Search Documents

By Paul Hewitt, Aaron Rastall

The New South Wales South Coast rail corridor is key infrastructure for both freight and passenger transport. Geomorphological and geological evidence suggests that land instability has been widespread throughout sections of the rail corridor, long before the first documented record of landslide activity in 1879. Major landslides occurred along a 25-km length of the South Coast Railway connecting Sydney and Wollongong because of significant rainfall events of the late 1980s. Since this time, several sites have been identified as subject to instability and treated progressively under a risk priority and safety management system. Two such sites comprise a station footbridge and overhead wiring structure (OHWS), both founded on high embankments overlying colluvial materials resulting in the structures’ potential movement and associated stability concerns. This paper presents these two sites as case studies, and discusses the project geology, geotechnical models developed, interpretation of monitoring data, and successful remediation of the rail structures using sleeved bored piles. The sleeved pile system was used to isolate bored piles, which separated the bridge foundations and OHWS from the moving soil mass to ensure the piles can carry the rail structure loads, unaffected by downslope soil movements.

Nov 1, 2022

By Sumit Kumar Biswas, Moyukh De, Sibapriya Mukherjee

"The piles often are also subjected to lateral (horizontal) forces and moments. In fact, there are some structures where the primary function of piles is to transfer lateral loads to the ground. Proper analysis of laterally loaded piles is very important to the geotechnical and civil engineering profession.In the present investigation an experimental study has been carried out with free head short model cast iron hollow piles of outer diameter of 24 mm and L/d ratios of 8, 10, and 15. The experimental results have been supplemented by numerical techniques using PLAXIS-3D Foundation version 2.1 software. The results have been found to agree reasonably well with the experimental results. Further finite difference approach has been adoptedto reduce the computational time and to calculate the coefficient of modulus of subgrade reaction (?h) from the load- deflection data obtained from PLAXIS output at different pile depths. The parametric study has been extended for the non-dimensional form defined as flexibility ratio (F.R.),where ?h, L, Ep and Ip are the coefficient of modulus of sub-grade reaction, the embeddedlength of model pile, elastic modulus of pile material and the moment of inertia of model pile about the central axis respectively).The variation of coefficient of horizontal modulus of sub-grade reaction (?h) has been studied with respect to the following parameters for homogeneous soil system: relative density andL/d ratio. It has been found that the logarithm of flexibility ratio increases with increase inrelative density and increase inL/d Ratio. The values of ?h obtained by the proposed method have been, found to be close to the numerical results.As output of this research, graphs have been generated in respect of different parametric variations to gain an insight into behavior of piles under lateral load for short piles."

Jan 1, 2015

By Flor De Cock

The paper reflects part of the work from the European Regional Technical Committee on Piles (ERTC3) during its mandate between 1994 and 1999, and, in particular, describes the find­ings from an International Seminar held in 1997 in Brussels on European practice for design­ing axially loaded piles. The seminar included contributions from 17 European countries, each of which provided a synopsis of their respective national design approaches. This paper pays particular attention to the design methods based on laboratory and in-situ test data for both bored and displacement piles.

Jan 1, 2002

By Aaron S. Bradshaw, Ryan M. Coulson

The offshore wind industry in the United States is slowly emerging with the recent construction of the first offshore wind farm located off the coast of Rhode Island. The turbines at the Block Island wind farm are supported by piled jacket structures, which historically have been used for much heavier oil and gas platforms. Offshore wind turbines have unique design requirements and the axial behavior of the supporting piles under cyclic loading is important to design. Cyclic degradation along the pile shaft can affect the capacity, deformation, and stiffness performance of the foundation and of the structure as a whole. This paper proposes a strain-based approach to estimate the fatigue (or endurance) limit of a cyclically loaded pile that may be applicable to long-term service loading. The method is applied to an existing load test dataset and the analysis results appear consistent with the observed pile response. INTRODUCTION The demand for renewable energy has been increasing in recent decades and wind power has seen a dramatic increase in popularity. In Europe, as of 2017 there were 4,149 grid-connected offshore wind turbines across 11 countries (windeurope.org), many of which are supported on monopile foundations. It wasn’t until recently (2016) that the first offshore wind farm was constructed in the United States off the coast of Block Island, Rhode Island. The project included 5 piled jacket structures founded in terminal moraine deposits. Future offshore wind development along the U.S. eastern seaboard could possibly utilize jacket structures in granular foundation soils. Loads from wave, wind, and turbine rotation induce cyclic loads on the foundation that have on the order of 108 loading cycles over the service life on the structure (Schneider and Senders 2010). Turbines located along the U.S. east coast have the added risk of hurricanes. As shown in Figure 1a, the lateral loads on a jacket structure are transferred primarily as axial compressive and possibly tensile loads on the supporting piles depending on the weight of the structure. The friction along the shaft of the pile can be prone to cyclic degradation, leading to reduced pile capacity and stiffness, and increased deformations. An offshore wind turbine foundation must be designed for a variety of limit states including ultimate, serviceability, and fatigue limit states. For a jacket structure this would include an analysis of the ultimate axial pile capacity, axial stiffness, and axial deformations, all of which can be affected by cyclic loading both under extreme (i.e. storm) conditions as well as long-term service conditions. Axial pile stiffness is needed, for example, to estimate the natural frequencies of the structure as a whole and to assess dynamic and fatigue loads. The structure must be designed such that its natural frequency remains outside the loading frequencies of the waves and turbine blade passing frequencies to avoid resonance. Therefore, prediction of the axial response of the piles is important to the design of these structures.

Jan 1, 2018

By Klaus Pöllath

The Netherlands RandstadRail project makes use of a large range of sophisticated geotechnical techniques to allow a shield driven tunnel to approach the central station of Rotterdam. This paper describes the construction of three deep excavation pits constructed with 1.2 m and 1.5 m thick diaphragm walls. Besides the presentation of the actual diaphragm wall activities special consideration is given to the break-in and break-out situations of the TBM into the deep excavations pits using sealing blocks and partly glass fibre reinforcement in the diaphragm walls.

Jan 1, 2006

By Ryan Higbie, King Chin, Matthew Anderson, Mike Huggins, Rian Johnson, Dave Sinsheimer

"The Permanent Canal Closures and Pumps (PCCP) project is the capstone piece of New Orleans’ extensive hurricane risk-reduction system constructed following Hurricane Katrina. The project consists of three discrete pump stations and flood gates on the shore of Lake Pontchartrain which provide a storm surge barrier and pump rainwater from the City of New Orleans’ primary drainage canals. The depth of the pump station structures ranged between 39 and 45 feet below sea-level. USACE developed the PCCP project for design-build delivery; granting the project team latitude to develop innovative, cost effective solutions for the project. The use of OPEN CELLTM cofferdams to construct the pump station structures was one such innovation. OPEN CELL structures utilize the strength of the retained soil to anchor cellular sheet pile face arcs; allowing a free-field of construction within the cofferdam. This cofferdam design did not require ground improvement or dewatering around the perimeter of the cofferdam. The free-field cofferdams streamlined construction and large equipment installation within the structures with no encumbrance from internal bracing. Meticulous force-based design, soil-structure numerical modeling, and physical testing were all techniques used to present and gain USACE acceptance of the design on this vital element of the work.PROJECT DESCRIPTIONThe Permanent Canal Closures and Pumps (PCCP) project is the capstone piece of the City of New Orleans’ extensive hurricane risk-reductions system constructed following Hurricane Katrina in 2005. The project encompasses three separate pump stations and floodgate structures located at the mouths of three outfall canals (17th Street, Orleans, and London) on the south shore of Lake Pontchartrain. These three canals, running from the south to north, act as the primary conduits for discharging water from the New Orleans area. Prior to Hurricane Katrina, these canals were operated with pump stations two to three miles upstream of the mouths at Lake Pontchartrain. This left long stretches of levee on each side of the canals exposed to storm surges entering from the lake. Three levee failures occurred along these canals during Katrina; two at London Canal and one at 17th Street Canal. The failures resulted in major flooding of the surrounding neighborhoods, significant damages, and loss of life.Following initial canal levee repairs after Hurricane Katrina, USACE, in partnership with the Louisiana Coastal Protection and Restoration Authority (CPRA), took action to move the line of flood protection to the mouths of these three canals at the edge of the lake. By cutting off the storm surges from Lake Pontchartrain at the entrance to the canal, over ten miles of canal levee would no longer be exposed to storm surge water elevations, significantly decreasing the risk of failure."

Jan 1, 2017

By Leena Korkiala-Tanttu, Noora Lindroos, Juha Forsman

"Construction works at the Helsinki city sea shoreline requires dredging and handling of contaminated sediments. Most of these soft dredged sediments are regarded as too poor quality material for earth construction purposes. Mass stabilization technology has been applied to improve the technical and environmental properties of the dredged sediment in order to utilize the material in construction. The treatment site presented in this article is placed in the West Harbor where the dredged sediments are disposed in basins, mixed with binders by mass stabilization and transported to utilization sites. The volume of these basins is about 90 000 m3. So far these basins have been used three times during the years 2011-2014. The most applied binder has been cement. Its high price and carbon footprint have encouraged use alternative binders. Other used binder materials include fly ash and end product of desulphurization from coal combustion, and fly ash from combustion of Estonian oil shale. The technical and environmental properties of stabilized sediments have been studies in the laboratory and in situ thoroughly. Some properties of the stabilized sediments which have been studied are: compression strength, modulus, hydraulic conductivity, leaching of contaminants, etc. The leaching test results show that heavy metal leaching is very low with all binder materials tested.1. INTRODUCTIONContaminated marine sedimentsMarine sediments in the coastal areas are often contaminated as a consequence of industrial and port activities, as well as the influence of cities located there. Construction activities and reclamation of shore line require dredging and handling of contaminated sediments since the level of contamination inhibit dumping of dredged sediments into the sea. Based on their technical properties, most of these dredged soft and watery sediments (clay, gyttja, etc.) are regarded as too poor quality material for earth construction purposes. Economic, sustainable and environmentally safe management of contaminated, dredged sediments is a key issue in many construction sites.In the City of Helsinki, mass stabilization technology has been applied to improve the technical properties of the dredged sediments in order to utilize the material in construction. Owing to stabilization / deep mixing / solidification, also the contamination is encapsulated in a monolithic solid of a high structural integrity. Thus, contaminants migration is restricted by the decreased surface area exposed to leaching.The treatment site presented in this article is placed in the West Harbor (a place of Helsinki called Jätkäsaari) where dredged sediments are disposed into stabilization basins, mixed with binders by mass stabilization and then transported to final utilization sites. The location and principle of these basins is presented in Figures 1-4. The overall volume of these four stabilization basins is about 90 000 m3."

Jan 1, 2015

By J. Hartikainen

Kemi cardboard mill is founded on the alluvial bed of Kemi river at the north-eastern cost of Botnic Culf in Northern Finland. The alluvium consists of sandy and silty layers underlain by thick medium dense silty moraine layer. The first cardboard machine, having a belt width of 7,4 m, was constructed in 1972 on 7,5 to 9,5 m long wedge-shaped precast driven piles. Because of the excessive differential settlements and sometimes unexpected dynamic malfunctioning of the machine it was decided to strengthen the foundation before installing the partly new machine and increasing the running speed from 500 to 750 m/min. Piling was done under extremly strick limitations concerning space, vibrations, settlements, dust etc. Extra vertical support was made by using 23...25 long x-form steel piles driven by compressed air pile hammer down to rock. The piles were held together with old piles by a conctrete frame with diagonals, which made the total system - machine - foundation frame, piles and ground - ridgid enough to avoid resonance during dynamic loading.

Jan 1, 2010

By Sridhar Krishnan

This paper presents the results of a comprehensive pre-production pile testing programme for the US$ 800 million 1400MW Coal-Fired Jimah Power Plant Project in Negeri Sembilan, Malaysia. The testing programme included high-strain dynamic testing and fully instrumented static axial and lateral load testing of driven prestressed concrete piles and bored cast-in-place piles. A highlight of the testing programme was the pioneering use of the Global Strain Extensometer (GloStrExt) Method, a deformation monitoring system that uses advanced pneumatically- or hydraulically-anchored extensometers and a novel analytical technique to monitor loads and displacements down the shaft and at the toe of driven prestressed concrete piles. The experience with the testing programme for the Jimah Project also demonstrates the possibility of achieving notable breakthroughs, not only in the monitoring, evaluation and reporting of pile foundation behaviour dynamics but also in our understanding of the mechanisms that underpin such behaviour. These significant gains are undeniably a direct result of the committed and co-operative relationship among the project owner, design/builder, specialist piling subcontractors, pile suppliers and pile instrumentation and testing specialists.

Jan 1, 2006

A technical exhibition was held in conjunction with the 4th DFI International Conference on Piling and Deep Foundations, Stresa. The exhibition was located in the ground floor of the Conference Hall. It was open from 15.30 on Monday April 8 till 16.30 Thursday April 11, 1991. The following is an alphabetical list of firms who took part. 1) A.P. VAN DEN BERG MACHINENFABRIEK B.V. P.O. BOX 68 8440 AB HEERENVEEN The Netherlands Tel: +31 5130 31355 Fax: +31 5130 31212 Stand Executive: A. Duyfjies

Jan 1, 1994

By A. Mazzucato

This paper presents the experimental results of driving and load tests on an instrumented pile driven into a test pit filled with fine homogeneous sand.

Jan 1, 2010

By James A. Schneider

The successful installation of long piles driven into very dense sands relies on the occurrence of the reduction in local friction with increased pile embedment, a phenomenon known as ?friction fatigue?. The underlying mechanisms controlling friction fatigue are poorly understood, with some design methods including an adjustment for the influence of pile diameter while others do not. This paper back calculates the installation resistance of 0.356m to 2m (14in to 78in) diameter open ended piles driven into very dense sands using wave equation analyses. Cone penetration test data are used to link soil properties to installation resistance. The study illustrates consistent interpretation of a variety of case histories of open ended piles driven in very dense sands using newly developed analysis techniques and normalized parameters. Results provide information on methods for incorporating friction fatigue into drivability studies as well as a discussion of mechanisms related to pipe pile installation resistance in sandy soils.

Jan 1, 2010

By Musbah A. Hasan, Ahmed M. Nasr, Fauzi Jarushi

Many transmission towers, high-rise buildings and bridges are supported by piles. These structures may be subjected to large lateral loads. Therefore, experimental investigations on model piles under lateral loads were conducted in uniform dry sand. Small-scale model tests were carried out considering the influence of pile length, pile diameter, sand density, roughness of pile surface and vertical load on the lateral resistance of a pile. Furthermore, the effect of pile load eccentricity (e/L) on the ultimate lateral resistance was studied. Investigations, of the influence of various parameters on the magnitude of the coefficient of subgrade reaction (nh), were also performed. It was found that the lateral load capacity of piles increases with increase in pile length, pile diameter, pile surface roughness and increase in the sand density. The results also showed that the coefficient of horizontal modulus of subgrade reaction, (nh), decreases with deflection increase. From the results, the coefficient of subgrade reaction for a smooth pile embedded in medium dense sand would decrease by (134%) when the lateral pile head deflection (yg) changes from (2% to 5%) of pile diameter.

Jan 1, 2017

By Brandon M. Robinson, Osman F. Besler, Dominik Gaechter

The Sandbukta-Moss-Såstad (SMS) project is a part of the Intercity development project, which is part of the largest transport project in Norway, consisting of 270 km of new double-track rail. The SMS project consists of 10km of double-track railway including three open stretches and two tunnels. Soil conditions consist of quick clay underlain by Bedrock. Dry soil mixing (DSM) was considered as the main soil improvement method to allow for excavation of the quick clay and construction of the D-Wall panels. The preliminary design revealed around 25,000 ton of binder installation. Therefore, a test field has been conducted to evaluate binder alternatives in means of improved soil strength by considering CO2 emissions. Multicem and Standard cement (Standard FA) have been compared for that purpose. Multicem is a type of binder which mainly consists of Portland cement and cement kiln dust (CKD). CKD is a fined-grained, solid, highly alkaline material removed from the cement kiln exhaust gases. reverse column penetration test (FOPS) and pre-drilled column penetration test (FKPS), which are common tests to evaluate DSM strength have revealed comparable strength outcome for both binder types. Therefore, Multicem has been selected as the main binder type to be used further which provided a reduction in CO2 footprint of up to 40%.

May 1, 2022

By Ramin Motamed, Farshid Ghazavi, Joseph A. W. Toth

"Post-disaster reconnaissance of areas affected by earthquakes has documented extensive damage to buildings with shallow foundations located in liquefaction-prone areas. Currently, estimation of liquefaction settlement is based on empirical correlations that evaluate settlement in the free-field environment and are based on one-dimensional consolidation. However, observations have shown that liquefaction settlement under buildings can be considerably greater. This research is based on a series of 1- g shake table experiments using a transparent soil box to reproduce liquefaction-induced building settlement. Building settlements were evaluated using a scaled model of a building foundation representing a 1-2 story building. Comprehensive parametric study was carried out to establish the effects of several parameters on free-field and building settlements such as building width and thickness of liquefiable soil layer. The experiments utilized accelerometers and pore-water pressure sensors to monitor ground accelerations and buildup of pore-water pressures in both the free-field and model building footprint. Results of these experiments are compared to available centrifuge tests and field observations and conclusions are drawn with respect to the potential scaling effects. Lastly, this paper discusses the feasibility of installing helical piles as a mitigation strategy to reduce the building settlements by presenting some of the exploratory experimental data obtained from this series of 1-g shake table tests.INTRODUCTIONThe 2010-2011 Canterbury earthquake sequence and the 2011 Great Tohoku earthquake are some of the most recent examples where large numbers of low-story structures sustained damage resulting from liquefaction-induced settlements. This damage has commonly been observed in residential and commercial areas developed over loose, unconsolidated and saturated coarse grained soils resulting from both natural and man-made deposits. Damages incurred from the 2010-2011 Canterbury earthquake sequence occurred in the largely unconsolidated fluvial environment bordering the Avon River in Christchurch (Henderson 2013). Similar damage was also incurred during the 2011 Great Tohoku earthquake where liquefaction of soils occurred in both young alluvial deposits and fill materials (Ashford et al. 2011). Figure 1 presents typical modes of failure to structures resulting from the effects of liquefaction. Current practices in evaluation of liquefaction settlement rely on empirical correlations (Tokimatsu et al. 1987; Ishihara et al. 1992) developed for liquefiable soils in the freefield environment (Dashti et al. 2010a). However, recent observations of the performance of foundations suggest that settlement of rigid shallow foundations in liquefiable soils are commonly greater than those predicted in the free-field. Therefore, new correlations should be developed to better predict the degree of settlement of shallow foundations in liquefiable soils. Current research is beginning to focus on the mechanisms of settlement during liquefaction in regards to confining stress, pore-water pressure and shear stress induced from foundations (Dashti et al. 2010b)."

Jan 1, 2016

By Jean J. Abiassi

The Boston Marine Industrial Park (BMIP) VENT 6 project is a cut and cover tunnel, part of the Central Artery / Tunnel (CA/T) in the city of Boston. The BMIP job will serve as the south approach to the Third Harbor Tunnel crossing. The alignment is approximately 2500 Ft long and is made up of four sections starting from west to east: 1. West Tunnel 2. Boat Section 3. East Tunnel 4. Tunnel inside Vent 6 Cofferdam and connection to the Third Harbor Tunnel. The support of excavation (SOE) system for the West Tunnel, Boat Section, and East Tunnel are all a part of this project whereas the SOE for Tunnel inside the Vent 6 Cofferdam was a part of the contract for the Third Harbor Tunnel.

Jan 1, 1994

By Patrick J. Hannigan, Alex Ryberg, Rozbeh B. Moghaddam

Driven piles are widely used for foundation support. In the vast majority of cases, an increase in pile capacity occurs with time which is referred to as “set-up.” However, in a very limited number of cases, a decrease in capacity with time can occur. This phenomenon is referred to as “relaxation.” This paper will provide a brief review of the relaxation phenomenon, as well as pile driving information and dynamic test data on cases where relaxation has occurred. The pile types in the presented relaxation cases include H-piles, open-end and closed-end pipe piles, prestressed concrete piles, and prestressed concrete piles with H-pile stingers. The soil conditions where relaxation occurred includes dense to very dense fine sands, heavily over consolidated clays, and weak laminated rocks. Relaxation information from 36 piles at 26 sites is assessed. The collected data will assist foundation designers by identifying the subsurface conditions where relaxation has occurred, as well as by documenting the corresponding relaxation magnitude. One method of addressing relaxation when it is encountered is to drive the foundation piles to a greater end of initial driving capacity than required long-term. Hence, the identification and quantification of the relaxation magnitude will be beneficial to foundation designers installing similar pile types in similar subsurface conditions. The paper will also present pertinent observations and recommendations on mitigating relaxation when encountered. INTRODUCTION One of the earliest observations of a decrease in redriving resistance following initial driving was reported by Miller (1937). He reported that piles driven into a saturated, coarse grained soil could lose 40 to 50% of their resistance when redriven 24 hours after initial driving. Yang (1956) similarly reported that after a break in driving, a decrease in driving resistance could be encountered for piles driven in dense fine sand, inorganic silt, or stiff fissured clay. Parsons (1966) in his paper that described piling difficulties in the New York City metropolitan area termed this phenomenon “relaxation”. In this time period, pile capacity was most often evaluated from a pile driving formula frequently checked by a static load test. Hence, the true magnitude of the capacity decrease on a given pile was often poorly quantified. Furthermore, dynamic measurements that could determine what influence driving system performance variation had on the observed redriving resistance were not yet readily available.

Jan 1, 2019

By Z. Q. Zhou

It is the first worke in design of pile foundation to determine the carring capacity of single pile, and a static loading on site is considered to be the lost derect and reliable way. All values P and settlements S induced can be plotted as a broken-line. Since soil is a kind of elasto-plastic and cohesive material, the increasing of settlements is generally greater than that of loads. Different value Pu nay be given by different tester on his P-S diagram, because of erroys in the test and complicated, characteristics of soil. The analytical method of exponential equation shown in this paper derives a specified solution. After using an exponential curve to regress values of loads P and corresponding settlements S from on-site test, coeficients A and B of exponential equation can be obtained. With this curve an ultimate carrying capacity of single pile can be determined. The resistant forces of pile shaft and pile tip can also be defined by the tangent of the calculated knee point, as it is called (tangent method). At last, an example is given to show how the ultimate carrying capacity of f 500mm bored pile is obtained with this method for a project in Kunming.

Jan 1, 2010

By Patrick J. Hannigan, Frank Rausche, Rozbeh B. Moghaddam

The Top-Loaded Bi-Directional Test (“TLBT”) is a new method to apply bi-directional loads to a deep foundation element with the loading source located above the foundation head. In the TLBT reusable load assembly, loads are applied to the foundation using the R-System which consists of two stacked steel plates located at the geotechnical resistance balance point or at the foundation base connected to the load assembly via vertical elements. The top plate or the Shaft Bearing Plate (“SBP”) will transfer loads to the foundation upper portion, and the bottom plate or the Base Bearing Plate (“BBP”) will transfer loads to the foundation lower portion as well as the foundation base. At the surface, above the foundation head, a hydraulic jack is located between a Top Load Assembly (“TLA”), and the Bottom Load Assembly (“BLA”). The TLA and BLA are connected to vertical elements which are consequently connected to the R-system. As the jack is pressurized and expanded at the surface, the R-System plates are separated, and the foundation is bidirectionally loaded. This paper presents a brief description of the conventional Bi-Directional Load Test (“BDLT”) including benefits and limitations followed by the TLBT method introduction including its benefits and advantages over other testing methods.

Sep 8, 2021

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