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Using prestressed concrete wall foundations in residential construction to mitigate structural damage induced by mine subsidence

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Title:
Using prestressed concrete wall foundations in residential construction to mitigate structural damage induced by mine subsidence a finite element evaluation
Creator:
Dyni, Robert C
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
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English
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ix, 72 leaves : illustrations ; 29 cm

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Prestressed concrete construction ( lcsh )
Prestressed concrete construction ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Bibliography:
Includes bibliographical references (leaf 72).
Thesis:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Department of Civil Engineering
Statement of Responsibility:
Robert C. Dyni.

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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.
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22927272 ( OCLC )
ocm22927272
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LD1190.E53 1990m .D95 ( lcc )

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USING PRESTRESSED CONCRETE WALL FOUNDATIONS IN RESIDENTIAL CONSTRUCTION TO MITIGATE STRUCTURAL DAMAGE INDUCED BY MINE SUBSIDENCE A FINITE ELEMENT EVALUATION by Robert c. Dyni B.A., Monmouth College, 1983 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Master of Science Department of Civil Engineering 1990

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This thesis for the Master of Science degree by Robert C. Dyni has been approved for the College of Engineering and Applied Science by 50hn R. Mays

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Dyni, Robert c. (M.S., Civil Engineering) Using Prestressed Concrete Wall Foundations in Residential Construction to Mitigate Structural Damage Induced by Mine Subsidence -A Finite Element Evaluation Thesis directed by Associate Professor Judith J. Stalnaker Subsidence induced by underground mining poses a serious threat to surface structures. The horizontal and vertical ground movements associated with mine subsidence are often responsible for the damage or complete destruction of structures in to active or abandoned underground mining operations. In particular, residential structures, often located tn subsidence-prone areas, are frequently affected by the ground movements induced by the collapse of underground mine workings. In an effort to the damaging consequences of mine subsidence on residential structures, this thesis evaluates the effectiveness of using prestressed concrete wall foundations in controlling the damagecausing bending stresses induced by a subsidence event. A series of prestressed and non-prestressed two-dimensional finite element foundation wall models was constructed and subjected to ground movements typical of a subsidence event. The majority of the nonprestressed concrete wall models subjected to these ground movements experienced bending stresses that exceeded the ultimate strength of the wall material. The prestressed models were then subjected to the same ground movements; the resulting bending stresses in the prestressed models were all below the ultimate

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strength of the wall material. Based on the results of this f1n1te element analysis, prestressing is a viable mitigative foundation design technique for controlling damaging subsidence-induced bending stresses. The form and content of this abstract are approved. I recommend its publication. Signed ___ iv

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CONTENTS Figures vii Tables.................................................... ix CHAPTER 1. 2. 3. 4. INTRODUCTION 1 Problem................................................. 1 Purpose and Scope of Thesis............................. 3 SUBSIDENCE 5 Defined................................................. 5 Subsidence Development............................... 6 Room-and-Pillar Mining........................... 7 Ltingwall Mining 8 Common Subsidence Parameters......................... 12 Status of Subsidence Research........................... 15 Subsidence Characterization.......................... 16 Subsidence Prediction 17 Subsidence Mitigation................................ 18 Typical Values -..... 19 Longwall Subsidence.................................. 20 Room-and-Pillar Subsidence........................... 21 STRUCTURAL FOUNDATIONS SUBJECTED TO SUBSIDENCE 23 Surface Movements....................................... 23 Foundation Response to Ground Movements PRESTRESSED CONCRETE FOUNDATIONS 24 28 Overview of Prestressed Concrete........................ 28 Potential Advantages................................. 29

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5. NUMERICAL FOUNDATION ANALYSIS 34 Analysis Overview....................................... 34 Mode 1 Type. 35 Model Development....................................... 35 Geometry. . . . . . . . . . . . 35 Material Properties.................................. 41 Loads................................................ 42 Mode Shapes.......................................... 44 Final Model Configurations........................... 47 Model Run Procedure..................................... 47 6. RESULTS AND CONCLUSIONS 53 Results . 53 Non-Prestressed Wall Stresses........................ 55 30-ft Models..................................... 58 50-ft Models..................................... 59 Prestressed Wall Stresses 60 30-ft Models..................................... 60 50-ft.Models..................................... 65 Conclusions............................................. 70 REFERENCES 72 vi

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FIGURES Figure 2.1. Typical room-and-pillar mine workings.................... 7 2.2. Subsidence development resulting from roof failure in room-and-pillar mine workings............ 2.3. Subsidence development resulting from pillar failure in room-and-pillar mine workings......................... 9 2.4. Typical longwall mine workings........................... 10 2.5. Subsidence development over longwall mine workings....... 11 2.6. Typical subsidence trough and associated parameters...... 13 3.1. Structural response to typical subsidence wave........... 26 4.1. A-series mode shapes and model approximations 30 4.2. B-series mode shapes and model.approximations............ 30 4.3. C-series mode shape and model approximation.............. 31 4.4. Effect of prestressing:. (a) non-prestressed and (b) prestressed.................. 32 5.1. Typical keyed-footing foundation......................... 39 5.2. Two-dimensional finite element model parameters.......... 40 6.1. Maximum bending stress vs. mode shape, model set 2 (30-ft long, 10-ft deep)..................... 61 6.2. Maximum bending stress vs. mode shape, model set 4 (30-ft long, 4-ft deep)...................... 61 6.3. Maximum bending stress vs. mode shape, model set 6 (30-ft long, 8-ft deep)...................... 62 6.4. Maximum bending stress vs. mode shape, model .set 8 (50-ft long, 10-ft deep)..................... 62 6.5. Maximum bending stress vs. mode model set 10 (50-ft long, 4-ft 63 6.6. Maximum bending stress vs. mode shape, model set 12 (50-ft long, 8-ft deep)..................... 63

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6.7. Maximum top bending stresses vs. mode shape, model sets 2, 4, and 6 (30-ft wall length)............... 67 6.8. Maximum bottom bending stresses vs. mode shape, model sets 2, 4, and 6 (30-ft wall length)............... 67 6,9. Maximum top bending stresses vs. mode shape, model sets 8, 10, and 12 (50-ft wall length)............. 68 6.10. Maximum bottom bending stresses vs. mode shape, model sets 8, 10, and 12 (50-ft wall length)............. 68 6.11. Maximum bending stress vs. depth/length ratio............ 69

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TABLES Table 2.1. Typical Longwall Subsidence Geometry..................... 20 2.2. Typical Room-and-Pillar Subsidence Geometry.............. 22 5.1. Finite Element Foundation Wall Model Schedule............ 48 6.1. Maximum Bending Stresses for Non-Prestressed Wall Models 56 ix

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CHAPTER 1 INTRODUCTION Problem An unfortunate consequence of underground mining 1s the occurrence of subsidence. The movement of the ground surface caused by the collapse of underground mines can either damage or completely destroy surface structures. Although research quantifying the behavioral characteristics of subsidence and the response of surface structures to mining-induced subsidence have been conducted, virtually nothing has been done to design viable structural systems capable of minimizing or completely negating the damaging effects of subsidence. Structures overlying active or abandoned mining operations are subject to the damaging consequences of mine subsidence. The problems of structural damage caused by subsidence are rapidly growing as land-use interests increasingly conflict with underground mining operations. The ground surface overlying both active and abandoned mining operations is considered useless for development due to the highly unstable nature of the ground surface during a subsidence event. In the case of active mining operations, the behavior of subsidence is fairly predictable, and overlying surface development can be fitted around a subsidence prone area with a fair degree of

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accuracy. Also, mine operators can establish m1ne layout to avoid mining under existing surface structures. Obviously, residential or commercial property development in locations of known subsidence is seriously limited. Yet as mining continues to develop 1n populated areas, the problem of subsidence and overlying surface structures 1s an important concern to m1ne planners, surface developers and regulatory officials. In the case of .abandoned mines, however, poor or non-ex1stent mine maps documenting the extent of mining force surface developers to provide mass1ve "cushions" of undeveloped land around 111-def1ned subsidence prone areas to insure that a subsidence event will not affect any overlying surface structures. Unfortunately, this method of surface development is not very reliable; there have been many instances of structures built over abandoned mine workings that have been either damaged or destroyed simply because the presence of the workings was not identified. To compl1cate the problem, many structures built over abandoned mining operat1ons are not damaged or destroyed, simply because the underlying mine workings have not collapsed and subsidence has not occurred. This is a particularly dangerous situation, because it provides surface developers with a false sense of security. In order to minimize or eliminate the damaging impacts of active or abandoned mine subsidence on overlying surface structures, the methods used in the past of providing massive barriers of unmined material beneath surface structures (in the case of active mining 2

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operations) or providing massive areas of undeveloped ground surface around a subsidence-prone area {in the case of abandoned mining operations) are not in the best interests of either the surface developers or the mine operators. The first option causes the permanent loss of large areas of mineable resources, which is not in the best economic or strategic interests of the energy and mineral needs of this country. The second option results in large surface areas remaining unproductive, which significantly reduces land values and land use possibilities for large areas. Purpose and Scope of Thesis In light of the ineffectiveness of the above two mitigative options presently used by. the mining industry to minimize the hazards of underground mine subsidence to overlying structures, this thesis proposes investigating a third option: to design structural systems capable of withstanding the ground-surface deformations caused by active or abandoned mine subsidence. Specifically, it is the intent of this thesis to evaluate the effectiveness of using prestressed wall foundations to successfully mitigate the damaging effects of ground movements associated with underground mine subsidence. For the purposes of this thesis, only typically sized, residential-type poured wall concrete foundations are evaluated, since a major portion of surface development in this country is 3

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used for res1dential purposes. and a widely used foundation design is the poured concrete wall. Using a commercially available finite element method (FEM) structural analysis computer code, models of various wall geometries common to residential-type structures are subjected to a series of ground surface deformations common to a typical subsidence event. Each non-prestressed poured wall geometry is subjected to these deformations; each wall is then prestressed, and subjected to the same deformations. The resulting stresses of the prestressed and non-prestressed walls subjected to the subsidenceinduced deformations are then compared and-evaluated to determine if prestressing actually minimizes or eliminates the subsidenceinduced stresses that can ultimately lead to structural failure. 4

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CHAPTER 2 SUBSIDENCE In order to formulate a mitigative foundation design that will minimize or eliminate the damaging effects of underground mine subsidence, it is important to become familiar with genera 1 subsidence characteristics and behavior. a general understanding of how subsidence develops in response to the collapse of underground mine workings, valid mitigative foundation designs cannot be formulated. The following sections of this chapter are devoted to defining subsidence, outlining the general behavior of subsidence as it develops in response to mine collapse, and providing some general definitions and basic parameters common to most subsidence events. Defined Subsidence, in very general tenms, can be defined as the distortion of the ground surface caused by the collapse of underlying mine workings. There are obviously many factors that influence the behavior of subsidence, including the composition and material properties of the material overlying the mine workings (overburden), mined geometry of the underground excavation, topographic variations, and depth below the ground surface of the mined area. Subsidence behavior is actually quite site-specific,

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but broad conclusions have been drawn towards predicting its general behavior for various mining regions both 1n this country and abroad. Deformation of the ground surface overlying a mining operation occurs when underground openings collapse due to high stress concentrations or high overburden pressures or due to the failure of either man-made or natural underground mine support systems such as roof bolts and trusses or material left unmined to act as structural columns (pillars). When an underground opening collapses, the overlying material either bends or breaks, resulting in a net downward displacement of all overburden layers including the ground surface. Subsidence Development To understand how subsidence occurs, it is important to become familiar with the various aspects of underground mining that induce subsidence. There are only a few different methods of underground mining. The two methods that commonly cause subsidence are the room-and-pillar method, and the longwall method. It is important to note here that subsidence development, no matter what the cause, does not happen instantaneously. Rather, subsidence "grows," in that the development of a subsidence trough takes anywhere from many months (in the case of 1 ongwa 11 subsidence, for example), to just a few hours (in the case of shallow room-and-pillar mine subsiden_ce). The lateral propagation of the subsidence, either in response to active mining, or in 6

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response to the collapse of abandoned workings, is called the subsidence wave. The profile of the subsidence wave is simply the profile of the trough at any given time in the subsidence event. Room-and-Pillar Mining. The room-and-pillar method of underground mining has long been used for extraction of coal, salt, gypsum, and other sedimentary deposits. This method is simple in concept: mining machinery is used to drive entryways into the mineral depo.sit in such a way as to leave large load bearing "pillars" of material behind to provide structural support for the entr1es (fig. 2.1). With th1s method, 1t i_s conmon to lea.ve 50 pet oooOL JOOL OOODODODODDDOOOODDDO OOOODDDODOOODODOOODD OOOODODDDDOODODDDDOO DODD DDDDDDDDODDDD DODO OODOOODDDDODO DODD DDOODOODOOOOO oooo ooooooooooqooo DODO ODDOODDDODDDOO DODO DDDDDDDDDDOOOO DODO DODD[ DODD DODO ooooooooooc ODDDDODDDDC ODDDDDODOOC DODO[ iDOOOC ggQQ 0 200 400 Sc:ale, feet Figure 2.1.-Typical room-and-pillar mine workings. 7

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or more of the material unmined 1n the form of permanent roof support pillars. However, resource recovery can be increased by a method known as 11Pi11ar robbing. This type of mining simply consists of returning to a previously mined room-and-pillar section of a mine, and mining the pillars to smaller dimensions. With room-and-pillar mining, and more so with pillar robbing, subsidence occurs when the roof of the mine collapses as a result of the pillars crushing out under the weight of the overburden and other stresses caused by mining. Interestingly, many of the subsidence problems experienced by many communities along the Front Range of the Rocky Mountain coal region are directly due to old, abandoned room-and-pillar mines whose pillars are simply deteriorating and are no longer able to support the overburden. Subsidence can take anywhere from several hours to several years to fully develop in the case of room-and-pillar mining. The profile of the subsidence trough continually changes.throughout the entire subsidence development process as shown 1n figure 2.2. However, in the case of large room-and-pillar sections, the development of subsidence may propagate in such a fashion as to maintain a constant subsidence profile (fig. 2.3). Longwall Mining. Longwall mining, found virtually only 1n the coal mining industry, is a method whereby virtually 100 pet of the coal 1n a section of a mine can be successfully extracted. The longwall method of mining requires the use of extremely expensive equipment. Basically, development entries are driven to isolate a 8

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.. : .. ,. : .. :_. ._. .' .. ..... . . . . ... : .. : . Figure 2.2. -Subsidence development resulting from roof failure in room-and-pillar mine workings. Subs ide nee trough .... --.. ........._ . .. . _...,. .,.,., --. . ... ----:-:---:_......:.._ ---.. . .. .' . ...; '-'--:..... .. -:--:-. ..,.._ .. . _..;..--;/ . ----. ........... ;-.. ..:... . . ---'-------. ---::-. / . .. :_..... ;./ ---. / __ -;' Pi II or Room Figure 2.3. -Subsidence development resulting from p_illar failure in room-and-pillar mine workings. 9

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block of coal to be mined by the longwall equipment (fig. 2.4). Th1s block of coal typically can be 4,000 to 8,000 ft long, 400 to 1,000 ft w1de, and 6 to 15 ft th1ck. After the development entries are completed, the equipment is moved into place. This equipment consists of a series of hydraulically operated canopies or shields, approximately 6 ft wide, that are designed to hold up the roof and protect the miners and the mining machinery from roof collapse (fig. 2.5). There are typically 100 to 200 shields placed side by side to make up the longwall assembly. or double: 0 200 400 Development entries Scale, feet Figure 2.4. -Typical longwall mine workings. 10

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------:--....... ........... --Subsidence / trough -------:---.---------------------:-----------:----------------:--_:__. ___ _:._ ... ----.:.. .. ---__ ., _______ -----=-.. ____ __ __:_ _______ Longwall shield _-.... .......... ---------2.5. -Subsidence development over longwall m1ne workings. drum shearing machine is used to cut the coal; th1s machine moves back and forth along the working face of the coal block. all the while being protected by the shields. The cut coal falls from the face and moves along a conveyor located along the bottom of the shields. and out to locations for removal from the mine. Subsidence is an expected occurrence with the longwall method of mining. As the longwall face advances through the block of coal. the void left behind the shields eventually collapses. and surface subsidence results. Literally hundreds of acres can be affected by subsidence due to just one longwall panel: a single m1ne can incorporate dozens of longwall panels in the mine plan. so it is 11

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clear that vast amounts of acreage are affected by a single mine. The development of the subsidence trough for longwall mining is fairly predictable. As mining commences, the overlying subsidence trough responds by increasing maximum vertical extent, which alters the shape of the subsidence profile. As mining progresses, the maximum possible subsidence is achieved, and the subsidence trough continues to propagate along the direction of mining without changing its profile (fig. 2.5). Common Subsidence Parameters A typical surface depression caused by the collapse of an underground opening is shown in figure 2.6. This figure illustrates some of the common terms and concepts associated with mine-induced subsidence (1)1 The terms of interest for this study are: Angle of Draw (d) Profile (subsidence) The angle of inclination from the vertical of the line connecting the edge of the mine workings and the edge of the subsidence area A curve depicting a twodimensional vertical slice of a subsidence trough 1Underlined numbers in parentheses refer to items in the list of references at the end of this thesis. 12

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9 max I \ \ \ \ ' / I I I I I Subsidence profile Un-11ined area I m Figure 2.6. Typical subsidence trough and associated parameters. Seam Th1ckness (m) Slope (g) The thickness of the seam extracted The slope of any part of a subsidence trough 13

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Stra1n (e) Subsidence (S) Subsidence Factor (a) Subsidence Development Transition Point (t} The change 1n length per un1t length of the ground surface in a subsidence trough (positive values are tension, negative values are compression) The vertical movement within a subsidence trough The ratio of complete subsidence (S) to seam thickness (m) The manner in which surface subsidence begins, increases and finishes 1n relation to the position of the advancing face of an underground excavation The point of transition between concave and convex curvature of a subsidence profile Trough (subsidence) The surface depression by subsidence It should be emphasized here that all of the above definitions are very much dependent upon site-specific geologic, lithologic, topographic, and mining conditions. However, for the purpose of evaluating foundation response to mine induced subsidence, certain generalities are valid. 14

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Status of Subsidence Research Subsidence due underground mining has long been of great concern to mine operators and land owners because of the resulting damage to the ground surface and overlying structures. As a result, much research has been conducted to characterize the behavior of subsidence so that predictive methods can be developed and used to assess the impacts of future mining on the environment. The earliest record of subsidence research appears to be a .. Belgian study in 1825 of damage to the ground surface mine workings in Liege; the major conclusions drawn from this study were that surface. damage was principally caused by mining operations within a depth range of approximately 300 ft below the surface (,). Throughout the first half of the nineteenth century, many subsidence research studies were conducted in European mining regions, and it was during this time that the first subsidence theories were developed. As a matter of interest, it was not until the late nineteenth century that subsidence was first recognized as a problem in the United States and subject to study Historically, subsidence research has been directed towards several major areas of concern: subsidence characterization, subsidence prediction, and subsidence mitigation. Subsidence research 1s a field of study that has long been conducted by various schools and universities, as well as by Federal and State agencies. Perhaps the recognized leader in subsidence research 1n this country is the Department of the Interior, Bureau of Mines. 15

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In particular, three of the Bureau's research centers, the Pittsburgh Research Center, the Twin Cities Research Center, and the Denver Research Center all have established expertise in subsidence characterization, prediction, and mitigation. An excellent reference containing a bibliography of over 700 research and technical publications dealing with subsidence characterization, prediction, and mitigation is found in Bureau of Mines Information Circular 9007 (!). Subsidence Characterization Many subsidence research efforts have been directed towards characterizing, or simply observing, the behavior of subsidence occurring over specific active and abandoned mine sites. The results of such studies usually contain very site-specific subsidence values for the particular subsidence event. Such values most often include subsidence parameters obtained by_simple surveying methods, such as total .areal extent, subsidence profiles, angle of draw, subsidence factor, and total vertical and horizontal deformation. These studies are fairly useful to mine planners and surface land developers because they provide information on how subsidence behaved for a particular mining configuration in a given mining environment. This information can be used as a very general "rule of thumb" for other mining operations in a very localized area. 16

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Subsidence Pred1ct1on Much less subsidence research has been directed towards actually developing subsidence prediction methodologies than simply characterizing subsidence events. Subsidence prediction is a very difficult field of research, because history has shown that subsidence is indeed a fairly site-specific phenomenon. Some mining regions of this and other countries, however, have such lithologic, and topographic properties that many of the complex variables that influence subsidence can be either eliminated or greatly simplified. For example, the Appalachian coal region of the United States has been extensively studied, and several predictive methodologies have been developed by various Federal and State agencies that seem to provide acceptable predictive capabilities. Unfortunately, not all mtning regions lend themselves to valid prediction development. Numerous case studies of subsidence occurring over underground mining operations in the western United States, for example, clearly show that no similarities exist from one subsidence event to another, even when the mining operations are even several miles apart. The main reason for this is due to the vast geologic and topographic variations found from site to site in the western part of the country. Thus, successful predictive methodologies have not yet been developed for the West, and predictive methods developed for other mining regions around the country and around the world are not valid for western u.s. conditions. 17

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Subsidence Mitigation Much work has been done in the past ten years to evaluate subsidence and its effects on structures. There are generally two ways to minimize subsidence damage to structures: design structures capable of withstanding a subsidence event, or prevent the subsidence from occurring. Most of the studies involve analyses of how the deforming g'round surface reacts with structural systems, and how the structural systems respond to these deformations. Other studies involve actual case studies of specific structures subjected to underground mine subsidence, and still others deal with evaluating measures designed to minimize subsidence induced structural damage to ex1st1ng structures. Unfortunately, very little work has been done to develop structural systems designed to withstand subsidence. events with little or no damage. A recent research study conducted by Marino () deals with increasirig the stiffness of existing residentialtype concrete block foundations to mitigate structural damage associated with a subsidence event. This retrofitting procedure involves installing steel straps onto the block walls, thereby providing additional resistance to subsidence-induced bending stresses. This strapping technique has been proven by laboratory studies to be a viable technique for minimizing damage to existing structural foundations. Virtually no has been done, however, 18

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to design residential dwelling foundations specifically to survive a mining-induced subsidence event. The other area of subsidence mitigation research deals with actually preventing subsidence from occurring by incorporating pneumatic stowing or backfilling techniques. These techniques involve actually filling underground mine voids with materials such as concrete, fly ash, sand, mine refuse, or other materials in an attempt to construct load-bearing columns that are capable of preventing mine roof collapse. This method of subsidence control seems to hold limited promise for mines, but due to the high expense of using this method, mine operators are reluctant to adopt this method of ground control. Additionally, this method is not always successful in completely eliminating the occurrence of subsidence, and can only be used where mine void accessibility is not a problem. Typical Subsidence Values In order to successfully test any mitigative foundation design against the detrimental effects of mine subsidence, a quantitative understanding of subsidence-induced ground surface deformations must be achieved. Fortunately, although subsidence behavior varies from site to site, overall behavioral patterns are usually quite similar. For the purposes of this thesis, only general subsidence behavior will be discussed and only average values will be used. The two mining methods that most frequently induce subsidence 19

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damag1ng to surface structures are the room-and-p1llar method, and the longwall method; therefore, the general parameters and character1st1cs of subsidence induced by both of these methods will be discussed below . Longwall Subsidence As stated earlier, subsidence is an expected occurrence over longwall mining operations. Since 100 pet of a longwall panel is mined, the large, unsupported roof left behind as the longwall face advances inevitably collapses, usually immediately behind the longwall shields. Table 2.1 shows typical values of maximum subsidence, angle of draw, and affected. surface area associated with a typical longwall Table 2.1. -Typical Longwall Subsidence Geometry Subsidence Value Parameter Angle of Draw 15 to 35 deg Maximum Subsidence 5 to 10 ft Total Area Affected 100 to 1,000 acres1 1Depends on number of longwall panels mined in a given area. subsidence event. These values are simply averages; obviously each value will differ and can actually be greater or less than the values provided below, depending on specific mining and geologic

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conditions. However, these values provide an insight into the overall geometry of a typical longwall subsidence event. Room-and-Pillar Subsidence Room-and-pillar subsidence is much less predictable than longwall subsidence. In fact, room-and-pillar sections can remain intact for years after mining has been completed. There is an additional factor found in room-and-pillar mine subsidence not found in longwall subsidence; time plays a very important factor in detenmining the extent and duration of a room-and-pillar subsidence event. In abandoned room-and-pillar minesespecially, the amount of time required for a subsidence event to occur depends largely on the existing in the mine itself. For instance, 1f the mine is filled with water, the pillars may erode quickly and collapse, or they may be insulated from damaging atmospheres that might oxidize the material and induce rapid failure. The composition and amount of.overburden is also a factor. Shallow mines tend to develop sinkholes, while deeper room-and-pillar mines tend to develop large saucer-shaped troughs similar to longwall type subsidence (fig. 2.3). The total areal extent of room-and-pillar subsidence obviously depends on how many pillars fail structurally. Table 2.2 shows typical values of maximum subsidence, angle of draw, and affected surface area associated with typical room-and-pillar subsidence events. Again, these values are only averages; many .room-and-pillar subsidence 21

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geometries can have values greater or less than those shown in table 2.2. Table 2.2. -Typical Room-and-Pillar Subsidence Geometry Subsidence Value Value Parameter (sinkhole) (trouah) Angle of Draw 0 to 35 deg 15 to 35 deg Maximum Subsidence 1 to 10 ft 1 to 5 ft Total Surface Area Affected 100 to 2000 ft2 2 to 50 acres 22

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CHAPTER 3 STRUCTURAL FOUNDATIONS SUBJECTED TO SUBSIDENCE The first step in fonmulating mitigative measures designed to protect structures from damage caused by mining-induced subsidence comes with an evaluation of how a structure. or more specifically. a structural foundation reacts to mining induced ground surface deformations. When a structure is subjected to the vertical and hortzontal ground-surface movements caused by mining-induced. subsidence. stresses in the foundation and superstructure will change in reaction to these movements. No portion of a structure is immune to these stress changes (unless the structure is somehow articulated or hinged to accommodate ground-surface movements without inducing additional stresses. or if the entire structure is extremely rigid and "floats" on the ground surface and does not undergo any defonmations other than global translation or rotation). Surface Movements Defonmat1on of the ground surface is seen to have two components; the horizontal component is expressed as either compressive or tensile surface strain, and the vertical component 1s defined as subsidence. All subsidence events contain both of

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these components, but each event can have differing ratios of one component to another. Vertical deformation, as shown in figure 2.6, is seen to have a convex-up portion of the profile, as well as a convex-down portion. The transition point between convex-up and convex-down is usually situated at a relative depth of 50 pet of total vertical deformation (but this 1s not always the case). Horizontal deformation, as shown 1n figure 2.6, always contains both tensile and compressive values. Note the differences between the strain profile for a sub-critical mining width, for a critical width, and a super-critical width. Note also.that the transition point where tensile strain becomes compressive strain coincides with the transition point for the subsidence profile. Foundation Response to Ground Movements The changes in stress of a structure subjected subsidence depend entirely.on the dynamic process of ground surface deformation. Changes in stress of the entire structure begin at the foundation level; the foundation is the direct conmun1cat1on link between the ground surface and the superstructure of any structure. Therefore, when the ground surface subsides, the foundation inmediately reacts with stress and strain changes and transfer these induced stresses and strains to the superstructure that the foundation supports. 24

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' A structure subjected to subsidence will experience a variety of defonmations. as shown in figure 3.1. This figure shows the subsidence wave propagating without any changes in profile dimensions. but as indicated in Chapter 2, this may not always be the case. The first illustration shows that the structure is subjected to negative bending moments along its base. The second illustration shows that as the subsidence wave continues underneath the structure. the structure is now subjected to a combination of positive and negative bending moments along its base. The final illustration shows that as the subsidence wave continues past the structure. positive moments are induced onto the structure at its base. It should be noted that a typical foundation is a threedimensional structural unit; the addition of structural elements orthogonal to the direction of travel of a dynamic subsidence trough will influence how foundation reacts to subsidence. Also. the subsidence trough itself is a three-dimensional structure. and this may also influence the behavior of foundation response by introducing torsional defonmations. From figure 3.1. it is obvious that both tension and compression zones are created within the foundation material as a foundation is subjected to subsidence. In the zones of tension. which can be located either above or below the neutral axis of the foundation depending on the orientation of the subsidence trough, cracking will occur when the magnitude of strain exceeds the ultimate tensile strain of the material. Cracking of this type is 25

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Figure 3.1. Structural response to typical subsidence wave. an unwanted occurrence for a variety of reasons. Most importantly, tensile cracking of a concrete member immediately renders that member useless for continued tensile load carrying capacity. Cracks segment the foundation into separate units, especially if no reinforcing steel is used, and the foundation can no longer act as a single load-bearing member. This becomes especially important, because as the subsidence event cracks and segments the foundation, the horizontal ground surface tensile and compressive strains can act on each unit of the cracked foundation, which can ultimately destroy the foundations load carrying altogether. As with tension cracking, the crushing of foundation material by compression is dependent upon the specific orientation of the 26

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propagating subsidence trough. When the compressive strength of the foundation material is exceeded by the excessive moments induced by subsidence, the material will begin to fail. This is also an unwanted occurrence in that once a material is crushed, its useful load bearing capacities are substantially reduced. Once crushing has occurred, that particular portion of a foundation is no longer capable of carrying either tensile or compressive stresses. {The confining stresses induced by the material surrounding a failed portion of a foundation may in fact allow the failed material to support a smaller of load, but th1s phenomenon is not within the scope of this. thesis.) 27

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CHAPTER 4 PRESTRESSED CONCRETE FOUNDATIONS Overview of Prestressed Concrete Concrete is a material that has high compressive strength, but has very little strength in tension. The practice of prestressing concrete, originally introduced as a practical application by the French engineer Eugene Freyssinet in 1940 (.)., involves the application of internal, permanent compressive stresses to a concrete member so as to counteract tensile stresses in that resulting from external loading. These induced compressive stresses are normally applied before application of service loads by means of high-strength steel tendons which are tensioned and permanently attached to the concrete member. There are several important benefits of using prestressed concrete in construction. Prestressing ordinarily prevents the formation of tension cracks in a concrete member. This is an important advantage, because cracks in a concrete element reduce the effective cross-sectional area, which reduces the overall strength of the member, and can also lead to early structural fatigue. Cracks also lead to premature weathering of the concrete and any type of steel reinforcement. The expansion and contraction of water allowed to accumulate within any cracks in a concrete .member will further crack and damage that member; the water will

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also corrode steel reinforcement, rendering that reinforcement less effective. In addition to crack control, prestressing techniques allow for the control of deflections. By eliminating cracks, the entire cross-sectional area remains effective for stress, and the member is rendered much stiffer than a nonprestressed member of similar dimensiohs. This actually allows for smaller and lighter structural members. Potential Advantages A typical poured wall foundation used for residential construction is not designed to undergo any type of displacementinduced stresses. Specifically, many residential foundations are not designed with longitudinal reinforcing steel to control tensile stresses, simply because such foundations are not ordinarily subjected to movements or loads that would cause tensile stresses anywhere within the foundation material. Unfortunately, residential foundations subjected to mining-induced subsidence are subjected to ground surface defonmations that induce large positive and negative moments in the foundation walls, as shown in figures 4.1 through 4.3. These induced moments create large tensile stresses in the concrete both above and below the neutral axis of the walls, depending on the configuration of the ground surface defonmation. These tensile stresses often exceed the modulus of rupture of the concrete, and ultimately lead to structural failure of the foundation. 29

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Rea I (expected) deflections j L.------1 ,, Negative moments Model approximation Superstructure Mode shape A4: x = L A3: X = 5L/6 A2: X = 2L/3 A1: X = L/2 Figure 4.1. A-series mode shapes and model approx1mat1ons. Rea I (expected) deflections Positive & negative moments Model approximation Superstructure Mode shape 81: X = L/2 82: X = 2L/3 83: x = SL/6 Figure 4.2. B-series mode shapes and model approx1mat1ons. 30

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Real (expected) de f I ec t ions Model approximation Superstructure .. '""'""'""'" ""0 E; :-: ... E::: Finite :::3 ,; Q. .. ... =L---tl .. Mode shape C1: X = L Figure 4.3. C-series mode shape and model approximation. By using prestressed concrete wall foundations, the stresses induced by the subsidence event can be controlled in:such a manner as to eliminate any type of tensne failure of the material caused either by differential settlement or surface strains, thereby maintaining structural integrity of the entire foundation. To illustrate the benefits of using prestressed concrete foundation walls to mitigate the effects of mining-induced subsidence, consider the beam shown in figure 4.4a. Th1s simply supported, unreinforced concrete beam 1s subjected to the single concentrated gravity load, W, at its midspan. As the magnitude of load W increases, the magnitude of the tensile (ft) and compressive 31

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w fc 1 rc ft fr ft w (a) Plain concrete bea1 A Ap Co1pression Compression c .. ,,.,,;'"M Tension Stress due Prestress to load fc fcp 1 + ft fcp =ft fc B 1 + ft fcp >ft fc 1 + ft fcp < ft (b) Prestressed concrete beam B Final streu 2fc p 0 fc1 > 2fc [7 fc2
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(fc) stresses of the beam also increase; this increase will be 11near as shown assuming that the concrete 1s stressed w1th1n its elastic range. When the magnitude of the tensile stress along the. bottom of the beam reaches the modulus of rupture (f), or tensile r strength, of the concrete, the beam will develop tension cracks and ultimately fail with no further increase in load. Now consider beam in figure 4.4b; it is identical to beam A, but now it has been prestressed with the compressive load P as shown. The prestressing load P creates a uniform axial compressive stress (fcp) across the entire cross section of the member. The resulting stress profile clearly indicates that the bottom of the be&n, which was previously in tension, now can be adjusted to be in compression, tension, or have no stress at all simply by adjusting the magnitude of the prestressing force P. It is clear by the above example that the stress distribution of a prestressed concrete foundation wall subjected to a damaging condition can have a more desirable stress distribution than a non-prestressed wall subjected to the same condition. 33

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CHAPTER 5 NUMERICAL FOUNDATION ANALYSIS Analysis Overview To determine if using prestressed concrete walls in a typical residential-type foundation can successfully mitigate the damaging consequences of mining-induced subsidence, a series of two dimensional finite element analyses were performed. The models formulated for these analyses were patterned after the overall dimensions of poured foundation walls typically seen in residential construction. Two wall lengths and three wall depths were chosen for the overall dimensions of the models. The analyses began by subjecting non-prestressed versions of the wall geometries to eight different support conditions, known as mode shapes, to simulate the progression of a generalized subsidence event propagating underneath each model. Each non-prestressed model experienced tensile failures throughout the duration of the application of the subsidence event. After subjecting the non-prestressed walls to this eight-mode subsidence event, the models were altered to simulate a prestressed condition. The same wall geometries, now prestressed, were subjected to the eight-mode subsidence event, and the stresses were to the non-prestressed wall stresses for each mode

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condition to determine if prestressing was actually beneficial to reducing or eliminating the tensile stresses that cause foundation failure or damage. Model Type The finite element method was chosen for the analyses of the foundation walls due to its recognized ability to quickly and accurately solve structural engineering problems. The SAP90 finite element structura 1 analysis program (Z) was used .to conduct all analyses of this Model Development The development of the series of models involved several considerations. The overall geometries, material properties, loading conditions, and support conditions (mode shapes) of the foundation walls were all determined in order to develop valid numerical models. For the determination of numerical values for each of the above design constraints, certain assumptions had to.be made. These assumptions, however, were made to allow for the most effective and valid numerical simulations either practical or possible. Geometry The overall dimensions of the foundation wall models were chosen to best reflect typical wall dimensions commonly found in residential construction. Two wall lengths, a constant wall width,

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and three wall depths were incorporated into the final configurations of the non-prestressed models, resulting in six different wall geometries. For the prestressed models, the wall lengths and depths were identical to those of the non-prestressed walls, but the constant wall width was increased slightly. The models were developed in a two-dimensional environment. Due to the simplicity of the foundation wall geometries and support conditions, _it was apparent that very little differences would occur in stress or displacement results if the models were constructed in two or three dimensions. Therefore, since twodimensional model construction takes less time than three dimensional construction, and since the SAP90 code solves twodimensional solid element problems by incorporating the width of each element, the decision was made to construct all models twodimensionally. An additional consideration that needed to be addressed before deciding on two-dimensional model construction was that of the contribution of forces on the behavior of the foundation walls. These orthogonal influences included the effects of any type of lateral confining forces exerted on the wall exteriors by the surrounding soils outside of the walls, and the effects of other walls joining the walls at the corners. After discussions with practicing structural engineers, it was concluded that any type of confining stresses exerted by the surrounding soils on the sides or bottom of a foundation wall would not appreciably affect 36

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the behavior of the wall when subjected to the subsidence event. This conclusion was based on the fact that material resting against a foundation wall, although providing a certain amount of normal stress along the wall length, would not have the capacity to induce any significant amounts of shear stress along the wall-soil interface that might possibly affect the magnitudes of tensile or compressive axial stresses induced in the wall by the subsidence event. Additionally, the horizontal ground surface strains associated with a subsidence event would not in themselves be capable of providing sufficient shearing stresses to tension or compress a foundation wall to failure owing to the nature of the interface; however, these strains could certainly provide sufficient forces to assist in the damage or destruction of a wall already affected by differential vertical deformations. For the contribution of any type of effects of orthogonal wall connections at the ends of the walls being modeled, it was apparent that the major contributing forces of these orthogonal walls would be some type of action on the modeled walls caused by a differential settlement in the orthogonal direction. Since the subsidence wave being simulated is a two-dimensional phenomenon, the decision was made not to include any type of three-dimensional ground-surface deformations. This, of course, would not be a valid assumption if the wave could not be modeled twodimensionally, such as would be found in the case of a small diameter sinkhole subsidence event, for example. The scope of this 37

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thesis, however, assumes that the subsidence event being modeled remains isoparametric in the direction orthogonal to the wall sides. The two wall lengths used for the non-prestressed walls were 30 and 50 ft, and the three wall depths were 4, and 10 ft. The wall width for the non-prestressed walls was 8 in, or 0.67 ft. For the prestressed walls, the wall width was increased to 10 in, or 0.83 ft, to provide room for prestressing tendon ducts and to. ensure that the maximum compressive strength of the concrete was not exceeded as the prestressed walls were subjected to the subsidence event. (Preliminary tests indicated that a 0.67-ft wide prestressed wall model subjected to the 8-mode subsidence event could exceed the maximum compressive strength of the concrete depending on the particular length and width of the wall, and by increasing the wall width to 0.83 ft this problem could be avoided.) The determination was made to not incorporate any type of foundation footing into the model design, because typical residential poured concrete foundation footings are poured prior to the walls, and no direct continuous connection from the footings to the walls are present. The footings can, however, possess a 11keyway,11 or channel, in which the walls rest (fig. 5.1), but this design is only to prevent the walls from moving laterally on the footings. These keyed footings do not, however, provide vertical restraint from separation of the walls from the footings and thus 38

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Wall Footing ___, Keyway Figure 5.1. -Typical keyed-footing foundation. do not contribute to the behavior of a foundation wall subjected to subsidence-induced ground movements. The actual finite element meshes created for each wall model are shown in figure 5.2. Each mesh contains a regular array.of 1-ft square, 4-noded elements. These elements are defined by the structural analysis program as 11ASOLID11 elements, in that they are all isoparametric, plane stress structures. The nodes have various restrictions on their degrees of rotational and translational degrees of freedom, depending on support conditions (mode shapes}. All nodes are restricted against translation in the global Xdirection, since all models are constructed in the global Y-Z 39

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311 2111 24t 211 117 ,,. 123 .. II ;q z X' 311 Model sets 1 and 2 321 3 lJt 11 21 z Model sets 3 and 4 lJI 341 ltD m 211 217 ,. till 124 IS 21 31 12 y t 'EliiiiiiiiiiiiiiiiiiiiiiiiiiiiiiL X 1 I 11 II 21 21 31 511 -.. ., 251 2111 l!lf liD Ill z X 511 24t 211 117 ,,. 125 .. II 32 z X' 521 254 "' 11 Model sets 5 and 6 251 214 II Model sets 7 and B 531 531 Sf I 21 21 31 Z Model sets 9 and 10 :1'14 m 211 217 ,. till 124 IS 12 21 31 y 511 IIIII 41 511 SIO .. .. .., 2111 lDf tiD till .. 51 y I m m m m m m m s 251 11111111111111111111111111111111111111111111111111:: y X I I II 21 21 31 :II 41 .. 5I .. ., 251 2111 I !If liD 51 z X 414 411 424 11 Model sets 11 and 12 421 ..,. Qt 21 21 31 ... ... ... .. .. .., lDf ISS 102 41 .. 51 y Figure 5.2. -Two-dimensional finite element model parameters. 40

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plane. All nodes are also restr1cted from rotation about the global X, Y, and Z-axes, because the models are representing twod1mens1onal solids. The nodes along the bottom of the models are free to translate in the global Y and Z directions, provided that they are not a support node; otherwise they are restricted in one or both of these directions depending on the support condition. All other nodes are free to translate in the global Y and Z directions for every model. Material Properties The mater1al properties required to fully define each model included only the properties of the concrete. The analysis program required four material properties of the concrete: Poissons ratio, compressive strength, Youngs modulus, and weight per cubic ft. These values were calculated on the basis of typical concrete properties of non-prestressed concrete used in typical residential construction, and of prestressed.concrete used in typical applications Note that the compressive strength of the concrete used for the prestressed models is substantially higher than that of the concrete used for the non-prestressed models. High compressive strength concrete has a greater modulus of elasticity than low strength concrete, which reduces loss of prestress force to the elastic shortening and creep of the concrete. H1gh compressive strength concrete also has a greater strength, which delays the formation of flexural and diagonal tension cracks. 41

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Below are the material properties given to each model. Poissons ratio 0.2 (non-prestressed), and 0.2 (prestressed). Compressive strength m 2500 psi (non-prestressed, typical), and .. 6000 psi (prestressed, typical). Youngs modulus 57000(fc)112 (10) = 57000(2,500 ps1)112 4.10 X 108 lb/ft2 (non-prestressed), and = 57000(6,000 ps1)112 = 6.36 X 108 lb/ft2 (prestressed). Weight= 150 lb/ft3 (non-prestressed), and 150 lb/ft3 (prestressed). Loads For each non-prestressed wall model, there is an applied superstructure loading and a self-weight loading. For each prestressed model, there is a prestressing loading in addition to the superstructure and self-weight loads. The uniform superstructure load, representing the entire structure being supported by the foundation is approximated by a series of point loads applied to all nodes at the top of each wall model. A range of typical values for residential-type superstructure loads were obtained by consulting with several practicing structural engineers, and a median value of 2,500 lb/lineal ft was chosen as being typical for residential construction. This uniform load value was then approximated by 42

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point loads of 2,500 lb placed at each of the nodes on top of each wall model. The self-weight load was simply applied by activating the Z direction gravitation multiplier option in each models input file; this multiplier option activates the self weight of the structure and addl this weight to the other loading conditions. The prestressing load, approximated by end-loading each wall model with a series of point loads approximating a uniform end loading condition, was calculated such that all wall models received a 2,500 psi compression force across the entire cross section when the models were in an undisturbed, or fully supported state. Each wall depth required a different magnitude of point load applied at all nodes at each end of the models. The magnitudes of the nodal prestress loads were determined by __ (_n_)P __ ,.. 2500 psi 2 (b) (h) ft2 where n number of end nodes, P nodal prestress. load, lb, b wall width, ft, and h wall depth, ft. Using the above equation, nodal prestress force P = 239040 lb for the 4-ft-deep walls, P = 265600 lb for the 8-ft-deep walls, and P = 271636 lb for the 10-ft-deep walls. 43

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Note that only the net effect of prestressing tendons is being modeled; the tendon (or tendons) required to produce the 2,500 psi initial compressive stress within each wall are not modeled, nor are they discussed in this thesis. A simplifying assumption was made to not model the tendons and how the ma_gnitudes of tendon forces relax or increase with the changing deformations of the walls caused by the mode shapes. However, for the scope of this analysis, the amount of tendon relaxation or increased tension as a function of wall deformation does not appreciably affect the results of this study. Mode Shapes The eight different support conditions, or mode shapes, that each model is subjected to, were designed to approximate the ground-surface deformations associated with a typical subsidence event. These mode shapes were determined by evaluating typical subsidence parameters associated with room-and-pillar and longwall subsidence events as in Chapter 2. The "worst case" ground surface deformations were considered so that the support modes would subject the models to maximum possible bending deformations to provide the greatest magnitude of subsidence-induced stresses. are three major categories of mode shapes: those that induce negative moments throughout the wall (A-series mode shapes), those that induce both positive and negative moments throughout the wall (B-series}, and those that induce positive moments throughout the wall (C-series). 44

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The A-series mode shapes, designated A1 through A4, simulate the subsidence wave as it first begins to influence the foundation wall (fig. 4.1). Mode shape A4 provides a fully supported condition by providing a support at each node along the bottom of the wall. This is accomplished by restricting the degrees of freedom of the bottom nodes. As shown in figure 4.1, the bottom nodes are_ rollered; the degree of freedom in the global Z direction has been restricted but the degree of freedom in the global Y direction has not. The bottom left node has been restricted tn both directions to act as a pinned connection (required so the model w111 be stable). Mode shape A3 represents the support condition where 5/6 of the foundation is supported. Mode shape A2 represents the support condition where 2/3 of the foundation is supported, and mode shape A1 represents the support condition where 1/2 of the foundation is supported. As the subsidence wave continues past the Al condition, the entire foundation will tip, and suddenly be supported at only two locations; this begins the a-series of support conditions. The a-series mode shapes begin with 81; this support condition has one rollered support at the midpoint of the wall, and a pinned support at the end of the wall (fig. 4.2). Mod.e 82 has the separation of the pinned end of the wall and the rollered support to be 2/3 the length of the wall, and mode 83 has this separation at 5/6 the length of the wall. When the separation between the 45

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pinned end and the rollered support becomes the full length of the wall, the Cl support condition exists. Support condition Cl represents a simply supported beam, with a ptnned end on one end, and a rollered support on the other (fig. 4.3). As the subsidence wave continues to pass underneath the wall, the wall will once again be fully supported, and revert back to mode A4, which is now labeled A4' for clarity. It be noted here that when the pinned reaction is shown on the very end of the wall, it is actually placed one node from the end of the wall, due to the limitations of the analysis program. The program cannot allow a fully restrained node to experience an applied load; this is not a problem for the nonprestressed walls, but the prestressed walls load every side node. Therefore, to load every side node, it is necessary to move the end reaction over one node. This, however, does not appreciably affect the results. It is evident that the mode shapes representing an entire subsidence event are actually a measure of time. Mode shape A4 represents time t=O, and also represents the time of completion of the subsidence event (mode A4'). All other mode shapes represent intermediate times in the development of the subsidence event. It should be noted, however, that the separation of time between mode shapes is not necessarily a constant. For example, the amount of time between mode Cl and A4' is clearly larger than the time between modes A4 and AJ. 46

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Final Model Configurations There were 96 two-dimensional finite element foundation wall models constructed for analysis. Table 5.1 shows the organization and labeling of each model. The models were grouped into sets to assist in organizing and accessing each model. The models were divided into 12 sets of eight models apiece. Each model set represented a particular wall geometry and prestressing condition to be subjected to the eight mode subsidence event, and each of the eight models within each set varied by the mode shape. The model sets were divided 1.nto two major categories; model sets 1 through 6 contained 30ft wall lengths, and sets 7 through 12 contained 50 ft wall lengths. In model sets 1 through 6, sets 1, 3, and 5 contained non-prestressed wall configurations, and 2, 4, and 6 contained prestressed walls. In model sets 7 through 12, sets 7, 9, and 11 contained non-prestressed wall configurations, and 8, 10, and 12 contained prestressed walls. Model Run Procedure Once the construction of the 96 two-dimensional finite element foundation wall models was completed, the analysis of these models could begin. Each model was submitted in the order shown 1n table 5.1 to the SAP90 structural analysis computer program to obtain the stresses and displacements resulting from the particular geometries, loads, prestressing constraints, and support conditions unique to each model. 47

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TABLE 5.1. F1nite Element Foundation Wall Model Schedule MODEL SET NO 1 MODEL lENGTH DEPTH WIDTH PRESTRESS MODE CONCRETE NUMBER (ft) (ft) (ft} fosU 01A4 30 10 0.67 NO A4 2,500 01A3 30 10 0.67 NO A3 2,500 01A2 30 10 0.67 NO A2 2,500 01A1 30 10 0.67 NO A1 2,500 01B1 30 10 0.67 NO B1 2,500 01B2 30 10 0.67 NO B2 2,500 01B3 30 10 0.67 NO B3 2,500 01C1 30 10 0.67 NO C1 2,500 MODEL SET NO. 2 MODEL lENGTH DEPTH WIDTH PRESTRESS MODE CONCRETE NUMBER (ftl (ftl (ftl fos1\ 02A4 30 10 0.83 YES A4 6,000 02A3 30 10 0.83 YES A3 6,000 02A2 30 10 0.83 YES A2 6,000 02A1 30 10 0.83 YES A1 6,000 02B1 30 10 0.83 YES B1 6,000 02B2 30 10 0.83 YES B2 6,000 02B3 30 10 0.83 YES B3 6,000 02C1 30 10 0.83 YES C1 6,000 MODEL SET NO. 3 MODEL lENGTH DEPTH WIDTH PRESTRESS MODE CONCRETE NUMBER (ftl (ftl (ftl (1lSU 03A4 30 04 0.67 NO A4 2,500 03AJ. 30 04 0.67 NO A3 2,500 03A2 30 04 0.67 NO A2 2,500 03A1 30 04 0.67 NO A1 2,500 03B1 30 04 0.67 NO 81 2,500 0382 30 04 0.67 NO 82 2,500 0383 30 04 0.67 NO 83 2,500 03C1 30 04 0.67 NO C1 2,500 48

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TABLE 5.1. (contd.) MODEL SET NO. 4 MODEL lENGTH DEPTH WIDTH PRESTRESS MODE CONCRETE NUMBER (ft) (ft) (ft) (DSi) 04A4 30 04 0.83 YES A4 6,000 04A3 30 04 0.83 YES A3 6,000 04A2 30 04 0.83 YES A2 6,000 04A1 30 04 0.83 YES A1 6,000 0481 30 04 0.83 YES 81 6,000 0482 30 04 0.83 YES 82 6,000 04B3 30 04 0.83 YES B3 6,000 04C1 30 04 0.83 YES C1 6,000 MODEL SET NO. 5 MODEL lENGTH DEPTH WIDTH PRESTRESS MODE CONCRETE NUMBER (ft) (ft) (ft) (DS1) 05A4 30 08 0.67 NO A4 2,500 05A3 30 08 0.67 NO A3 2,500 05A2 30 08 0.67 NO A2 2,500 05A1 30 08 0.67 NO A1 2,500 0581 30 08 0.67 NO Bl 2,500 05B2 30 08 0.67 NO B2 2,500 0583 30 08 0.67 NO 83 2,500 05Cl 30 08 0.67 NO Cl 2,500 MODEL SET NO. 6 MODEL lENGTH DEPTH WIDTH PRESTRESS MODE CONCRETE NUMBER (ft) (ft) (ft) Cosn 06A4 30 08 0.83 YES A4 6,000 06A3. 30 08 0.83 YES A3 6,000 06A2 30 08 0.83 YES A2 6,000 06A1 30 08 0.83 YES A1 6,000 0681 30 08 0.83 YES Bl 6,000 0682 30 08 0.83 YES 82 6,000 0683 30 08 0.83 YES B3 6,000 06Cl 30 08 0.83 YES Cl 6,000 49

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TABLE 5.1. (contd.) MODEL SET NO. 7 MODEL LENGTH DEPTH WIDTH PRESTRESS MODE CONCRETE NUMBER (ft) (ft) (ft) (ps1) 07A4 50 10 0.67 NO A4 2,500 07A3 50 10 0.67 NO A3 2,500 07A2 50 10 0.67 NO A2 2,500 07A1 50 10 .0.67 NO A1 2,500 07B1 50 10 0.67 NO B1 2,500 07B2 50 10 0.67 NO B2 2,500 07B3 50 10 0.67 NO B3 2,500 07C1 50 10 0.67 NO C1 2,500 MODEL SET NO. 8 MODEL LENGTH DEPTH WIDTH PRESTRESS MODE CONCRETE NUMBER (ft) (ft) (ft) Cos1l 08A4 50 10 0.83 YES A4 6,000 08A3 50 10 0.83 YES A3 6,000 08A2 50 10 0.83 YES A2 6,000 08A1 50 10 0.83 YES A1 6,000 08B1 50 10 0.83 YES Bl 6,000 08B2 50 10 0.83 YES B2 6,000 08B3 50 10 0.83 YES B3 6,000 08C1 50 10 0.83 YES C1 6,000 MODEL SET NO. 9 MODEL lENGTH DEPTH WIDTH PRESTRESS MODE CONCRETE NUMBER (ft) (ft) (ft) Cos;) 09A4. 50 04 0.67 NO A4 2,500 09A3 50 04 0.67 NO A3 2,500 09A2 50 04 0.67 NO A2 2,500 09Al 50 04 0.67 NO Al 2,500 09B1 50 04 0.67 NO B1 2,500 09B2 50 04 0.67 NO B2 2,500 09B3 50 04 0.67 NO B3 2,500 09Cl 50 04 0.67 NO C1 2,500 50

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TABLE5.1. (contd.) MODEL SET NO 10 MODEL lENGTH DEPTH WIDTH PRESTRESS MODE CONCRETE NUMBER (ft) (ft) (ft) Cosi) 10A4 50 04 0.83 YES A4 6,000 10A3 50 04 0.83 YES A3 6,000 10A2 50 04 0.83 YES A2 6,000 10A1 50 04 0.83 YES A1 6,000 10B1 50 04 0.83 YES B1 6,000 10B2 50 04 0.83 YES 82 6,000 10B3 50 04 0.83 YES 83 6,000 10C1 50 04 0.83 YES C1 6,000 MODEL SET NO 11 MODEL lENGTH DEPTH WIDTH PRESTRESS MODE CONCRETE NUMBER (ft) (ft) (ft) 1Ds1l 11A4 50 08 0.67 NO A4 2,500 11A3 50 08 0.67 NO A3 2,500 11A2 50 08 0.67 NO A2 2,500 11A1 50 08 0.67 NO A1 2,500 1181 50 08 0.67 NO 81 2,500 1182 50 08 0.67 NO 82 2,500 1183 50 08 0.67 NO 83 2,500 11C1 50 08 0.67 NO C1 2,500 MODEL SET NO. 12 MODEL lENGTH DEPTH WIDTH PRESTRESS MODE CONCRETE NUMBER (ft) (ft) (ft) Cos1) 12A4 50 08 0.83 YES A4 6,000 12A3 50 08 0.83 YES A3 6,000 12A2 50 08 0.83 YES A2 6,000 12A1 50 08 0.83 YES A1 6,000 1281 50 08 0.83 YES 81 6,000 1282 50 08 0.83 YES. 82 6,000 1283 50 08 0.83 YES 83 6,000 12Cl 50 08 0.83 YES Cl 6,000 51

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Each model run generated several output files containing the desired information. Since these files were quite large, they were edited to retain only the axial stress information related to the top and bottom nodes and elements of each model, since these nodes and elements possess the maximum values of stresses. Th1s reduction in output file size significantly reduced the computer d1sk storage space required for each model output file, and greatly simplified the task of accessing the desired information. 52

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CHAPTER 6 RESULTS AND CONCLUSIONS Results The data obtained from the 96 two-dimensional finite element foundation wall model runs organized into a series of graphs and tables to provide easy identification of all stresses occurring in the models. These graphs and tables assisted in detenmin1ng whether prestressing a typical residential-type concrete wall foundation would indeed eliminate or lessen damage due to ground.surface deformations associated with a mine subsidence event. When evaluating the results of the model runs, it is important to note that the stresses resulting from each models specific load and support conditions reflect a linear behavior of the concrete wall, and do not take into account the ultimate tensile or compressive strength of the concrete. Therefore, any value of tensile or compressive stress shown in the following graphs or tables that exceeds the specified compressive or tensile strength of the concrete simply means that the concrete has either cracked or crushed, and the wall is assumed to be damaged. These values that exceed the strength of the concrete have no meaning other than to indicate that structural failure within the concrete has occurred. The (nodes) where these values occur, however, are quite valid. Since the models are behaving elastically up to

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the point of failure, the relative magnitudes of these stresses throughout the walls remain constant, and thus the location of the greatest tensile stress within each model occurs at the location of the first structural failure. Although a particular model set may contain more than one failure-inducing mode shape, it is the first mode shape at which failure occurs that is of the most importance. This is because once a tensile crack has been introduced into the wall, no further increase in bending moment is necessary to propagate the crack throughout the entire depth of the wall. Thus, the wall is considered to no longer be a competent structure. This, however, does not necessarily mean that stresses induced in the model during mode shapes following the mode shape first inducing failure are entirely invalid. For instance, if a tensile crack is initiated in the top surface of a wall and does not propagate completely through the depth of the wall, this crack can possibly close up when the stresses in the wall at this location pass from tensile to compressive. This would allow the wall to maintain a degree of structural integrity into the following mode shapes. Crack healing of course depends on how the crack propagates through the wall depth; this phenomenon is beyond the scope of this thesis. However, for purposes of this thesis, all mode shapes subsequent to the first failure mode shape for any wall model set are included to illustrate the overall behavior of the walls throughout the entire subsidence event. 54

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The failure stress locations are the same for both non-prestressed and prestressed walls with similar wall geometries and subjected to the same mode shapes. This is not surprising, since the addition of the prestressing load simply changes the relative magnitudes of the stresses within the walls and does not change their locations along the wall lengths. To determine when a wall model has failed structurally, it is important to obtain values for the maximum tensile and compressive stresses of the wall material. As specified in the American Concrete Institutes Building Code Requirements for Reinforced Concrete (ACI 318-83) (1Q), the modulus of rupture of the concrete is taken to be f = 7 5 ( f I ) 112 r c = 7. 5 (2500) 112 ,. 375 psi (non-prestressed) .. 7.5(6000)112 = 581 psi (prestressed) where compressive strength has been previously specified as f c = 2500 psi (non-prestressed) .. 6000 ps1 (prestressed). Non-Prestressed Wall Stresses Table 6.1 shows the maximum stresses and their locations along the wall top and bottom for all non-prestressed wall models. For ease in identification of all stress values that exceed the maximum ' 55

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Table 6.1. -Maximum Bending Stresses for Non-Prestressed Wall Models MODEL SET NO. 1 (30-ft long, 10-ft deep) MODEL NO. MAXIMUM MAXIMUM LOCATION BENDING (node) BENDING STRESS (node) (BOTTOM. osi) _{TOP. D_S iJ 01A4 0 -0 -01A3 -109 25 31 333 01A2 -291 20 111 330 01A1 -568 15 240 326 01B1 -696 15 217 326 01B2 79 4 86 332 01B3 149 13 12 340 OlCl 235 16 -236 327 MODEL SET NO. 3 (30-ft 4-ft deeo) MODEL NO. MAXIMUM LOCATION MAXIMUM LOCATION BENDING STRESS (node) BENDING STRESS (node) (BOTTOM os1) (TOP. osn 01A4 0 -0 -01A3 -225 25 140 150 01A2 -747. 20 528 *3 146 01A1 -1571 15 1199 141 01B1 -1496 15 1208 140 01B2 241 8 523 146 01B3 719 13 115 151 01C1 1167 16 -1167. 141 MODEL SET NO. 5 (30-ft 8-ft deep) MODEL NO. MAXIMUM LOCATION MAX LOCATION BENDING STRESS (node) BENDING STRESS (node) CBOTTOM osil 1TOP. DS 1) 01A4 0 -0 -01A3 -123 25 44 272 01A2 -353 20 160 268 01A1. "-699 15 352 264 01B1 -760 15 331 264 01B2 82 4 137 270 0183 213 13 22 276 OlCl 342 16 -343 265 1Positive values indicate tension, negative values indicate compression. 2Refer to figure 5.1 for node locations. 3Asterisk indicates stress exceeds tensile or compressive strength. 56

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Table 6.1. (contd.) MODEL SET NO. 7 (50-ft lena. 10-ft deeo' MODEL NO. MAXIMUM MAXIMUM LOCATION BENDING (node) BENDING STRESS (node) (BOTTOM. osi) CTOP. osi) 01A4 0 -0 --01A3 -208 42 74 551 01A2 -691 33 308 544 01Al -1353 25 658 *3 536 01B1 -1431 25 640 536 01B2 145 12 282 545 01B3 428 21 48 555 01C1 662 26 -662 537 MODEL SET NO. 9 (50-ft long. 4-ft deep) MODEL NO. MAXIMUM LOCATION MAXIMUM LOCATION BENDING STRESS (node) BENDING STRESS (node) (BOTTOM_._ _a_s 11 CTOP. osi) 01A4 0 -0 --01A3 -502 42 340 247 01A2 -1985 33 1543 239 01A1 -4125 25 3354 231 01Bl -3881 25 3407 230 01B2 700 13 1554 239 01B3 2141 21 318 248 01Cl 3336 26 -3336 231 MODEL SET NO. 11 (50-ft 1 on a 8-ft deeo MODEL NO. MAXIMUM LOCATION MAXIMUM LOCATION BENDING STRESS (node) BENDING STRESS (node) (BOTTOM osi\ (TOP" 01A4 0 -0 --01A3 -247 42 105 450 01A2 -869 33 450 442 01A1 -1736 25 968 435 01B1 -1665 25 958 434 0182 209 13 428 443 0183 625 21 eo 453 OlCl .970 26 -970 435 1Pos1tive values indicate tension, negative values indicate compression. 2Refer to figure 5.1 for node locations. 3Asterisk indicates stress exceeds tensile or compressive strength. 57

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tensile or compressive capacity of the concrete walls, an asterisk appears to the right of all stress values exceeding 375 psi (tension) or 2,500 psi (compression). Note that all model sets indicate no bending stress for mode A4; this mode is the fully supported condition, and no induced bending stresses are possible. 30-ft Models. Model set 1, representing the shortest and deepest of the non-prestressed wall models, is shown in table 6.1 to contain no values of tensile or compressive stress exceeding the lim1t1ng values. Therefore, this particular wall configuration has "survived" the a-mode subsidence event without experiencing any type of bending failure. The location of maximum tensile bending stress occurred at the midspan of the wall at node 326 during mode A1; this stress is approximately 64 pet of the tensile strength of the concrete. Model set 3, representing the shallowest of the 30-ft-long nonprestressed wall models, first experienced tensile failure along the top of the wall at node 146 during mode A2. The location of maximum tensile bending stress occurred at the midspan of the wall at node 140 during mode 81. This model set experienced tensile stresses that exceeded the tensile capacity of the concrete on both the top and bottom surfaces during the 8-mode subsidence event. Although model set 5, representing the 8-ft-deep, 30-ft-long non-prestressed wall did not experience any bending stresses exceeding the maximum allowable stresses of the wall, the maximum tensile stress is approximately 94 pet of the tensile strength of 58

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the wall. As with model set 1, the maximum tensile bending stress occurred at the midspan of the wall at node 264 during mode Al. 50-ft Models. The three 50-ft-long non-prestressed models all e.xperi enced tens 11 e fa 11 ures both on top and bottom of the wa 11 s during the 8-mode subsidence event. Model set 7, representing the deepest of the 50-ft-long non-prestressed wall models, first experienced tensile stresses exceeding the maximum allowable value during mode A1 along the top of the wall at midspan at node 536. The maximum value of stress that occurred during the 8-mode subsidence event also occurred at midspan of the wall along the bottom surface at node 26 during mode C1. Model set 9, representing the shallowest of the 50-ft-long nonprestressed wall models, first reached tensile failure at node 239 along the top of the wall during mode A2. This wall also reached compressive failure at node 25 during mode A1, which represents the maximum compressive value within the wall during the 8-mode subsidence event. The maximum value of tensile stress that occurred during the subsidence event was located along top of the wall at midspan at node 230 during mode 81. Model set 11, representing the 8-ft-deep, 50-ft-long nonprestressed wall, first experienced tensile failure at node 442 during mode A2. The maximum value of tensile stress that occurred during the subsidence event occurred at along the bottom of the wall at midspan during mode C1. 59

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It is apparent from the results obtained from the nonprestressed wall model runs that the location of maximum stresses always occurred at the midspan of the walls during modes Al, Bl or Cl. This is not surprising, since the Al,. B1, and C1 support conditions clearly induce the greatest amounts of bending moment in the walls. These mode shapes are actually quite similar, in that they approximately the same amount of maximum tensile bending stress at midspan. In model set 1, the tensile stresses at midspan induced by these three mode shapes are within 90 pet of one another. For model set 3, the stresses are within 97 pet of ohe another; 94 pet for model set 5; 97 pet for model set 7; 98 pet for model set 9; and 99 pet for model set 11. It 1s clear from table 6.1 that the longer and shallower nonprestressed concrete wall models experienced larger magnitudes of bending stresses that ultimately lead to structural failure. Except for model sets 1 and 3, each model set experienced bending stresses that exceeded the strength of the concrete walls, and thus destroyed their structural integrity. Prestressed Wall Stresses The prestressed wall stress results for each individual model are presented in figures 6.1 through 6.6. These six figures show the maximum compressive bending stress occurring in each prestressed wall.model as a function of mode shape. 30-ft Models. Figure 6.1, representing the stress results of model set 2, indicates that the 30-ft-long, 10-ft-deep wall model

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rn rn IV '"' ...,J -2000 Cll -3000 QD 1::::: =8 1::::: -3500 IV c:l '"--' ' --TOP --BOTTOM / .... ./ ,. --I / I, I ' A4 A3 A2 A1 B1 B2 BJ C1 A4' Support Mode Figure 6.1. -Maximum bending stress vs. mode shape, model set 2 (30-ft long, 10-ft deep). -1000 ..... rn-2000 0.. rn rn IV -3000 '"' ...,J Cll ..... -o 1::::: IV c::l -5000 --TOP --BOTTOM I I\ I \ I \ I \ A4 A3 A2 A1 81 82 83 C1 A4' Support Mode Figure 6.2. -Maximum bending stress vs. mode shape, model set 4 (30-ft long, 4-ft deep). 61

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-2000 .... rn 0..-2500 rn rn Q) r.. CIJ -3000 tW Q .... "'t:: Q -3500 Q) o:l ' --TOP --80TIOM -J / / / A4 AJ A2 A1 81 82 83 C1 A4' Support Mode Figure 6.3. -Maximum bending stress vs. mode shape, model set 6 (30-ft long, 8-ft deep). -1000 -1500 .... CIJ 0..-2000 CIJ CIJ -2500 Q) r.. CIJ -3000 ' ' tW / Q -3500 .... "'t:: Q -4000 Q) o:l -4500 --TOP --80TIOM / / --J A4 AJ A2 A1 81 82 83 C1 A4' Support Mode Figure 6.4. -Maximum bending stress vs. mode shape, model set B (50-ft long, 10-ft deep). 62

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2000 1000 .... en o c. .-1000 en en Q) -2000 J.. ..,J (f) -JOOO bLI-4000 d ..... "0 -5000 d Q) lil -6000 ' --TOP \ / \ I \ I \ I \--I I I f I \ I \ \ \ -7000 -BOTTOM -8000+---r--r--,----"T----r---.--....,...----., A4 AJ A2 A1 91 92 BJ C1 A4' Support Mode Figure 6.5. -Maximum bending stress vs. mode shape, model set 10 (50-ft long, 4-ft deep). 0 ..... -1000 en c. en -2000 en Q) J.. ..,J en -Jooo bD d ;a.-4000 c Q) IIl-sooo .... .... .... --TOP --BOTT0'-1 ' / / / I t, I \ I A4 AJ A2 A1 91 92 83 C1 A4' Support Mode Figure 6.6. -Maximum bending stress vs. mode shape, model set 12 (50-ft long, 8-ft deep). 63

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experienced only compress1ve stresses throughout the 8-mode subsidence event. As is shown in the figure, the stresses along the top and bottom of the wall were both 2,500 psi compression modes A4; this indicates the unifonm prestressing load that was applied to the wall in the fully supported condition. The stresses along the top and bottom of the wall at the conclusion of the subsidence event (mode A41 ) also indicate 2,500 psi compressfon as the wall once again becomes fully supported. The maximum compression that occurred during the subsidence event was along the bottom of the wall at midspan during mode 81 at node 15. The magnitude of this compressive stress was 3-,091. psi; this value of stress is approximately 52 pet of the compressive strength of the wall. The minimum value of compression was 2,290 psi, and occurred during mode A1 at the midspan node 326. Since no tensile stresses developed, the wall did not experience tensile cracking. Figure 6.2, representing the 30-ft-long, 4-ft-deep prestressed wall (model set 4), also experienced only compressive stresses along the top and bottom during the 8-mode subsidence event. The maximum value of compression experienced in the wall during the subsidence event was 3,799 psi; this stress occurred along the bottom of the wall at midspan node 15 during mode A1. This value of stress is approximately 63 pet of the compressive strength of the wall. The minimum value of compression, 1,501 psi, occurred at midspan along the top of the wall at node 140 during mode 81. 64

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Figure 6.3, representing the 30-ft-long, 8-ft-deep prestressed wall (model set 6), is seen to have compressive stress values between those experienced by model sets 2 and 4. The maximum stress of 3,130 psi compression occurred along the bottom at midspan node 15 during mode 81; this stress is approximately 52 pet of the maximum compressive strength of the wall. The minimum value of compressive stress of psi occurred along the top of the wall at node 264 during mode A1, and as with model sets 2 and 4, is well within the maximum tensile capacity of the wall. It 1s clear from figures 6;1 through 6.3 (model sets 2, 4, nd 6) that prestressing eliminated any type of subsidence-induced tensile stresses. Model set 4, representing the shallowest and therefore the most moment-sensitive 30-ft wall, still only reached 63 pet of the maximum compressive strength of the concrete. The midspan of each 30-ft-long prestressed wall always contained the maximum and minimum value of compressive stress resulting from the 8-mode subsidence event. 50-ft Models. Figures 6.4 through 6.6 show the maximum stress response to subsidence of the 50-ft-long prestressed models. Due to the increased wall length, the resulting stresses induced by the 8-mode event were correspondingly higher than were experienced in the 30 ft prestressed walls. Model set 8, representing the deepest of the 50-ft-long prestressed models, experienced only compressive stresses throughout the 8-mode subsidence event, as shown in figure 6.4.

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The maximum value of compressive stress occurred along the bottom of the wall at midspan node 25 during mode Bl. This maximum compressive stress of 3,721 psi is approximately 62 pet of the maximum compressive strength of the wall. The minimum compressive stress of 1,926 psi occurred along the bottom of the wall at midpoint node 26 during mode C1. Model set 10 represents the shallowest of all of the 50-ft-long (and 30-ft-long) prestressed model sets. As a result, this model set experienced the greatest magnitude of stresses of any of the prestressed models. The maximum compressive stress occurred during mode A1 along the bottom of the wall at midspan node 25 (fig. 6.5). This maximum stress of 5,912 psi compression is approximately 99 pet of the compressive strength of the concrete. Additionally, this model configuration underwent a maximum tensile stress of 319 psi during mode 81 along the top at midspan node 230; this maximum tensile stress is approximately 47 pet of the maximum tensile capacity of the concrete. Model set 12, representing the 8-ft-deep, 50-ft-long prestressed model, experienced stresses between those of model sets 8 and 10 (fig. 6.6). The maximum compressive stress of 3,969 psi occurred at bottom midspan node 25 during mode A1. This stress is approximately 66 pet of the maximum compressive capacity of the concrete. The minimum compressive stress_of 1,675 psi also occurred along the bottom of the wall at midspan node 26. 66

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Figures 6.7 through 6.10 show the stress profiles found 1n figures 6.1 through 6.6 to illustrate the influence of wall depth on stress magnitude. -1000 -1500 ..... fn Q..-2000 fn fn -2500 cu 1-4 CJ) -3000 bD ..... -a -4000 cu Ill -4500 4 ft deep / .... --, / \ ,./Sftdeep' ... ... .... ----------.,, \ ::.--10 ft deep ,,\ ', I I I A4 A3 A2. A1 B1 B2 B3 C1 A4' Support Mode Figure 6.7. -Maximum top bending stresses vs mode shape, model sets 2, 4, and 6 (30-ft wall length). ..... fn c.. fn fn -1500 -2000 -2500 cu CJ) b0-3500 ..... -e. -4000 cu Ill -4500 -' ..... '". ' ', ..... __ ," \ 8 ft deep 1 \ I \ ,' \ I ... ---, 4 ft deep ,, I \ I \ I \ I \ I \ I / '\ ,' I I / 1/ -sooo+--.-----....;__---.---r--"T""""-.-----.--, A4 A3 A2. A1 B1 B2 83 C1 A4' Support Mode Figure 6.8. -Maximum bottom bending stresses vs. mode shape, model sets 2, 4, and 6 (30-ft wall length). 67

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1000 0 ..... rn Q..-1000 rn rn-2000 Q) ""' C/)-JOOO tiD c -4000 ..... "'0 c -5000 Q) 1:;1 -6000 4 ft deep 1--' I \ I I \ I \ / 8 ft deep / --. \ \ .,.. ......... ---.... -t-..::::...--' ' I I I A4 AJ A2 A1 91 92 9J C1 A4' Support Mode Figure 6.9. -Maximum top bending stresses vs. mode shape, model sets 8, 10, and 12 (50-ft wall length). 1000 0 ..... rn g,.-1000 rn -2000 rn Cl) J.. -JOOO Cll tiD-4000 c -5000 c Cl) -6000 -7000 .... ' ', "'-,., \ 8 ft deep \ I \ \ I \ I \ I ___ .... 4 ft deep A4 AJ A2 AI 91 92 9J C1 A4' Support Mode Figure 6.10. -Maximum bottom bending stresses vs. mode shape, model sets 8, 10, and 12 (50-ft wall length). 68

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The 1nfluence of wall depth-to-length (d/1) rat1o on max1mum bend1ng stress was also 1nvest1gated for the prestressed wall models. The results are shown in graphical form in figure 6.11. -2000 .... rn -Jooo Q. rn rn QJ -4000 1-o .., ['J) d ..... "tS d 30 ft QJ m -sooo -7000 -trrrTTT""""TTT1rTTT"rTTTTTTI"TTT1rTTT"TT""I'TTTTI......,.,rTTTTTI 0.08 0.1 J 0.18 0.23 0.28 O.JJ Depth/Length F1gure 6.11. -Max1mum bending stress vs. depth/length rat1o. Besides the data points computed for the 4, 8, and 10-ft deep walls, add1t1onal computer runs were perfo.rmed to generate data po1nts for 6-ft deep walls to provide smoother stress prof11es. The abscissa of each data point 1s depth-to-length ratio of a 69

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particular foundation wall, while the ordinate is the maximum compressive stress that occurred in the wall during the 8-mode subsidence event. As is shown in figure 6.11, the stress profiles trend towards the horizontal as the d/1 ratio increases. It is evident that the curves_ from d/1 = 0.08 to approximately 0.2 are much steeper than from d/1 = 0.2 to 0.33. This indicates that the maximum bending stress magnitudes occurring in the walls are much more sensitive to changes in the d/1 ratio in the 0.08 to 0.2 range than they are in the 0.2 to 0.33 range. Conclusions The. overall goal of this investigation was to determine the viabi 1 ity of prestressingtypical residential-type concrete wall foundations to lessen the damaging effects of ground movements associated with mine subsidence. Based on the results of finite element analyses of 96 prestressed and non-prestressed concrete foundation wall models, it is clear that prestressing foundation walls to eliminate damaging subsidence-induced bending stresses is a viable option. Using foundation wall models representing the geometry and comp.ressive strength of typical poured wall foundations found in residential construction, the finite element study showed failure in four of six non-pre-stressed wall models due to ground movements associated with mine subsidence. None of the prestressed wall models experienced any type of tensile or compressive failure. 70

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It might be assumed that increasing the compressive strength of the non-prestressed wall concrete from 2,500 psi to 6,000 psi (equal to the prestressed wall concrete strength) might have reduced or eliminated the structural failure of the non-prestressed walls. Since the modulus of rupture of 6,000 psi strength concrete is 581 psi, it is clear by table 6.1 that none of the model sets that failed structurally with 2,500 psi strength concrete would have survived the subsidence event by using a high strength concrete. It 1s thus apparent that the practice of prestressing residential-type concrete wall foundations.to eliminate damaging bending stresses induced by ground-surface deformations associated with mine subsidence can be a valid design alternative. 71

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REFERENCES 1. National Coal Board, Production Department. Subsidence Engineers Handbook. London, 2nd ed., 1975, 111 pp. 2. Whittaker, B. N., and D. J. Reddish. Subsidence: Occurrence, Prediction and Control. Elsevier, 1989, 528 pp. 3. Heasley, K. A. Computer Modeling of Subsidence and Subsidence-Control Methods. M.S. Thesis, The PA State Univ., State College, PA, 1988, 203 pp. 4. Fejes, A. J., R. C. Dyni, J. A. Magers, and L. B. Swatek. Subsidence Information for Underground Mines: Literature Assessment and Annotated Bibliography. BuMines IC 9007, 1985, 86 pp. 5. Marino, G. G., and W. L. Gamble. Repair and Strengthening of Subsidence-Damaged Concrete Block Foundation Walls. Paper in Proceedings of 5th North American Masonary .Conference, Urbana, IL, 1990 6. Nilson, A. H. Design of Prestressed Concrete. Wiley, 2nd 1987, 592 pp. 7. Wilson, E. L., and A. Habibullah. SAP90: A Series of Computer Programs for the Static and Dynamic Finite Element Analysis of Structures-Users Manual. Computers and Structures, Inc., Berkeley, CA, 1988. 8. Ferguson, P. M., J. E. Breen, and J. 0. Jirsa. Reinforced Concrete Fundamentals. Wiley, 5th ed., 1988, 746 PP 9. Hassoun, M. N. Design of Reinforced Concrete Structures. PWS Publishers, 1985, 766 pp. 10. ACI Committee 318. Building Code Requirements for Reinforced Concrete (ACI 318-83). Am. Concrete Inst., Detroit, MI, 1983, 111 pp. 72