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By Orestis Zarzouras, Amalia Giannakou, Jacob Chacko

"When designing structures in seismically active areas, foundations of critical structures are typically located away from known faults. Indeed many seismic codes prohibit construction in the immediate vicinity of seismically active faults establishing minimum setbacks from the faults. However, for long structures such as bridges, tunnels and pipelines, a fault maybe unavoidable, and fault rupture risk impossible to preclude. This paper presents a case study of a bridge foundation design that incorporates the consequences of fault deformations passing through the foundation. A series of site surveys were conducted to characterize the fault environment, and fault displacement hazard analyses were conducted to develop design displacement demands. Subsequently, numerical analyses were performed to evaluate the fault rupture-induced demands on a pier foundation in terms of displacements and rotations. Initially, analyses were performed that model the free field fault rupture propagation to the ground surface of the fault to ensure that the basic site characteristics are captured. Subsequently, the foundation elements were introduced in the model and the fault rupture is simulated again. The interaction and influence of the foundation on the fault rupture propagation is calculated, and the consequent demands and distortions of the foundation block provide a basis for structural engineers to design the bridge.IntroductionThe Izmit Bay bridge, a 3-km-long suspension bridge that crosses Izmit Bay in Turkey, is planned to be constructed in one of the most seismically active places in the world. The south approach structures for the Izmit Bay Bridge along the western side of the Hersek peninsula bring the bridge down from on the order of El. 60 meters at the South Anchorage to an elevated embankment approximately 1.3 km farther south (Figure 1). The south approach structures are located within a zone of secondary deformation around the primary trace of the North Anatolian Fault. The concept design team has developed a concept design for a “viaduct” structure that consists of 10 spans with lengths varying between 136 m and 100 m and two back spans one of 125 m, attached to the main bridge and the other of 74 m attached to the south embankment."

Jan 1, 2017

By RavikiranVaidya, Vishal Dhamecha

Low Strain Pile Integrity Testing has been used in India since 1990’s and several have tried to demonstrate the utility and benefits of this method. However, use of this technology was limited till 1998 as not enough data maybe was not available to justify its use and application on major infrastructure and real estate projects. The first author has done significant work in this method resulting in its use in practically all sectors of the industry that use concrete bored pile foundations as a supporting element. The paper explains various signal enhancers or modifiers involved in processing of low strain test data and its implication on the final output. It also describes how the method can lead to abuse or can provide poor interpretation if incorrectly used. The current effort is to demonstrate that data collection and evaluation becomes complex with changes in soil stratum and pile profile. The paper highlights the present testing practices and provides a guideline for classification of pile integrity into few simple categories in Indian context rather than writing complex interpretations.

Sep 1, 2022

By Mohammed Faizal, Abdelmalek Bouazza

"The operation of ground source heat pumps combined with foundation piles can have an effect on the thermal behaviour of the pile and the surrounding soil. This paper presents the effects of continuous heating, continuous cooling, and alternate heating and cooling operations on ground and pile temperatures as well as the thermo-mechanical behaviour of a field scale energy pile. The effect of pile operation on the ground temperatures is highest near the pile and reduces with increasing radial distance. The results of the present studies generally showed that the thermal elasticity of the pile is not affected.INTRODUCTIONGeothermal energy piles are foundation piles used as underground heat exchangers to maintain thermal comfort in buildings, via the use of ground source heat pumps (GSHPs). Ground source heat pumps are more economical and environmental friendly compared to conventional heat pumps. Energy piles can be combined with supplemental surface heaters or coolers, known as hybrid systems, for forcefully recharging the ground during non-operational times of the GSHP. Alternative heating and cooling of the GSHP improves geothermal energy usage and alleviates heat build-up in the ground and provides a balance of ground temperatures around the heat exchanger (Jalaluddin and Miyara, 2012).The temperatures induced in the piles during GSHP operation can lead to a complex response of thermal strains and stresses in the pile concrete. An assessment of the thermo-mechanical response of energy piles for various thermal loads may assist engineers in the design process. Furthermore, an assessment of ground temperatures will also highlight any potential thermal interactions with other energy piles in actual building operations.At present, the thermal strain and stress distribution in field scale energy piles has mostly been studied for continuous operation (Laloui et al., 2006; Bourne-Webb et al., 2009; McCartney and Murphy, 2012; Akrouch et al., 2014; Mimouni, 2014; Murphy and McCartney, 2014; Murphy et al., 2014; Wang et al., 2015). These studies have contributed considerably to the understanding of the axial thermal strain and stress distributions in the piles and have shown that pile thermal behaviour is mostly thermo-elastic without inducing major structural concerns.The present paper adds to the current knowledge by assessing the pile thermo-mechanical and ground thermal response for continuous and alternating thermal loads of a field scale energy pile. The operation modes studied are 24 hours continuous cooling (Faizal et al., 2015), 24 hours continuous heating, (Wang et al., 2015) and alternate heating and cooling operation (Faizal and Bouazza, 2016). The forced ground thermal recharging is done during the non-operating times of the cooling unit, simulating a solar hybrid GSHP system for a scheduled intermittent mode of operation."

Jan 1, 1900

By Albert Neumann, Franz-Werner Gerressen, Giancarlo Santarelli

"Diaphragm walls are known as underground structural elements commonly used for retention systems and permanent foundation walls or elements. In addition they are also quite often used as deep groundwater barriers, named Cut-Off-Walls (COW). Due to the requirements of each particular job site, e.g. the need for carrying high loads or as seepage barriers, there is an increasing industry demand for efficiently cutting into rock. Besides the removal of boulders, cutting through rock, is always the most difficult part of the excavation process of a diaphragm wall or COW.There are a number of influencing factors which have an impact on the rock cutting performance. Besides the influence of the rock characteristics itself, which is not always the same, there are other factors related to equipment, tooling as well as the operating staff. In addition to RQD, the most commonly available rock property found in geotechnical reports is the Unconfined Compressive Strength (UCS) value. There are however some other related properties, such as weathering, bedding, inclination, abrasiveness, etc.,which can have a major impact on the achievable cutting performance. This paper will discuss the various parameters, and how they can be considered for performance estimation. Based on experiences gained on over 100 projects, a performance estimation chart was developed to allow for a better approach to these kinds of projects. This paper also explains the general installation process in as well as some specific features related to specific site conditions. In addition, some job site references will give more detailed information about such type of site conditions and how to deal with them.Keywords: Diaphragm wall, Cut-Off-Wall, Trench Cutter, RockINTRODUCTIONDiaphragm walls are known as underground structural elements commonly used as retention systems for excavation pits, shafts, permanent foundation walls and load bearing elements.It can be anticipated that, with the increasing trend of utilizing more and more underground space to accommodate environmental considerations and urban/suburban development, there will be an increasing requirement for diaphragm wall usage in even more difficult conditions.In addition diaphragm walls can also be used as deep groundwater barriers (Cut-Off-Walls). This market has demonstrated that the demand for these types of walls is reaching ever more difficult soil conditions and greater depths which are surpassing the current industry standards. The trench cutter is the most important tool for performing this type of work."

Jan 1, 2016

By Don C. Warrington

This paper describes a new wave equation analysis program called ZWAVE, which is a program specifically for external combustion hammers. The program is de-scribed in detail, the discussion dealing with topics concerning the program such as 1) the numerical method the program uses to integrate the wave equation, which is different from most other wave equation programs; 2) the modelling process of both cushioned and cushionless hammers; 3) the automated generation of mass and spring values for both hammer and pile; 4) the method of dealing with plastic cushions; 5) the use of a recently developed model for computing shaft resistance during driving; 6) the computation and generation of values based on basic soil properties such as shear modulus, Poisson's Ratio and soil density; 7) the completely interactive method of feeding data to the program; 8) the method used to compute the anticipated rebound and the energy used to plastically deform the soil; and 9) the format of the inter-active input of the program and the program's output. Sample problems for the program, along with comparison of the program results with data gathered in the field, are presented.

Jan 1, 1988

By Joram M. Amir

During recent years, the integrity testing of piles has made considerable progress. With the availability of portable and powerful computers, practically all integrity testing equipment is now digital. Using sophisticated software for data acquisition and analysis, today's testing systems can provide owners with important information regarding both the length and integrity of piles and drilled shafts. This sophistication carries a price: Very few clients, including experienced engineers, do understand the strange-looking graphs adorning the reports they get. In fact, most of them will never ask, some because they are too busy to care and others because they are ashamed to show their ignorance. This situation is well exploited by a few shrewd operators of test equipment. Facing strong competition and falling revenues, they simplify their task and cut their expenses by the following means: 1. Using old equipment until it falls apart, and then some, 2. Hiring under-qualified personnel, 3. Staying on site as little as possible, 4. Eliminating the analysis and evaluation stage altogether, 5. Confirming as-made lengths and reporting no defects.

Jan 1, 1999

By G. W. Plant

This paper describes the design philosophy and construction details of piles between 25m and 32m deep to support 160m high and 110m base diameter cooling rowers for a major power station. It is sited on deep expansive soil where a vast plantation of Eucalypts had been felled. The depressed water table is expected to rise, leading to swell of the soil and uplift forces on the piles. These forces, combined with the complex loading from the cooling towers, led to design tensile loads up to 20MN (2 000 tons) per pile. When competent stable material was present hand excavated underreams 3m in diameter were constructed for the piles sup-porting the shells. However, in some areas it was not possible to form an effective underream and an innovative solution was sought. This comprised unstressed dowels in the underlying sandstone which were formed by percussion drilling through void formers cast into the piles.

Jan 1, 2010

By Roberto A. Lopez, Eric Lindquist, Jon Bussiere, Dean Iwasa

"The new 11-story U.S. Federal Courthouse building in downtown Los Angeles demanded a cost effective foundation system capable of attaining a strict total settlement criterion of 0.5 inches (12 mm) under high applied loads. A design-build ground improvement system consisting of 3 ft (0.9 m) and 7 ft (2.1 m) diameter deep soil mix (DSM) columns embedded into the relatively soft Fernando Formation bedrock was selected for the project. The DSM columns support applied stresses of up to 8,800 psf from four large concrete core elements that transfer concentrated building loads to a 3 to 6 ft (0.9 to 1.8 m) thick reinforced concrete mat. The soil mixing ground improvement solution provided flexibility by allowing installation of the DSM columns around existing belled caissons left in place from prior structures, and by allowing repositioning of some of the DSM columns to avoid other existing obstructions in the fill. DSM spoils were used to construct a 2 ft (0.6 m) thick load transfer platform on top of the DSM columns. Quality control measures included utilizing equipment outfitted with automated data acquisition systems, performing three full scale load tests, performing daily wet-mix sampling and compression testing, performing full-depth coring and unconfined compression testing on core samples, and using a borehole acoustic televiewer to evaluate the uniformity of the DSM columns where core recovery was problematic. The results of subsurface investigation and the load tests were used to develop 3-dimensional finite differences models for evaluating stress distribution and deformation of the foundation system.INTRODUCTIONThe new U.S. Federal Courthouse building is currently under construction in downtown Los Angeles, California. The new courthouse will be 11 stories tall with one partial below-grade B1 basement level. The building will have four structural core elements that extend from the main building foundation at the B1 level to the top of the structure. The majority of the building loads will be transferred through the structural core elements to a new 3 to 6 ft (0.9 to 1.8 m) thick reinforced concrete mat beneath the central portion of the structure. The foundation pressures beneath each of the core element locations will be approximately 6,200 to 8,800 psf (300 to 420 kPa) with lower foundation pressures at locations farther away from the central core area."

Jan 1, 2015

By Eric Lindquist, John Compagnone, Gabriel Carvajal

"Condon-Johnson & Associates, Inc. (CJA) with the assistance of design consultant, Brierley Associates, designed and installed a water tight shoring system utilizing several ground improvement techniques jointly. Prior to the installation of the shoring system, a test program consisting of the installation and testing of 7 jet grout columns; 1 soil mix panel; 7 soil anchors and 3 tie downs was performed to verify design assumptions. State-of-the-art quality control measures were employed throughout the project.The shoring system consisted of:•,Deep Soil Mixing (DSM) wall utilizing triple axis tooling to install overlapping columns along the perimeter of the proposed excavation to a treatment depth of 54 feet.•,Installation of steel piles in DSM to provide rigidity to the wall.•,Installation of a jet grout bottom seal, installed from surface to a depth of 58 feet below existing grade.•,Installation of 153 soil anchors, 1-1/4” diameter and 47’-6” length, to tie the jet grout bottom seal to the native soil below to resist hydrostatic uplift, installed from existing grade to a depth of 91 feet.•,Installation of walers and pipe struts for internal bracing•,Installation and stressing of 117 tie downs, 1” diameter and 16 ft length, to tie the pump station mat slab to the jet grout bottom seal, installed from inside the excavated pit.Subsurface conditions at the site consist of uncontrolled fill materials to a depth of 20 feet comprised of sandy silt and clayey sand. The native soils underlying the fill generally consist of soft and compressible lean clay and silt with varying amounts of sands to a depth ranging from approximately 44 to 54 feet below ground surface, which in turn are underlain by dense to very dense silty sand. The groundwater elevation at the site is approximately 8 feet below ground surface.This paper covers the design aspects, construction, and quality control measures undertaken by the geotechnical contractor, with supporting figures.INTRODUCTIONThe owner, County Sanitation District No. 2 of Los Angeles County, designed upgrades to their existing Long Beach Main Pumping Plant Facility. The upgrades consist of a new pump station that includes a reinforced concrete below-grade wet well and dry well, a two-story operations building, two 78-inch diameter pipe inlets, two 42-inch diameter discharge pipelines connecting the existing manifold, two pipe junction structures, two insert-type junction structures, and electrical transformers. This paper focuses on the excavation shoring for the new pump station. The original shoring design concept for the pump station excavation illustrated on the contract plans consisted of pressed in sheet piles, a jet grouted bottom seal with soil anchors, 2 levels of internal bracing, and tie-down anchors to resist hydraulic uplift forces on the buried pump station."

Jan 1, 2017

By Gokhan Inci

Stability problems with dam spillways on existing landslides and appropriate mitigation measures to remedy them are ongoing concerns for geotechnical engineers. The first successful application of drilled piers as stabilizing structures under the spillway was at the Trinity Dam in Sicily, Italy. ?Underpinning? was considered as an alternative to spillway relocation during the Alpaslan 2 embankment dam design in eastern Turkey. Based on the available literature the first application of drilled piers to stabilize a spillway chute in the U.S. was at the Ralston Dam in Colorado. Ralston Dam, which is a 175-foot-high zoned fill dam located 15 miles northwest of downtown Denver, was built in the late 1930s. The concrete spillway for the dam was built on the Pierre Shale Formation in the left abutment. Since reservoir operations began, mass movements have occurred downstream of the chute area. These movements have required periodic spillway maintenance. After the occurrence of recent movements and because of high piezometeric levels, URS was contracted by Denver Water to develop a more permanent solution by the installation and monitoring of additional instrumentation, analysis of slope stabilizing measures, design, repair, and reconstruction of the distressed section of the spillway chute. With state of the art modifications that include: 1) a stabilizing berm with a toe trench that improves the global stability; 2) seepage prevention and control measures that prevent the infiltration of water; and 3) the structural support of the replaced chute section with drilled piers and reinforced concrete the probability of future displacements or other problems have been reduced for the Ralston Dam Spillway.

Jan 1, 2007

By E. W. Raabe

The paper discusses the increasing role of specialist grouting techniques to form water seals or cut-offs for deep basement construction. Raabe and Toth discuss the various grouting methods available for sealing applications and then concentrate on the use of Soilcrete Jet Grouting, a system particularly well suited to ground water control. The Soilcrete processes, suitable soil types and quality control methods are fully described, particularly with regard to the formation of cut-off walls and sealing slabs to prevent the progress of ground water or leachates. The authors have included case histories detailing their experience on designing and installing Soilcrete seals for various projects in West Germany. These include an underground rail project in Dortmund and a discharge structure for the Alz Canal at Burghausen.

Jan 1, 1989

By Garland Likins

High strain PDA testing has become common for verification of capacity of both driven and bored piles. It is equally applicable to Augered-Cast-in-Place (ACIP) Piles. It also evaluates other aspects of the installation such as integrity. The benefit of high strain dynamic test results for the relatively low cost of the tests compared to conventional static testing has resulted in widespread use. The method is described and specific procedures for testing ACIP piles are outlined. Example results demonstrate the application.

Jan 1, 2000

By Gregory M. Landry

"There is an old joke at Moretrench that defines dewatering as “that element of an underground construction project, which, when disregarded, will generate the low bidder.” Sigmund Freud wrote that all jokes are true, and the kernel of truth behind this one is that dewatering is often misunderstood or neglected until the last possible moment in the life of a project. The purpose of this article is to describe commonly used dewatering methods and to clear up a pervasive but fundamental misunderstanding about how to determine the amount of dewatering effort required for a project. The Tools of DewateringDewatering may be divided into two broad categories: (1) methods that remove water from the excavation after it has already entered and (2) methods that seek to exclude or intercept the water before it reaches the excavation. The former is generally self-performed by general or earth moving contractors using sumps and ditches, while the latter is usually done by a specialty contractor. SumpsProperly installed sumps can be an effective and economical way to control water inflow into a site. In this technique, groundwater is allowed to enter the site before being pumped away. Advantages of this method include lost cost, easy availability of equipment and the fact that a general contractor can self-perform the dewatering. However, caution should be used when deciding whether to use this method, and consideration should be given to the following factors:1. How will the soil behave under seepage forces? Will it run, potentially causing ground loss?2. How much groundwater lowering is required? If the groundwater only needs to be lowered a few feet, using sumps will be much more practical than for a situation that requires significant drawdown.3. Will the excavation subgrade soften or otherwise be damaged by allowing water to run over it?4. Is my workforce skilled enough to implement and manage the sumping plan?In the photo, the sump is capturing groundwater that has already entered the excavation by traveling under the sheets. In this instance, the house in the background of the photo was eventually purchased by the project owner after sustaining damage due to ground loss."

Jan 1, 2017

By Frank Haehnig

Ground freezing is a technique which is used more and more in tunnelling under complex ground conditions. This paper will present three case studies which highlight different aspects of the ground freezing technique when applied in urban environment. The first project is the City-Tunnel in Leipzig, Germany, which is being built beneath the central station and which is the largest ground freezing project currently under construction in Germany. The second case study is part of the North-South-Line project in Amsterdam, Netherlands where ground freezing will be carried out to al-low the TBM drive through old wooden foundation piles. The freeze tubes for this project will be driven using Horizontal Directional Drilling (HDD). The last project is the Hallandsas Tunnel Sweden where the ground freezing equipment has to be installed against high water pressure. The paper illustrates that ground freezing can be implemented in difficult ground conditions such as soft ground, highly fractured rock and high water pressure. The case studies highlight the importance of good workmanship. With the increasing numbers of large tunnels being constructed in difficult ground conditions the paper concludes that the complex case studies presented will be-come more representative for future tunnel projects in urban environments.

Jan 1, 2008

By Michael T. Lambert

The purpose of the this paper is to demonstrate the benefits of using additional instrumentation during load tests of auger-cast-in-place piles. Traditionally, only load and butt displacement are determined during load tests. The results from and methods used to instrument 15 auger-cast-in-place (ACEP) piles as part of six projects are included herein. By instrumenting the piles, the distribution of load along the pile length and load transfer can be determined, allowing the pile capacity to be adjusted or the length/diameter of the pile to be adjusted for the a given required load. The majority of the piles tested were designed as end bearing piles on either shale or limestone bedrock. No discussion of Geotechnical Instrumentation can be started without acknowledgement of the "Red Book." The actual title of the book is Geotechnical Instrumentation for Monitoring Field Performance, by Mr. John Dunnicliff, John Wiley and Sons, 1993. Anyone undertaking an instrumentation program should thoroughly review the Red Book, paying particular attention to Chapters 3 and 4. Instrumentation should not be done just because it can be done. There must be an unanswered question or questions that can be answered with measured data before instrumentation should be considered.

Jan 1, 2000

By Michael W. Oakland

Weidlinger Associates was retained to evaluate the foundations supporting ten oil storage tanks at a tank farm on the east coast. The tanks were constructed over the site of a landfill which was underlain by deep organic deposits. The tanks were typically 48 ft. in height and ranged in diameter from 60 to 150 ft. The tanks were supported on both wood and steel pipe piles. After more than 35 years of service, an inspection found that up to 25 percent of the piles had separated from the mat foundation. The operations at the facility were temporarily stopped pending further investigation. Weidlinger developed comprehensive finite element models of the foundations for each tank and used random generators to conduct Monte Carlo simulations the range of scenarios of detached support conditions since it was not possible to survey all the piles below the tanks. To confirm the modeled performance and verify stability, each tank was also load tested using water with electronic instrumentation installed by Geo-Instruments. The instrumentation provided real time, web based monitoring during testing in areas which would otherwise be inaccessible during loading. Through inspection, complex modeling and sophisticated load testing, Weidlinger and Geo-Instruments were able to show that all but one of the tanks could safely be put back into service. This paper details the analysis, Monte Carlo simulations and instrumentation and load testing performed for this unique project.

Jan 1, 2009

By Ed Kase

Cross-hole sonic logging (CSL) has become the universal standard, nondestructive testing (NDT) method used in evaluating the integrity of foundation structures to maintain quality assurance and quality control (QA/QC) of transportation facilities and infrastructures. Tomography, based on three-dimensional cross-hole sonic logging data processing technology, offers an improvement over the techniques currently used to characterize the interior structure of drilled shafts. The underlying concept for seismic tomography is based on the principle that acoustic waves propagate at different velocities through different types of material or the same material with different physical properties. Three-dimensional velocity tomographic images provide greater detail of the interior structure, making defects easier to classify with respect to size and location within the foundation structure. By accurately classifying these defects, an engineer has the information necessary to accurately assess whether these structures meet the applicable design requirements, allowing them to repair or replace inadequate foundation structures. The end result is that the foundation structures will meet the safety and service life requirements for their project. This paper will present applications of seismic tomography, illustrating how seismic imaging can provide accurate information regarding the integrity of foundation structures.

Jan 1, 2003

By C. O. Riggs

Geotechnical exploration in North America, in particular, exploration for deep foundations analyses, is currently and generally performed following the most basic sampling and insitu testing methods and techniques. Some would surely say that the state-of-practice severely lags the state-of-the-art. Probably more than 90% of all deep foundations, both driven piles and drilled piers, installed in North America are initially analyzed and designed, i. e. geotechnically, on the basis of either the soil penetration resistance obtained by performing the "Standard Penetration Test" (SPT), or from laboratory shear tests performed on samples obtained using 76-mm (3-in.) nominal diameter, thin wall, "Shelby tube" samplers. The use of design data obtained with other exploration methods and devices, such as bore hole pressure meters, flat plate dilatometers, even cone penetrometers, occur on the fringes of practice and often in conjunction with the use of the two simpler methods of analysis. This basic approach probably represents an attempt of the profession to use, as much as possible, common, easily understood and easily communicated procedures in all geologic environments. The characteristics of drill rigs with the required drilling and samplng tools vary somewhat from region to region in North America according to the physiography of the area of use, the types of exploration data required on a day-to-day basis, the philosophy of the engineers and geologists that use the exploration data and the financial resources of the drill rig owner. The physical capability of the exploration drill rig used on a project can have a significant effect on the quality of samples or insitu tests. The physical configuration and the quality of the drill and the drilling, sampling and testing tools not only provide the mechanical capability to obtain data but affect the attitude of the field exploration crew and the quality of work. This complete presentation is taken, for the most part, from a book in preparation for publication: "Geotechnical Exploration and Site Characterization" by C. Riggs, A. Hatheway and N. Schmidt. The book is scheduled for completion during 1987.

Jan 1, 2010

By K. E. Darnell

Drilled pier foundations have long been a favored foundation type for heavily loaded structures. Drilled piers derive their load-bearing capacity from end-bearing, and/or sidewall friction. This type of foundation is used in many geologic settings, including those areas underlain by hard carbonate rock, such as limestones and dolomites. When properly designed and constructed, drilled piers provide high load-carrying capacity in both compression and uplift. However, carbonate rock is often subject to intense differential weathering resulting in the formation of an irregular bedrock surface, sinkholes and caves; consequently, the investigation for, and the design of, drilled pier foundations is often complex. Further, the construction may be difficult and costly. This paper discusses geotechnical investigative procedures which can be employed to develop foundation design criteria and reduce the frequency of changed conditions. Finally, state-of-the-art construction practices and quality control techniques are discussed.

Jan 1, 2010

By T. G. Davies

The paper presents design equations for singly laterally loaded piles embedded in sand. These equations were obtained from a comprehensive nonlinear analysis of free and fixed head piles subjected to horizontal loads. The sand is modelled as an elastic-perfectly plastic material whose strength and stiffness are proportional to depth below ground level. The soil's response is described by means of a boundary element representation of the continuum while the pile itself is created as an elastic beam. Equations for the latter are derived directly from the Bernoulli-Euler theory and are coupled with those describing the non-linear soil response. The effects of bearing failure along the front, face of the pile, shear failure along its sides and tension failure at the back face are accounted for in the analysis. Simple equations are presented to describe both the elastic and inelastic responses. The only sol parameters required to use these equations are the angle of internal friction of the sand and a parameter characterizing the rate of increase of the sand's modulus with depth. The latter can be taken as equivalent to the modulus of subgrade reaction. The results of this analysis show that soil yielding is very significant at working load levels, resulting in substantial increase in bending moments and lateral deflection.

Jan 1, 2010