three different driven steel pile tests in clay were used to obtain a family of curves that relate the ratio of load transfer to soil shear strength versus pile movement. The types of piles were pipe, tapered, and rectangular, located in the San Francisco Bay area, Omaha, and Melbourne (Australia), respectively. Ten triaxial tests were performed on small model piles in clay for the purpose of finding load transfer values versus pile movement. Fligher load transfer values were obtained for rough model piles and for piles embedded in clays with lower water contents. Field and laboratory results confirm the behavior of soft clays near the pile-soil interface of driven piles where the loss of shear strength is due to remolding of the clay caused by the pile driving. However, with time, the shear strength will increase due to pore pressure dissipation. For most cases the comparison of the analytical method with data from field tests had a good correlation. Poulos and Davis (1968) Evaluated the performance of single incompressible piles and piers (drilled shafts) under axial load using elastic theory [4], based on Mindlins (1936) elastic equations. For the pier to be considered incompressible, the surrounding soil must be assumed soft compared to the pier; therefore, soft clay was used in the analyses. The pier length is divided into uniform elements (segments) to determine shear stress and displacements along the piers cylindrical sections. Three scenarios of shear stress along the soil-pier interface were considered; however, the most acceptable scenario was considered to be uniformly distributed shear stress along the circumference of the soil-pier interface. Various pier lengths to diameter (L/D) ratios were considered to account for the effect of pier dimensions on side shear distribution, displacement, and base load. Rough and smooth pier surfaces and variation of the soils Poissons ratio were also evaluated. Adhesion strengths between the pier and the clay, and the clays undrained shear strength were considered for the load-settlement behavior. Solutions were presented for piers embedded in a semi-infinite soil mass and a finite layer. 7 It was concluded that in undrained conditions approximately 90 percent of the total settlement will occur immediately after loading. Load transfer to the base of a pier was small, even for a L/D ratio of two the base receives about 25 percent of the total load. Belled base piers, which increase the load taken by the base, in soft clay are practical for relatively short piles with a L/D ratio less than 25. For increasingly higher L/D ratios, belled base piers will perform as a straight sided pier (without enlarged base). Mattes and Poulos (1969) This paper analyzes the behavior of compressible piers [5] and is considered a continuation of the research on incompressible piers performed by Poulos and Davis (1968). For the pier to be considered compressible, the surrounding soil must be considered as stiff. Elasticity theory is used to determine the behavior of soil and pier. The pier length is divided into equal segments, where uniform shear stress is developed around the circumference segment. Elastic modulus (Es) and Poissons ratio (vs) of the soil are assumed constant throughout the surrounding soil mass. The piers compressibility is evaluated by changing the pier stiffness (Aids) and comparing it to an incompressible pier (Aids = )- The effect of pier length to diameter (L/D) ratio, variation of Poissons ratio, belled base option, and pier stiffness were considered for settlement behavior. The analytical method was compared to the results obtained from a full-scale concrete pier load test in London clay (Whitaker and Cooke, 1966) with an average value of L/D of 15, obtaining good agreement. It was concluded that with increasing compressibility of the pier the shear stress will increase close to the ground surface and reduce near the base of the pier. Hence, the reduction in pier stiffness will increase the settlement at the top of the pier while reducing the settlement at the base of the pier. Ellison et al. (1971) Presented a two-dimensional finite element analysis of bored piles embedded in stiff clay emphasizing on the load-deformation mechanism [6]. Five instrumented load tests on bored piles in London Clay (Whitaker and Cooke, 1966) were used for calibration of the model and comparison of the results. The pile dimensions varied from 9.3 to 15.2 meters in length, and 0.64 to 0.94 meters in diameter. The soil modeling is considered in two parts, a linear and a nonlinear portion. Special attention is placed on the adhesion resistance between pile and soil, and on the elastic compression of the pile. It was found that the maximum adhesion at any location along the interface is dependant on the soil shear strength near that area. Tension 8 cracks developed in the soil near the edge of the base of the pile. Good agreement was obtained between the load-settlement curves of the finite element results and those of the field test. ONeill and Reese (1972) Evaluated the behavior of four full-scale axially loaded drilled shafts in the Beaumont Clay formation (Houston, Texas) [7]. Load transfer mechanisms of the instrumented drilled shafts embedded in stiff clay were investigated. Soil parameters were established for side shear and end bearing. Field explorations revealed six different soil layers to a depth of 18 meters. The Texas Quick Load Test Method was used creating an undrained loading scenario for the saturated clays. Shear strengths were obtained from unconsolidated-undrained (UU) triaxial compression tests. Moisture migration from the concrete into the soil was examined to determine side shear strength resistance. Undrained direct shear tests were performed on in-situ soil samples and on mortar cast against in-situ soil specimens obtained near the pile-soil interface. The adhesion coefficient (a) from each test was calculated as the ratio of maximum shearing resistance of the mortar-soil sample to the undrained shear strength of the in-situ soil samples. Plasticity index seemed to influence the value of a along the soil layers. Compared to Tomlinsons (1969) aavg values for driven piles in clay, the three drilled shafts constructed in dry resulted in slightly higher a values, where as the drilled shafts constructed using slurry resulted in slightly lower values. For all four tests at small displacements, the side resistance governed over base resistance; however, this effect was reduced after the peak side resistance was reached with additional displacement. The peak side resistance was reached for all drilled shafts at displacements between 5.0 to 10.0 millimeters and the residual side resistance was half of the peak. The use of drilling slurry was found to reduce side shear stress. Post-load inspection of the drilled shafts encountered increased moisture content near the base; this effect was considered to account for some of the reduction in load transfer near the base. It was concluded that base failure was reached at settlements of 3 to 6 percent of the base diameter and that a value of 9 for the bearing capacity factor Nc seemed reasonable when cohesion is obtained from UU triaxial tests. Inspection showed shear planes at about 3.2 millimeters from the soil-concrete interface, indicating side shear failure along the soil instead of the interface. Due to seasonal moisture variation, the shear resistance of the top 1.5 meters of clay soil was omitted. 9 Kulhawy and Jackson (1989) The undrained side resistance of drilled shafts was evaluated based on 106 axial field load tests (41 in compression and 65 in uplift) in cohesive soils; all of which were conducted on straight-sided drilled shafts [8], The total stress or alpha method (a), and the effective stress or beta method (/?) were used to evaluate the undrained side resistance. Since the alpha method was originally developed for driven piles in clay (Tomlinson, 1957), a new correlation of this method is presented specifically for drilled shafts. When local load test are available for calibration purposes, the total stress method can be used with simplicity. The effective stress method requires more input parameters, but it is more fundamentally rational. Also, the interrelationship of both methods was examined resulting in equations containing more readily accessible parameters. The design criteria for both methods will be explained in the next chapter. Originally the adhesion coefficient (a) was correlated directly to the undrained shear strength (cu), subsequent work suggested a correlation with the ratio of undrained shear strength to the effective overburden stress (cr'v). The best correlation obtained from the data base was related to the ratio of the atmospheric pressure (pa) to the undrained shear strength. The new total stress method correlation should produce slightly conservative results. Reese and ONeill (1989) A new design method for axially loaded drilled shafts is presented based on the analysis of 41 load tests in overconsolidated cohesive and cohesionless soil [9]. The design equations are limited to the range of conditions within the data base; i.e. diameters ranging from 0.52 to 1.20 meters, lengths from 4.7 to 30.5 meters, and other soil conditions. A design procedure for drilled shafts in rock is also presented. The method allows for a non-homogeneous soil profile, which is divided into various individual homogeneous layers of cohesive soil, cohesionless soil, or rock. The load- settlement characteristics are also presented assuming an incompressible drilled shaft. The method requires subsurface characterization; i.e. undrained triaxial test of cohesive soil, standard penetration test (SPT) for cohesionless soil, and recovery of rock cores. For cohesive soils the top 1.5 meters is omitted from the calculation of shaft resistance (a 0) due to seasonal moisture change. This consideration tends to make the adhesion coefficient approach a constant value (a = 0.55) which does not vary as a function of undrained shear strength. The constant value of a with depth may also 10 be due in part to the disturbance of the clay at the future shaft-soil interface from the mechanical excavation tool. In cohesionless soils, regardless of the in-situ conditions, the construction process tends to cause the interface friction and unit weight of the soil at the shaft-soil interface to converge to a near constant value. Therefore, the shaft resistance for cohesionless soils is affected mainly by the lateral effective stress between the soil and the drilled shaft. Results from the design method (calculated) fall within 25 percent of the measured ultimate capacity values for cohesive soils; mixed subsurface profiles would be slightly more conservative, while for cohesionless soils very conservative. The method estimates accurate to conservative values of the capacity and load-settlement characteristics of drilled shafts. Turner et al. (1993) This paper presents the results of 13 axial field load tests on drilled shafts in Upper Cretaceous shales [10]. Three of these tests were performed in the Denver Blue Formation, which is the most commonly geologic unit encountered in the Denver metropolitan area. The Denver Blue Formation consists mostly of weakly cemented claystone with some siltstone and sandstone layers. The measured side resistance of the drilled shafts was correlated to the compressive strength of the supporting rock. The measured load results were compared to published methods that predict the side resistance of drilled shafts in weak rock. A comparison of the measured side resistance to Denvers local practice was also evaluated. Denver and its vicinity have based the capacity of drilled shafts on the standard penetration test (SPT) number of blows (N-value) since the 1950s; where the end bearing capacity is taken as N/2 in kips/ft2, and the side resistance as N/20 or 10 percent of the end bearing. This relationship is used for drilled shafts supporting an axial load less than 4.45 MN (mega Newton). To date, no significant failures have occurred due to the use of this local practice. The ultimate side resistance of drilled shafts in Cretaceous shales of the region with compressive strengths less than 0.6 MPa (mega Pascal) should be evaluated using Kulhawys 1989 a method; for strengths greater than 0.6 MPa Horvaths 1982 method should be used. Hassan and ONeill (1997) Investigated the side load-transfer mechanisms of axially loaded drilled shafts socketed into cohesive intermediate geomaterials (IGM) [11]. Two-dimensional axisymmetric elastic-plastic finite element analysis was used. IGMs are considered materials between very stiff soil and very soft rock, a gray zone between soil and rock. Emphasis is made on the interface simulation of the socket, where a sinusoidal interface roughness similar to that observed in the field was modeled. Two types of sockets were modeled, rough and smooth interfaces. The cohesive IGMs were classified as those geomaterials with unconfmed compressive strengths (qu) in the range of 0.5 to 5.0 MPa (mega pascal). Drucker- Prager elastic-plastic parameters were used to model the cohesive IGM behavior. The adhesive bond between concrete and argillaceous IGM is considered zero for this study (nonporous IGM), given that interface shear tests performed by Hassan (1994) revealed that no cement paste penetrated into the clay shale. Research performed on Eagle Ford clay shale, which is considered a typical cohesive IGM, was used as a reference for this parametric study. It was found that within the elastic portion of the load-settlement curve the unit side resistance (f) increases with increasingly normal stress (crn). Also, the ultimate unit side resistance (/max) approaches the value of the shear strength of the cohesive IGM; therefore,^/max can be taken as qJ2 for rough sockets. For smooth sockets/max is described in terms of the adhesion coefficient (a). For side load-transfer in rough sockets asperities failed due to shearing beneath its bases followed by minor sliding and consequently gap formation below the asperities. Smearing of the socket, disintegration of the wall socket creating a soil-like material, may occur in some cohesive IGMs reducing the side load transfer significantly and therefore should be treated as a smooth socket in the design process. 2.3 Deep Foundations under Lateral Load McClelland and Focht (1956) This research focused on estimating the soil modulus (Es) based on results from full- scale driven pile lateral load tests and consolidated-undrained (CU) triaxial tests on undisturbed clay samples [12]. Correlations were based on soil reaction pile deflection (p-y) curves from the pile tests and stress strain (a-s) curves from laboratory tests. The lateral load test was conducted in 1952 on a 61 centimeter (24 in.) diameter pipe pile driven 22.86 meters (75 ft) below ground line, embedded in normally consolidated marine clay located off the coast of Louisiana. The difference equation method was employed to compute laterally loaded pile deflections, bending moments, shear forces, and soil reactions. 12 Soil shear strengths were also determined from unconfined compression (qa), remolded unconfined compression, and field vane shear tests. However, the consolidated-undrained (CU) triaxial test exhibited stress-strain characteristics similar to those obtained from the pile load-deflection field test. The beam theory equation was modified to define the soil modulus as the ratio of the soil reaction to the pile deflection at the same point (depth). The soil modulus varied widely with depth and pile deflection; however, for a single applied load the soil modulus increased almost linearly with depth (22 strain gages installed). Matlock and Reese (1960) Proposed computation methods and equations for solving non-linear load- deformation characteristics of the soil for laterally loaded piles, for elastic and rigid piles supported in an elastic medium [13]. Their approach is a special case of a beam on elastic foundation, accounting for boundary conditions and the non-linear properties of in-situ soils. Several iterations of the elastic theory were performed until a satisfactory soil-structure response was obtained. The soil modulus along the depth of the pile was adjusted independently for each consecutive trial until adequate compatibility was reached among the predicted behavior of the soil and the load-deflection of the pile. The soil modulus is introduced as a function of both depth and a constant of soil modulus reaction (ks), and can also be obtained from p-y curves by the slope of a secant line drawn from the origin to any point along the curve. Two methods were used to calculate the soil modulus, power and polynomial, where the linear form is considered a special case of the previous two. A series of derivative equations were used in order to obtain, as a function of depth, values of pile slope, moment, shear, and soil reaction. Davisson and Gill (1963) Studied the results of a laterally loaded pile in a two-layer soil profile [14]. Subgrade reaction theory was employed to analyze the soil modulus variation with depth and/or with pile deflection. The first concept will create a fourth order linear homogeneous differential equation, while the latter will produce a nonlinear differential equation. The relative thickness and modulus of the soil layers were varied and analyzed for a complete range of values. One of the problem statements addresses the need of an analytical method to account for a subgrade soil modulus that varies together with pile deflection and soil depth. Suggesting that this issue may be solved by iteration of elastic methods with adjustment of the secant modulus of the pile load-deformation curve until field 13 compatibility is obtained. It was shown that the surface layer has great influence on pile deflection. The seasonal moisture may reduce or increase the soil stiffness of the upper layer; therefore, the ultimate resistance may vary with the season. Broms (1964a and 1964b) These journal articles recommended design methods to calculate the ultimate lateral resistance, lateral deflections, and maximum bending moments of piles under working loads. These methods were evaluated utilizing the theory of subgrade reaction. The 1964a article [15] refers to piles embedded in saturated cohesive soils, while the 1964b [16] deals with cohesionless soils. Possible failure mechanisms for both free-headed and restrained (fixed-headed) piles under lateral loads are evaluated. For free-headed piles, failure occurs when the applied lateral load in the pile creates a maximum bending moment that exceeds the yielding moment of the pile section creating a plastic hinge, typical of long piles; and when the lateral earth pressure caused by the pile exceeds the lateral resistance of the surrounding soil and the pile moves as a rigid unit through the soil, typical of short piles. For restrained piles, failure may occur under three circumstances. First case is when two plastic hinges form along the length of the pile due to maximum positive and negative bending moments in the pile exceeding the yield moment of the pile section, typical of long piles. Second, when one plastic hinge is formed and subsequently the lateral earth pressure caused by the applied load to the pile exceeds the lateral resistance of the surrounding soil and the pile rotates around a point below ground level, typical of intermediate length piles. Third, when the lateral earth pressure caused by the pile exceeds the lateral resistance of the surrounding soil and the pile rotates as a rigid unit, typical of short piles. The soil and pile are assumed to behave elastically under working loads, which are considered in the range of one-half to one-third the ultimate lateral soil resistance. Methods at working loads are used to compute lateral deflections, soil reactions, and the distribution of bending moments and shear forces based on the theory of subgrade reaction. The coefficient of subgrade reaction (kb) is assumed constant with depth for cohesive soils and linearly increasing with depth for cohesionless soils. Different equations were used to obtain the coefficient of subgrade reaction for short and long piles. Results from the suggested methods were compared with measured field test data and were considered adequate for cohesive soils; however, for cohesionless soils, the measured values exceeded the calculated by approximately 50 percent. Ultimate lateral resistance graphs and charts are presented for the different soil types, pile head boundary conditions, and failure modes. 14 Spillers and Stoll (1964) Analyzed the soil-pile response of a laterally loaded pile by simplified constitutive equations [17]. The soil mass was considered to be initially a continuous elastic medium and subsequently added more realistic properties to consider it as an elastic- plastic half space (iterative solution), while the pile remained elastic. Some of the limitations of the Winkler model and the subgrade reaction theory were mentioned. The elastic soil concept presents high stresses near the surface similar to Winklers uniform spring constant, which is not practical; hence, plastic yielding is added to improve the concept. Similar nonlinear curve results were observed with those obtained from full-scale field tests, where progressive yielding with depth is obtained. Broms (1965) Presented a summary of his previous two papers of 1964 for the design of laterally loaded piles in cohesive and cohesionless soils [18]. Over-load and under-strength factors were introduced. The ultimate lateral soil reaction was assumed equal to nine times the undrained shear strength for cohesive soils, while considered three times the passive Rankine earth pressure for cohesionless soils. For short piles, the ultimate lateral resistance was found to be controlled by depth of penetration, while independent of the pile section yield moment and vice versa for long piles. Poulos (1971) Evaluated the performance of piles subjected to lateral load and bending moment, assuming the surrounding soil to be elastically homogeneous, isotropic, and semi- infinite [19]. Soil modulus and Poissons ratio were assumed constant with depth. This elastic theoretical assumption was considered particularly satisfactory for cohesive soils when compared to observed pile behavior. Results from several cases from this method are compared to those obtained from the subgrade reaction theory and significant differences were observed. The basis of this method is considered similar to that by Spillers and Stoll (1964) with some enhanced assumptions. Two boundary conditions of the pile head were considered, free and restrained, while the pile was assumed as a thin rectangular strip of constant flexibility. It was observed that the soil modulus is more accurate if obtained from a full-scale pile load test. The most important variables affecting the performance of the pile were said to be the length-to-diameter (L/D) ratio and the pile flexibility factor. Pile displacement, moment, and rotation due to local yielding of the surrounding soil were evaluated. Furthermore, the accuracy of the method increases with more number of element divisions (segments) along the pile. 15 Yegian and Wright (1973) Presented a two dimensional nonlinear finite element model to develop a soil resistance-pile displacement relationship (p-y curves) for laterally loaded single and group piles in soft saturated clays [20], The stress-strain properties of the saturated clay were defined by a nonlinear hyperbolic expression up to the point of full mobilization of the shear strength and perfectly plastic beyond this point. Emphasis is made on the soil-pile interaction, where the maximum shear resistance (soil-pile adhesion) was considered directly proportional to the undrained shear strength of the clay. The p-y relationships obtained from the finite element model were compared to that of Matlocks (1970) procedure with some minor discrepancies found between the two methods. Reese and Welch (1975) Proposed a method for soil-structure interaction of laterally loaded deep foundations in stiff clays subjected to static or cyclic loading [21]. Experimental p-y curves were obtained by testing a laterally loaded instrumented drilled shaft with a diameter of 76 centimeters (30 in.) and a total length of 13.4 meters (44 ft) located in Houston, Texas. Theoretically, a difference equation method was used to satisfy the conditions of equilibrium and compatibility of the nonlinear p-y response. Values of bending moment, deflection, and rotation were measured along the length of the drilled shaft for different number of applied loads. Stress-strain conditions of undisturbed soil samples were obtained by unconsolidated-undrained (UU) triaxial compression tests, where the applied confining pressure replicated the in-situ overburden pressure. Results included deflection, slope, moment, shear, and soil reaction, all in function of depth. Randolph (1981) Reported the results of a parametric study of laterally loaded single and group flexible piles [22]. Simple and practical algebraic expressions were utilized to best-fit the results obtained from finite element analyses. Equations of maximum bending moment along the pile, as well as deflection and rotation at ground level were illustrated. The soil profile was assumed an elastic continuum and the soil modulus was represented as either homogeneous or varying linearly with depth. The critical length of a pile was evaluated and solutions for piles beyond this length are based on Hetenyis (1946) approach, where the pile is considered to behave infinitely long. Single pile results are extended for group piles using interaction 16 factors between piles. This method was compared to data obtained from two lateral load field tests, McClelland and Focht (1956) one pile, and Gill and Demars (1970) four single piles. The result comparison was deemed rather well for the various soil profiles; with the exception of a 20 percent under estimation of the maximum bending moment for the 1956 load test and a maximum 20 percent discrepancy of the pile stiffness value for the 1970 test. Davies and Budhu (1986) Analyzed the non-linear response of single piles under lateral load embedded in homogeneous heavily overconsolidated clay [23], Under small strain the soil is considered linear elastic and plastic past the yield level; hence, the stress-strain characteristics of the soil are modeled as elastic-perfectly plastic. The major soil parameters for this model are the undrained shear strength and the modulus of elasticity. The bearing capacity factor (Nc) is used to estimate the bearing stress in the front face of the pile, the adhesion coefficient is considered for estimating shear stress along the sides of the pile, while tension stress in the back face of the pile is also taken into account. Mindlins (1936) elasticity equations are used as the basis to solve soil deformation. The pile length is divided into segments and Bemoulli-Euler beam theory is utilized to obtain pile displacements. The capabilities and limitations of the p-y method were evaluated. The equations presented in this paper were utilized in an illustrative example and for result comparison on a case history (Reese et al., 1975), where good agreement was obtained. This method was considered useful for common practice. Wang and Reese (1993) This document presented a soil-structure computer program (COM624P) based on iterative differential equations to solve the behavior of piles under lateral load, including the mutual dependency of pile deflection (y) and soil reaction {p) [24], The nonlinear response of the soil is dependent on both pile deflection and depth of soil, where the pile is assumed to behave as a beam-column. The soil reaction is obtained for a considered depth by integrating the increased unit stresses caused by the pile deflection on that section depth; hence, obtaining an unbalance soil force which acts opposite to the deflection. Finite difference techniques are used to solve the differential equations for selected points along the pile. Four different types of lateral loading are considered: short-term static (field load test), cyclic (e.g. wind, waves), sustained static (time-dependent), and dynamic (vibrations). Selected boundary conditions at the top of the pile satisfy the conditions 17 of equilibrium and compatibility. The influence of the pile depth on ground surface deflection is analyzed under critical penetration. The stratum of soil from the ground surface to within a few pile diameters in depth is considered of great importance since it provides the major lateral support for the pile. The soil response is modeled as a system of discrete springs along the depth of the pile (points). When computing the ultimate moment and flexural rigidity of the pile it is considered to behave nonlinear with respect to bending moment. Soil properties, pile geometry, and type of loading are considered to have the most effect on a p-y curve. The method of installation is not taken into consideration for adjustment of the soil properties since beyond the pile wall an area of soil, several times the pile diameter, is stressed under lateral loading. Recommendations for computing p-y curves are suggested for clays (soft and stiff) and sands (loose and dense) above and below the water table, including vuggy limestone, layered soil, and sloping ground. Field load tests were used as a reference for computing p-y curves; however, field and laboratory soil tests are recommended. Computer results along the length of a pile include deflection, rotation, bending moment, shear, and soil resistance. It is also recommended that the solutions be verified for accuracy for any computer output. Ashour et al. (1998) Considered the use of the strain wedge model to predict the response of a pile under lateral load in a layered soil profile [25], The pile is assumed a flexible one- dimensional beam on elastic foundation, while three-dimensional nonlinear soil-pile interaction parameters are taken into account. Soil behavior is obtained by triaxial test stress-strain characteristics of undisturbed samples, both sands and clays are considered. The soil response in front of the pile is represented by a passive three- dimensional wedge which is eventually mobilized. Initial research of the strain wedge model was presented by Norris in 1986. The soil profile is divided into sublayers of constant thickness, where each sublayer can have its own soil properties. The horizontal subgrade reaction modulus (kh) is necessary for every layer during the pile loading in order to reflect proper nonlinear soil-pile interaction. Horizontal strain (s) formed in the passive wedge is estimated from triaxial test stress-strain relationships, where the major stress change is in the direction of the pile movement and is considered similar to the triaxial deviatoric stress. To solve this method, it requires basic soil parameters which can be easily obtained from standard subsurface investigations and correlations techniques. It is concluded that this model is based on accepted and known soil mechanics principles. 18 2.4 Deep Foundations under Combined Loads Trochanis et al. (1991) Investigated the three-dimensional soil-pile interaction under static and cyclic loading using finite element analysis (FEA), for both single and group piles [26], The nonlinear soil behavior was studied under axial, lateral, and combined axial-lateral pile loads. The influence of slippage and separation at the soil-pile interface are regarded as key factors in the piles overall response under axial and lateral loads, respectively. The pile was considered as an elastic material, while the soil (clay or sand) was modeled as a Drucker-Prager elastic-plastic continuum. An axial field load test performed on a square 30 centimeter concrete pile in Mexico Citys soft clay was used for comparison and validation of the finite element model. Elastic theory results from Poulos and Davis (1980) were also used as a comparison for purely elastic modeling of the FEA. Within the parametric study only single piles were investigated under single and combined loads, while pile groups (two piles) were subjected to either type of load. Pile-soil interface was modeled under two scenarios, allowing slippage and restricting it (bonded). The effects of pile width and slenderness ratio (length to diameter) were also studied for lateral load response. Compared to the field test data, the numerical results of elastic soil models tend to overestimate the realistic soil-pile interaction; hence, the importance of considering nonlinear elastic-plastic soil models. It is observed that the axial load capacity may increase under combined loading due to the increased shear resistance in the leading face of the pile. However, the lateral load-deflection curve seems unchanged under combined loading compared to that of lateral load alone. Phillips and Lehane (2004) Presented the performance of a full-scale driven concrete pile subjected to combined loads, axial and lateral, and of a second pile (reaction pile) under lateral load only [27]. Some interpretation of the field data obtained from the combined load test was necessary due to a movement restraint in the horizontal direction caused by the axial loading mechanism. The 35 centimeter square and 10 meter long reinforced concrete piles were embedded mostly in estuarine clayey-silt while the tips rested on a medium dense sand layer. The axial load test was performed 24 hours prior to conducting the combined load test. The maximum axial load of 168 kN (kilo Newton) was maintained until the end of the combined load test which had a maximum applied lateral load of about 60 kN. A second loading scenario was applied to the same piles, where the axial load was 19 reduced to 133 kN and the maximum lateral load applied was about 90 kN. The horizontal movement of the combined load pile (0.5 cm) was much less than that of the lateral load (single load) pile (2.5 cm) for the first loading. A similar trend was observed under the second loading scenario up until the maximum load, where the displacements are identical. The axial loading mechanism provided a degree of restraint which reduced the lateral load applied to the combined load pile. The instrumentation employed allowed to quantify the restraint and to properly interpret the results obtained from the field tests. 20 3. DESIGN PRINCIPLES OF DRILLED SHAFTS 3.1 Introduction This chapter is concerned with the current state of practice for the design of single drilled shafts (groups will not be considered) under static axial or lateral load. As mentioned in the previous chapter, drilled shafts are used to support a variety of engineering structures. The loads applied to the drilled shafts due to these structures are generally axial, acting in the direction of gravity; however, uplift (axial), horizontal (lateral), bending moment, and torsion loads may also be present. A structurally sound drilled shaft will function properly only if the supporting soil is adequate for the loading conditions. An overstressed soil can result in excessive displacement of the soil which can cause damage to the structure being supported. Therefore, when designing drilled shafts, it is important to analyze them as a combined soil-structure system. In addition to the effects of dead and live loads, drilled shafts should be designed to withstand the worst conditions expected throughout the lifetime of the structure. Drilled shafts can be designed from full-scale field load test results, empirical methods, analytical techniques, and numerical methods. It is recommended to calibrate one design method against another. Field tests provide load capacity and displacement data, which are reliable for similar subsurface conditions within the site. Empirical methods relate new design calculations with those of existing field load- displacement databanks for similar soil conditions. Analytical techniques are based on soil mechanics principles and require information of the subsurface condition, soil properties, and the drilled shaft. Numerical methods have an advantage over empirical and analytical methods by taking into account the continuity of the soil mass. Two of the most commonly used analytical techniques are the allowable stress method and the limit state method [28], The allowable stress method ensures that the drilled shaft load is transmitted to the supporting stratum without causing shear failure to the soil. This is achieved by applying safety factors to the maximum load that would cause failure in the bearing soil. The limit state method focuses on ultimate loads, which result in excessive displacement, causing collapse or disruption of the functionality of the structure. 21 Structurally, drilled shafts are considered long and slender column-type elements that may buckle under axial load. However, drilled shafts have enough lateral support along their length from the embedding soil, so typically there is no concern about buckling. The following analytical methods will assume that the drilled shafts have an adequate structural design to carry the design axial and lateral loads. 3.2 Drilled Shafts under Axial Load The total ultimate axial downward resistance (Axjai) of a drilled shaft is based mainly on the soil properties, dimensions of the drilled shaft, location of the water table, and construction method. The total axial load that can be supported by the drilled shaft is provided by the sum of the shaft wall (side friction or adhesion) resistance (Ahaft) and the base (end bearing) resistance (Aase), as shown in Figure 3.1 and described below: (Axial C^shaft (Aase (3.1) Ahaft =/'As = f-p-L = f (71 A) L (3.2) A>ase ~ tfb Ab A' A> 4) (3.3) Where, /= average unit area skin friction or adhesion between soil and drilled shaft surface, or shearing strength of the soil zone immediately adjacent to the drilled shaft surface As = drilled shaft surface in contact with soil along the embedded shaft length p = perimeter of the drilled shaft L = embedded length of the drilled shaft (below ground surface), L > 3 A A = diameter of the drilled shaft (straight segment) Ab = bearing area of the base of the drilled shaft A = diameter of the base of the drilled shaft, A = A for straight drilled shafts, A < 3-A 22 axial * z'A/7 t L r Figure 3.1 Axial load resistance of a drilled shaft If the properties or conditions of the soil change along the depth of the drilled shaft (length of embedment), the shaft resistance (Â£9Shaft) should be calculated by dividing the shaft length into layers (segments) [9], as shown in Figure 3.2 and expressed by: C?shaft=X f'PAL\ (3.4) i=i Where, f = unit side shearing resistance in layer i ALt = length of layer i For each layer, average properties should be used acting at the middle of the layer. 23 Â£?axial I Figure 3.2 Axial resistance of a drilled shaft by layers (from Das, 2005) The end bearing resistance ( failure of the supporting soil immediately below and adjacent to the base of the drilled shaft. The ultimate bearing capacity ( resistance (qu\t ~ q\>), is expressed by Terzaghis (1943) general equation for circular shallow foundations: quh=l.3-c-Nc + y'z-L-Nq + 0.3 Dh y\ Ny (3.5) Where, c = average cohesion of the soil within two shaft diameter below the base of the drilled shaft L = depth of the base of the drilled shaft below ground surface Db = diameter of the base of the drilled shaft y'z = effective unit weight of soil above the base of the drilled shaft y 'b = effective unit weight of soil below the base of the drilled shaft 24 Nc, Ny, Aq = soil bearing capacity factors that depend on the value of the angle of internal friction, , as shown in Figure 3.3 Angle ol internal friction, 0 Nc 0 5.14 5 6.5 10 8.3 15 140 20 14.8 25 20.7 30 30.1 32 35.5 34 42.2 36 50.6 38 61.4 40 75.3 42 93.7 44 118.4 46 152.1 48 199.3 50 266.9 Nq Ny 1.0 0.0 1.6 0.5 2.5 1.2 3.9 2.6 64 5.4 10.7 10.8 18.4 22.4 23.2 30.2 29.4 41.1 37.7 56.3 48.9 78.0 64.2 109.4 85.4 155.6 115.3 224.6 158.5 330.4 222.3 496.0 319.1 762.9 Figure 3.3 Bearing capacity factors (from McCarthy, 2002) The first term of the equation represents the contribution of the shear strength of the soil, the second term represents the effect of the surcharge pressure, and the third term represents the bearing resistance resulting from the weight of the soil. The weight of the soiled removed (drilled out) is usually assumed to be equal to the weight of the 25 drilled shaft (concrete and reinforcement). The following expressions are used to determine the bearing capacity factors [29]: For
For 0, Ac = (Aq 1) co\(j) (3.6) |