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By António A. Henriques, António Gomes Correia, Ana Teixeira

"Abstract Pile foundations are often used for important structures, and thus, reliability evaluation is an important aspect of the design. Reliability methods have become increasingly important as decision support tools in different areas. The main benefit of reliability analysis is that it provides quantitative information about the parameters (uncertainties) that most significantly influence the behaviour under study. In particular, the design of pile foundations still involves many limitations and uncertainties, particularly when there is not enough investment in soil characterisation and/or pile load tests. In addition to the uncertainties associated with soil characterisation, physical, statistical, spatial and human uncertainties exist. In this subject, the primary purpose of this paper is to demonstrate the application of reliability methods to geotechnical pile design (axial load). It also presents a simple and practical approach to performing it using Monte Carlo Simulations, intending to provide knowledge for code harmonisation and encouraging the development of such methodologies in geotechnical practice. Sensitivity analyses are shown to understand the influence of each uncertainty type coming from different sources. An application example indicates, corroborating other studies, that the model error is the most influent uncertainty. As such, when using the different models (SPT-, CPT- and PMT-based) for bearing capacity, the results emphasise the need for a well-defined and wellcharacterised resistance model, also these results allow the engineer to understand how important the load tests can be to achieve reliable results and economic designs.1 IntroductionUnlike the approach to reliability evaluation used in structural engineering, the traditional procedure used in geotechnical designs addresses uncertainties through high global or partial safety factors (SF), mostly based on past experience. However, this approach to addressing uncertainties does not provide a rational basis for understanding their influence on design.Furthermore, the new regulation codes and social concerns, such as the sustainability or the economy, are imposing geotechnical engineers to increase their ability to deal with uncertainty in a direct and more rational way. Designs should be economic, sustainable and reliable at the same time. Concerning the reliability part of design, different approaches can be done, but the most important thing to keep in mind is the simplicity and efficiency of the tools and applied methods."

Jan 1, 2014

By Jose L. Garcia

The following document aims to cover all issues concerning the three main methods employed for the in-situ survey of concrete pile integrity. Within it are described both sonic coring and low-strain tests and the frequency and time domain analysis of their results, which are the most advanced techniques currently in use in Spain. The survey techniques described were developed and began worldwide deployment in the 1960s, but it was not until the 1980s that they saw large scale implementation in Spain, largely thanks to the miniaturisation of electronics and computer equipment that made them easier to use on-site. Sonic coring, echo and frequency-response testing or mechanical impedance tests are spreading further every day. However, there appears to be a need for standardisation of the testing methods, as well as their implementation, interpretation and the presentation of results. The goal of these Spanish recommendations is to serve as a guideline for test standards and to provide examples for a correct and commonly agreed interpretation of test results, as well as settling any differences in the evaluation of defects detected in foundation works.

Jan 1, 2006

By J. Pei

The studies of dynamic measurements using stress wave theory has commenced in China. This paper introduces some practical experiences using "CASE method" in Shanghai showing applications of dynamic measurement to determine ultimate bearing capacity of pile, the change of capacity due to set up, determining the optimum bearing layer during pile driving, the efficiency of hammer system and integrity of pile and discussions of method concered.

Jan 1, 2010

By Chu E. Ho

Key variables that govern the jet cutting process are examined based on fundamental theories of jet hydrodynamics and soil mechanics. Under normal conditions of jet grouting operations, lift speed and rotation speed are found to be of less importance than the depth of jetting, nozzle pressure, nozzle diameter, and the soil bearing resistance, with regards to their influence on jet cutting distance. An analytical equation linking the governing variables is proposed, which allows for the possibility of evaluating column diameters achievable in different ground conditions based on theoretical calculations. When used in conjunction with shallow jet grouting field trials, the equation can provide a means for extrapolating trial results to conditions at actual depths for production jet grouting.

Jan 1, 2006

By Van E. Komurka

This paper presents a cost comparison of the driven pile foundations for two large Wisconsin Department of Transportation (?WisDOT?) projects in Milwaukee, Wisconsin: the Marquette Interchange South Leg, and the Canal Street Viaduct. The projects? geology is fairly similar, but their methods/approaches to pile foundation design and installation differ. Although the Marquette Interchange South Leg had deeper poor soils, its pile design was more-cost-effective than the Canal Street Viaduct?s. Potential reasons for cost differences between the projects are identified, and the effect of the different design and construction approaches on economics is discussed.

Jan 1, 2009

By Balu E. George, Subhadeep Banerjee, Shailesh R. Gandhi

"A three-dimensional analysis of laterally loaded helical piles installed in cohesionless soil is presented. Finite Element Analysis was conducted using commercially available Plaxis 3D AE version, assuming Mohr-Coulomb failure for soil. Pile is modelled as plate elements with a single helical blade attached to a hollow shaft. The ultimate load for various configurations is examined considering deformation criteria. The Bending Moment distribution and maximum lateral deflection are also discussed. It was observed that the ultimate lateral load carrying capacity increased by presence of helical blade and the maximum deflection also got reduced. The diameter of the helical blade was found to have significant effect on the lateral deflection, maximum bending moment and the ultimate load. However, the observations from the study suggest that the presence of helical blade seizes to produce considerable effect after a certain depth. Difference in failure pattern with regard to the distribution of soil resistance observed for different geometries considered for numerical analysis are also touched upon.INTRODUCTIONHelical piles or screw anchor piles have gained popularity due to fast installation, instant use, and other advantages over the traditional piles. They are usually used to support structures like solar panels, light houses, and other light structures which are subjected to uplift loads. However, such structures are often subjected to significant lateral loads as well. Under lateral loads, the response of helical piles can be different from that of a conventional pile due to the presence of the bearing provided by the helical blade. However, the proper design remains a concern due to lack of work carried out on the lateral capacity of helical piles.The lateral performance of helical piles is significant because they can act as efficient alternative to conventional piling systems in many applications.The lateral load capacity of screw anchor piles with different number of helices were examined by Mittal et al. (2010) by experiments in sand. They found that the lateral load capacity of piles increases with addition of helical blades. Prasad and Rao (1996) examined the lateral capacity of helical piles in clay by experiments on model piles and found that the lateral capacity of helical piles were more than that of the straight shaft piles. It was observed that the lateral capacity increase with embedment depth and shear strength of soil. Sakr (2009) studied lateral performance of two section helical piles in soft soil. The investigation by Prasad and Chari (1999) reported that the pressure distribution across the diameter is not uniform for circular piles, but it is maximum at the centre and almost zero at the two edges.Puri et al. (1984) after conducting model tests on single-helix, two-helix, and three-helix anchors installed in sand, proposed a mathematical model that was fashioned after Matlock and Reese’s elastic theory model. Elkasabgy and Naggar (2015) investigated he lateral performance of full scale large capacity helical piles in structured cohesive soils and reported the modulus of sub-grade reaction to be non linear."

Jan 1, 2017

By Timothy D. Stark

Jet grouting has increasingly become a ground improvement technology used to address seepage concerns and provide strength improvement to soils underlying dams. The technique of jet grouting uses high pressure/volume jet fluids to erode existing soil, evacuate some or most of the soil, and mix the remaining cuttings with cement slurry to form soilcrete. While considered a useful technology, this paper discusses some of the problems that can develop while jet grouting in or below a dam with an operational reservoir and seepage condition. Jet grouting experience at Tuttle Creek Dam indicates concerns with respect to ground fracture; spoil return, column diameter consistency, and homogeneity of resulting soilcrete. Recommendations are presented to increase monitoring of downhole parameters during jet grouting to better understand the downhole pressures and soil response during jet grouting.

Jan 1, 2012

By Y. Duraisamy

This paper presents the compressibility of tropical peat reinforced with cylindrical cement column. When a cement column installed vertically in peat, its compressibility was reduced because of the hardened skeleton matrix formed by cement particles bonding with adjacent soil particles in the presence of pore water. The effects of diameter, number of columns and cement proportions in cement columns on the compressibility have been investigated in this study. The results indicated that compressibility index Cc and Ca decreased with the increase in diameter of the cement column. Specimens with 45 mm and 60 mm diameter of cement column were cured for 28 days, after which they were subjected to Rowe Cell Consolidation test. Based on the results obtained, it shows that cement columns can successfully reduce the compressibility of tropical peat.

Jan 1, 2007

By Nuno Cruz, Saúl Rodríguez

"When executing offshore bored piles there are several specific factors and problems to consider in order to guarantee excavation stability. One of the methods employed to carry out this type of work consists in setting up a floating work platform, typically a barge, and implementing a soil stabilization system that combines a partial steel guiding casing with third generation polymeric drilling fluids. The main aspects to take into consideration when performing offshore pile boring works are soil stabilization, project design, work methodology and operational aspects. An example of a work methodology problem arises before any pile boring work takes place as the steel guiding casing contains water, sometimes salt water. What to do with this water in order to replace it by an adequate polymer fluid will determine the stabilization capacity as soon as the shaft advances below the protection of the casing. Another example of operational problem may derive from barge movements while executing boring activities. This study is the result of extensive field data collection and concrete logging analysis from marine projects using polymers in different continents. The bored pile stability target was set ranging between 2% to 15% of concrete overbreak. Values above 15% or below 2% mean that there is a stability problem. Then the off-target pile’s data is collected, analyzed and classified under categories. Thus, a direct correlation is established between the problem category and the final results. Modifying steps in the pre-established construction methods or operational variables guarantees target results without the need to replace the approved construction methods. As a general conclusion, the worldwide experience in large diameter marine works, allows to provide truthful information and solutions for these problems. In knowing how to follow a logical sequence of work and applying adequate work methodology will be the key for success.GENERALBackgroundTo carry out the drilling process of offshore bored piles there are two main options to take into consideration: drilling the pile by using full guiding casing until final depth; or using a combined system of partial steel guiding casing and support drilling fluids.The knowledge and situations described in this paper come from the experience acquired in different projects where the second method was employed. This construction method consists in installing a steel guiding casing by vibration and thus covering the water table and further stabilizing the soil below it with polymeric fluids until reaching the pile’s final depth. The Fig. 1 schematic shows an example of this method where H corresponds to the length of the steel guiding casing whereas the remainder of the shaft’s length is stabilized by polymer fluid. The entire bored length is full of slurry up to top of casing.In most cases this kind of civil works results from the need to build a bridge or executing port structures in places where the creation of temporary artificial peninsulas with fill material is impracticable or not allowed. Hence the need to use floating work platforms, commonly referred to as barges."

Jan 1, 2017

By Carlos Lam, Joram M. Amir, Erez I. Amir

"Abstract The modulus of elasticity of pile material (E) is an important parameter for the interpretation of both static and dynamic loading tests on piles. This value is commonly assumed to be constant with depth though it may not be true for deep bored piles due to the chosen casting method and/or selfweight consolidation. To provide evidence to support this proposition, the results of compressive strength tests on core samples taken from four different studies have been presented. The results show a marked increase in the strength and stiffness values with depth. The results of crosshole ultrasonic tests conducted at another site also confirm the same pattern. It is therefore recommended that before load testing a pile the distribution of the E values along the pile axis should be investigated. This will ensure the use of a realistic elastic modulus value and hence the correct interpretation of thedistribution between the shaft and end resistances.IntroductionThe modulus of elasticity of pile material (E) is an important parameter for the interpretation of both static and dynamic load tests on piles. Multiplying E by the strain measured by either strain gauges (e.g. ASTM D4945) or tell-tales (e.g. Geffen and Amir, 1971) gives the stresses acting at a given pile section. Typically, in the absence of better information, the value of E is derived from laboratory tests on concrete cubes or cylinder specimens taken on site and is assumed to be constant along the pile. While this may be correct for pre-fabricated concrete piles that are cast in horizontal molds, it may not be true for cast-in-place piles that are produced in the vertical position.There are at least two factors that may contribute to the change in concrete properties with depth in a bored pile. First, the casting methods may be by free fall in dry holes (e.g. Kiefer and Baker, 1994) or by using a tremie tube if support fluids are used. In the former case, the earlier batches reach the bottom of the pile bore at a higher velocity and are thus compacted under higher energy. Second, regardless of the casting method, the fresh concrete in the pile bore will always consolidate at least partially under its own self weight. The materials in the lower parts of the pile will therefore experience a higher consolidating pressure. This can reduce the pore volume and the water content in the wet concrete, thus changing the properties of the hardened concrete. Recent research by Justs et al. (2011) has shown that even a relatively small pressure can have a significant positive effect on concrete properties such as compressive strength and stiffness. However, the possible change of concrete properties with depth is commonly ignored by foundation engineers in the current design practice."

Jan 1, 2014

By M. B. Wechsler

An analysis is developed for determining the maximum loading, as well as the potential uplift of the piles on bridge pier foundations. There are considered piers supported on two through seven rows of piles, and related to two simply supported collinear superstructures of any structural material. The study leads to different types of influence lines for various load combinations. For load combinations containing vertical loads only, the related influence lines are similar to those as for the bending moments of a virtual span covering the two actual spans, as well as the gap between the two superstructures; and, in this case, the heavier loads should be positioned in the vicinity of the pier. While, in the case when vertical loads are acting together with hori­zontal forces, the related influence lines will indicate where the heavier live loads should be positioned. And they will also indicate on which portions of the spans the live load should be avoided.

Jan 1, 1989

By Y. Z. Xu

This paper presents a new dynamic method called Resonant Pile Test (HPT) for evaluating bearing capacity of pile. The basic conception of RPT is given in brief and the measuring system is also introduced. In addition, the influences of the magnitude of exciting force and of the mass of pile cap on test results are discussed. Finally, comparisons between values of bearing capacity given by RPT and by static load tests for a variety of pile types are listed.

Jan 1, 2010

By Sanket Rawat, Ravi Kant Mittal, Vikash Prasad

"The understanding of the response of pile foundations under various types of loads is a necessary prerequisite to analyze and design them properly. Therefore, this paper highlights and compares the provisions available in Indian Standard IS 2911:2010 to estimate the capacity of laterally loaded pile foundation with the provisions available in different country codes and existing literature. Comparisons are made between the Indian standard method, Broms method and Matlock & Reese method for the analysis of laterally loaded piles due to popularity and prevalence of the later methods in design offices worldwide. This has been achieved using a parametric study on pile embedded in pre-consolidated clay and sand for both fixed head and free head case in terms of displacement and ultimate load capacity. It has been found that there are various limitations to the Indian Standard method associated with various cases such as short pile analysis, complete moment distribution etc. Therefore, suitable recommendations have been made on the basis of the above comparison to improve the accuracy of the design in Indian perspective. The proposed comparison and subsequent area of improvements will present the design engineers all across the globe, a broad sight of design specifications of laterally loaded piles.INTRODUCTIONPiles in groups are very often subjected to both axial and lateral loads. In the 1960’s, designers used to assume that the piles could carry only axial loads and the lateral load is to be carried by batter piles. However, later, a large number of load tests authenticated that vertical piles also can transfer lateral loads through shear, bending, and lateral soil resistance rather than purely acting as axially loaded members. Initial attempts to analyze laterally loaded piles used the finite-difference method, as described by Howe (1955), Matlock and Reese (1960), and Bowles (1968). Matlock and Reese (1956) used the finite difference method to get a series of non-dimensional curves to enable the user to input the appropriate curve with the given lateral load and estimate the ground-line deflection and maximum bending moment in the pile shaft. Later, Matlock and Reese (1960) extended the earlier curves to include selected variations of soil modulus with depth."

Jan 1, 2017

By Derek Egan

"Abstract Construction clients want their foundation solutions to be right first time, every time; but it is often the geotechnical contractor who carries the most risk in achieving this. Robust validation to ensure that the installed geotechnical product is appropriate for the encountered ground conditions, will perform as required and be correctly measured for payment and record purposes is very important to minimise the contractor’s and the client’s risk. This paper outlines the development and operation of a robust real-time installation monitoring system which controls and validates the installation of driven cast in-situ (DCIS) piling. Using state of the art information technology the system allows the design engineer to interrogate the data acquired from the piling rig via his computer as the piles are completed. The use of the validation process, where data acquired during the driving of DCIS piles can be processed to estimate the finished pile performance, will be explained with reference to a new case study on large diameter DCIS piles. Examples of the routine use of the system will be presented to illustrate how automated monitoring of installation parameters can be used to raise the standard of reliability, efficiency and sustainability on piling projects. The conclusions to the paper will cover the key features and operational challenges characterising real-time monitoring of the execution of geotechnical works as developed from a number of years of experience of using a rig based data acquisition instrumentation system.INTRODUCTIONDriven Cast In-Situ (DCIS) piles have a long and successful history of use worldwide. The process, where a temporary steel drive tube, sealed at the bottom with a sacrificial base plate, is driven into the ground and filled with concrete before the tube is withdrawn, is well known (BS EN 12699, 2001 and Egan, 2013). Examples of large structures supported on DCIS piles installed by Keller UK include the Millennium Dome (now the O2 Arena) and the 2012 Olympic stadium in London.In recent times advances in piling rig instrumentation and telecommunications have enabled a new level of sophistication in the recording of installation parameters and the validation of pile performance. It is now possible to embed these features into the DCIS design and installation process which has improved the quality and efficiency of DCIS piling.This paper summarises the development and operation of a real time data acquisition and processing system for DCIS piling, but which is equally applicable to other forms of driven piling (for example concrete precast piling)."

Jan 1, 2014

By Vidyaranya Bandi, Madhav Madhira, Kota Vijay Kiran

"Using hyperbolic relationships for the non-linear responses of shaft and base resistances, a method is proposed for estimating initial shaft and base stiffnesses and ultimate shaft and base resistances of a pile from pile load test results. An iterative procedure is used to arrive at the values of shaft-soil and base stiffnesses and the ultimate shaft and base resistances. The method is applied to load - displacement data available from pile load test results to illustrate its efficacy.INTRODUCTIONA pile foundation is the most effective and economical solution in transferring large vertical loads to deeper depths. As the pile is subjected to axial load, the soil mass surrounding the pile is vital in providing vertical support for the pile. The nature of pile–soil interaction is three dimensional and to complicate the problem further, response of soil is nonlinear. Finding a closed form solution to such problem is extremely difficult. Several methods were developed to study and predict the response of the composite pile–soil system. Faruque and Desai (1982) implemented both numerical and geometric non-linearities in their three dimensional finite element model. Rajashree and Sitharam (2001) developed a nonlinear finite element model of batter piles under lateral loading using a hyperbolic relation for static load condition and modified hyperbolic relation, including degradation and gap for cyclic load condition.The ultimate capacity of the pile is estimated considering the strengths and unit weights of soil layers with depth, overburden pressure and other relevant parameters. The estimated capacities always need to be validated by conducting initial maintained load test. The estimated capacity may differ with the actual at site since the values of strength, stiffness, interface resistance between pile and soil, lateral earth pressure coefficient with depth and soil stratification, etc., differ from the design parameters considered for estimating the ultimate capacity of pile. The estimation of axial capacity of piles involves considerable uncertainties in selection of appropriate design parameters and the design rules are not always consistent with the installation procedures/processes involved."

Jan 1, 2017

By S. Narasimha Rao

Bored cast in situ piles are highly susceptible to construction defects like necking, discontinuity in concreting, poor compaction of concrete, improper end bearing condition due to inadequate cleaning of bore hole, exposure of reinforcement, segregation of concrete etc. There is a necessity to understand the behavior of piles so as to design effective foundation system. In this paper investigations of two field cases were discussed to bring out the effect of defective piles. In one case improper end bearing has been discussed for a concrete pile of length of 45m and diameter equal to 1.2 m and is reinforced with 32 no's of 28mm diameter steel bars and in another case necking of the pile has been discussed. Further model piles with preformed defects have been tested in laboratory to bring out the influence of defective piles.

Jan 1, 1996

By K. Rainer Massarsch, Bengt H. Fellenius

"Abstract Vibrations generated during the driving of piles or sheet piles can affect buildings or installations in the ground. However, observed building damage is not always caused directly by dynamic effects, but can also be related to foundation conditions. The importance of geotechnical conditions is usually not taken into consideration in most vibration standards. This paper describes how building foundations, and in particular mixed foundation types, are especially sensitive to ground vibrations. A method is presented for assessing the risk of settlement due to vibrations in granular soils. Also, a simple concept is proposed for estimating settlements in the vicinity of driven piles.1. INTRODUCTIONUnder unfavorable conditions, the installation of piles or sheet piles can cause damage to buildings or other structures on the ground. Frequently, such damage is attributed to vibrations of the building itself. In many countries, national or international standards are used to assess the risk of vibration damage to buildings. As such standards are often prepared by engineers with little or no geotechnical knowledge, the effects of ground conditions on vibration propagation and damage to building foundations are generally not recognized, and damage criteria based solely on the dynamic response of buildings neglect the importance of damage mechanisms governed by geotechnical conditions. One potentially important damage mechanism is differential settlement below buildings, especially when these are founded on loose granular soils. When seeking guidance in the literature, little or no information can be found regarding methods to assess permissible levels of ground vibrations with respect to risk for settlement.This paper focuses on building damage that can be attributed to foundation conditions. In the case of ground vibrations due to pile and sheet pile driving, differential settlements are of particular importance as the ground vibrations attenuate relatively rapidly from the source. Consequently, settlement below part of the building, which is located close to the vibration source, can be significantly larger than at a distance further away.Piles are often a cost-effective foundation solution for buildings on loose and compressible soil, frequently located in urbanized areas. Sheet piles are commonly used as support for deep excavations. While impact driving is most commonly used to install piles, vibrators are frequently used for driving (and extraction) of sheet piles. It is important to recognize the fundamental differences between impact and vibratory driving. During impact driving, the pile is subjected to stress waves of short duration. The driving process creates vibrations, which radiate from the shaft and/or the toe of the pile into the soil. The larger the intensity of the stress wave, the larger the dynamic force and the intensity of ground vibrations. In addition to the vibration intensity, which often is expressed in terms of particle velocity, also the vibration frequency is important. When the dominant frequencies of the generated vibrations harmonize with the resonance frequency of buildings or building elements, the risk of building damage increases."

Jan 1, 2014

By J. -M. Rescoussier

Due to Important settlements inducing major structural damages, the western part of the Grand Littoral shopping centre has been closed in 1997. The present paper describes the project of underpinning including not only micropiles under the structure of the building but also a reinforcement of the soil located between the shopping centre and the edge of the embankment surrounding the western part of the shopping centre. The aim of this reinforcement is to reduce existing horizontal movements to allowable values.

Jan 1, 2002

By Frederick C. Rhyner

Drilled shafts have become an economical foundation choice for bridges in the northeast United States, especially when they can be constructed over water without the use of cofferdams. For the Boscawen-Canterbury Bridge over the Merrimack River in New Hampshire, an unusual design was used to avoid the use of cofferdams and avoid the need for pier caps at the waterline. This design used a pair of integral drilled shaft ? columns to form a bent type of substructure for support. Drilled shafts were 8-foot diameter, about 90 feet deep, with 16-foot long rock sockets. These are integrally constructed with 6-foot diameter reinforced concrete columns extending 37 feet from the waterline to the superstructure. Design load cases focused on lateral loads from ice flows, stream flows, wind and seismic events. Alternative analyses using different methods were made to check the design results. This paper discusses the subsurface conditions, design of the drilled shafts and columns, rebar and joint detailing issues, and construction of the drilled shafts.

Jan 1, 2004

By Mostafa Mossaad, Ali Helwa, Manal Salem

Support of excavation (SOE) design practice tends to model SOE elements using two-dimensional (2D) analyses to avoid the complexity associated with three-dimensional (3D) analyses. Such practice overlooks soil arching in the horizontal plane and prevents designers from accounting for elements such as capping beams as part of the statical system. This study simulates square excavations supported by cantilever slurry walls in dry cohesionless soil using 2D and 3D finite element (FE) models. First, side support wall behavior is compared from 2D and 3D FE models for variable excavation length to depth (L/H) ratios. Second, the effect of slurry wall lateral bending stiffness on wall behavior is studied by modeling the wall using plate element with isotropic and anisotropic wall stiffness. Finally, the sensitivity of cantilever wall behavior to the presence of capping beam is illustrated. The study concludes that unbraced excavations with L/H ratios greater than 5 almost resemble plane-strain conditions. Slurry walls are better simulated in 3D FE models by dividing the plate element into discrete panels or by assigning anisotropic bending stiffness to the plate element. Finally, the presence of capping beam affects the behavior of cantilever walls resulting in reduction of deflections and redistribution of bending moments. INTRODCUTION Support of excavation (SOE) design practice ranges in complexity from conducting simple hand calculations to performing three dimensional numerical modeling depending on several factors among which is the geometry of the design problem. This paper addresses walls that are designed using numerical modeling, and discusses the factors governing the choice of the most suitable modeling approach. It has been believed for a while that modeling excavations using 2D numerical models would lead to a more conservative solution, which turned out to be incorrect in specific cases. This paper attempts to describe cases where 2D finite element modeling could be on the conservative side and other cases where it could be less conservative than the more complex 3D modeling.

Jan 1, 2018