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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 Aly M. Mohammad

State and federal agencies during rehabilitation of existing bridges may require the existing bridges to be evaluated under seismic conditions. If the bridge does not perform under the seismic event, the bridge may require seismic retrofitting. Bridges are classified as: Critical, Essential, and Others according to their importance. Geotechnical considerations play a major role in evaluating the bridge behavior under a seismic event. Subsurface conditions influence the magnitude of ground acceleration and hence the forces and moments on the superstructure. This paper will provide a detailed description of the geotechnical aspects associated with the seismic retrofit evaluation for the 12th Street and 14th Street Viaducts located in Jersey City, New Jersey. The paper will also present a description of the geotechnical investigation program including seismic cross-hole surveys to determine the dynamic soil parameters, including the results of site-specific response spectra for both the 475 and 2475-year events. Liquefaction assessment methodology utilizing an equivalent factor of safety will also be described and the design method used will be summarized. In general, the pile foundation is modeled as 6x6 foundation stiffness matrix with 36 stiffness coefficients at the center of the pile cap. The seismic loading on the foundation is evaluated in a pseudo-static analysis, where the dynamic earthquake-induced loads are presented by static forces and moments. The computer program FB Pier was used to evaluate the foundation stiffness. The moments, axial loads, and shear are input into the FB Pier model. The stiffness of the foundation is determined and the results are then input into the Structural model to determine new forces and displacements. Adjustments are made until the loads are compatible with the stiffness used. The understanding of the geotechnical conditions at the 12th Street and 14th Street Viaducts and the coordination between the Bridge and Geotechnical Engineers were able to provide significant cost saving to the Owner. The Design Engineers were able to retrofit the existing Viaduct foundations with reasonable number of additional piles. It is believed that the results and finding presented in this paper will benefit both the Bridge Engineers and Geotechnical Engineers by highlighting the importance of interaction between the two disciplines.

Jan 1, 2006

By Hiren J. Shah

The urban environment and geology create unique challenges for design and construction of deep foundations. The effect of these is prominently experienced in New York City. Three such project case histories are presented in this paper. The first project is a multi-use development. Relatively unusual glacial geology was observed at the site during the subsurface investigation phase. This played an important role in the selection of deep foundations as well as during construction. The design and construction aspects of the pile foundations, settlement estimates, a pile drive test program during design, piling equipment and production pile installation are discussed herein. A relatively smaller project is the second case history. A combination of drilled and driven deep foundations was employed in one area of the project due to its unique conditions. In another area of the project, an addition to a structure required the use of supplemental foundations to resist new additional loading. Tight space and load sharing with the existing foundations were important considerations in the design and construction. Finite element modeling of the existing and completed structure was performed which was an interesting aspect of the project. The third project case history involves a very large multi-billion dollar project in which various different types of deep foundation elements were used. The aspects requiring the use of such a variety of types and sizes of deep foundation elements included: geologic conditions, re-use of existing foundations, protection of adjacent infrastructure, construction staging, restricted space, loads, deep excavations, cost and schedule.

Jan 1, 2011

By P. K. Ray, Sudip Kumar Koley, Sainath M. Reddy, Devulapalli L. S Rasagna

Bangalore Metro Rail Project- phase II is one of the technological challenging project, particularly construction of underground metro rail system. The Bengaluru city is very congested area and connecting metro rail system with existing transportation networks is equally challenging. In this phase-II, the Underground metro is being constructed by blasting hard rock formation and supporting the shear zone. Most of the subsurface rock formations comprise of granitic Gneissic formations are of Precambrian age and shear zones that includes friable a thin weathered rock formation. With such subsurface geological conditions, , the anticipated construction challenges include : A) deep excavation of hard rock mass under old and sensitive structures and buildings, by controlled blasting; B) variation in the rock grade from grade I to grade V; C) weak rock mass at shear zone resulted in planar failure beneath the retaining wall; D) water seepage along shear planes; E) selection of a suitable method to conducted blasting near high voltage electrical machinery or power cables. This paper describes the methods adopted to mitigate these technological challenges and to meet stringent environmental compliances. These includes study and application of various geological, geotechnical parameters to develop a proper line drilling and controlled blasting techniques to minimize the ground vibrations and controlling the rock fragmentation and to optimize the equipment performance in terms of productivity and time schedules. The “Phase 2” software of “Rocscience” has been used and Regression analysis has been carried out by using MCD (Maximum Charge per Delay) and PPV (Peak Particle Velocity) to estimate with FOS (Factor of safety) for sensitive places such as nearby high rise buildings and electrical transformers.re.

Sep 1, 2022

By Pierre Gouvin, Michael Oakland

"This paper covers the rapid response methods used to monitor the emergency response to damage to an historic structure. An architectural gem, the latest incarnation of the old south Church was completed in 1875, utilizing local conglomerate (pudding stone), combined with brownstone and other materials to make an incredible showcase for priceless stained glass and other details epitomizing the height of the American Industrial Revolution. As part of required American with Disabilities retrofits to the adjacent Metropolitan Boston Transit Authority Station (MBTA), a support of excavation system was implemented with tradition sheet piles. During excavation (SOE) it was determined that Jet Grouting would need to supplement the sheeting to close openings in the SOE. During Jet Grouting, the eastern side of the structure was bisected, and lifted over 2 inches up and to the south. The movement occurred rapidly, within minutes, and subsided when Jet grouting was discontinued. The paper will describe the nature of the immediate response to get a real time monitoring program established, and the follow on monitoring program that ensued to provide the needed information to the stakeholders about this critical structure to evaluate stability, safety and to develop a long term remediation plan. The real time systems and instruments used consisted of Automated Motorized Total Stations (AMTS) and Automated Crackmeters. The Paper will describe the techniques used to control construction in safe manner.INTRODUCTIONThe Old South Church of Boston was constructed in 1875 and is one of the best examples of High Victorian Gothic Architecture in the Northeast. (Fig. 1) shows the newly constructed Old South in 1882. The Roxbury Conglomerate used to construct the church combined with large stained glass window by Clayton and Bell of London provides its unique appearance. Like most of the structures constructed in Boston’s Back Bay at that time, the church is founded on timber piles which penetrate the fill and organic soils to bear in the upper Boston Blue Clay. The churches interior includes high vaulted plaster ceilings and a 1920’s E. M. Skinner organ with exposed pipes as long as 32 ft. in length. The Church was added to the list of National Historic Landmarks in 1970 and is a featured Boston attraction."

Jan 1, 2017

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 Joanna Bzówka

Nowadays, there are some new requirements for the supermarket floors. The floors are loaded by high point- and moving-loads. In spite of this fact, it is necessary to ensure the stiffness of the floor and the stiffness of its support. When pile foundations are designed in the case of weak soil, the piles are recommended under the foundations of the supermarket and also under the floor layers. The example of foundation of a typical supermarket located on long­standing municipal dumping ground is presented. Indirect foundation - CFA piles, 0.5 m in diameter and 4.5 to 20.0 m long, was de­signed. Fifteen trial loading tests were carried out.

Jan 1, 2006

By Ramon Varghese, A. Boominathan, Subhadeep Banerjee

Pile raft foundation system has been accepted as an economic foundation design for high rises and heavily loaded structures. Seismic response analysis of PR foundation systems involves complex pile-soil-pile interaction as well as raft-soil-pile interactions, for which simplified methods have limitations. Kinematic rocking of a pile group is known to be influenced significantly by the pile configuration. The presence of an embedded pile cap, or a raft, as in the case of a piled raft can further alter the dynamic characteristics of a pile group-soil system. In the present study, frequency dependent kinematic response factors are evaluated for piled raft foundation, using the substructuring approach based ACS SASSI program. Performance of the numerical analysis methodology is first evaluated with results from analytical and experimental studies reported in literature. The effect of pile layout on kinematic response is then studied for a piled raft in clay system based on a centrifuge shaking table test reported in literature. Kinematic response factors and horizontal impedances were determined for varying pile spacing ratios. The influence of raft has been found to increase kinematic translation by up to three times in the piled raft in clay system. Pile configuration is found to play a significant role in kinematic rocking of piled rafts. The presence of raft is observed to significantly reduce dynamic rotational stiffness coefficient in the dimensionless frequency range of 0.23 to 0.6, and increase damping coefficient after a dimensionless frequency of 0.4, for all pile configurations studied. The effect of an embedded raft is hence an important consideration while evaluating foundation input motion as well as impedances of piled raft foundations. INTRODUCTION The Piled raft foundation (PR), is a composite foundation system that facilitates load sharing between pile and raft. It is an economic foundation option for high rises and heavily loaded structures. Soil structure interaction (SSI) in PR system involves raft-soil-pile, and pile-soil-pile interactions which needs to be considered in static or dynamic SSI analysis. The effect of pile can have substantial influence on foundation input motion, for seismic analysis (Di Laora et al. 2017). Piles are observed to depress a wide spectrum of the seismic excitation (Fan et al., 1991, Di Laora & de Sanctis, 2013). Although kinematic response of pile groups have been extensively studied in the past, the influence of the presence of raft on kinematic response characteristics of pile groups has not received much attention.

Jan 1, 2018

By Eric Rehwoldt, Walt Rabe, Jesús Gómez, Tim Myers

"An expansion plan for Washington Dulles International Airport is currently underway to prepare for growth at this northern Virginia facility in the future. While Dulles currently serves more than 20 million passengers a year, when the Master Plan for the Airport is fulfilled, it will be capable of handling approximately 55 million passengers a year. The current Capital Construction Program underway at Dulles will take the Airport one step closer to its full potential.As planned, work includes a new Airport Traffic Control Tower, expansion to existing concourses, a fourth runway, additional parking, and other improvements. One of the most interesting features of this project is the construction of a two-track passenger train system (Automated People Mover, or APM) linking the main terminal and concourses, which will largely replace the Mobile Lounge transportation system, thus greatly reducing surface traffic. Construction of the APM system involves deep excavations along the tunnels and at the transfer stations. This poses special challenges because the settlement-sensitive terminal, original Airport Traffic Control Tower, and concourse buildings, as well as other facilities, exist near the proposed below-ground stations. The site is also underlain by a tight grid of underground utilities that include jet fuel, gas and central communication lines, in addition to more mundane electric, sewer and water mains.One of the most interesting features of this project was the extensive and skillful utilization of micropiles for support of existing structures adjacent to the excavations. Without the use of micropiles, the cost and difficulty of the excavations would likely have been much more. Several important lessons were learned about the use of micropiles, which advance that technology.Throughout the project site, bedrock was generally encountered at 25-ft depths or more. The rock consists of micaceous and highly calcareous siltstone rock. This rock is typical of the sedimentary component of the Culpeper Basin, a Triassic Age geologic feature extending from south central Virginia to western Maryland. The siltstone beds dip gently to the west at about 10 to 20 degrees. Joint planes typically dip 60 degrees to vertical. The rock underlies a sequence of fill materials and residual soils of varying thickness."

Jan 1, 2009

By Tiruvengala Padma, Nilesh Naik

Piles are common type of deep foundation elements used for the special bridges, transmission towers, Jetties, and tall structures. Lateral loads on the structures can be due to either earth pressures, wind, waves, impact, moving vehicles and eccentric application of axial loads or in combination of the loads. Hence the lateral capacity of piles plays a major role in determining the pile dimensions. The laterally loaded pile analysis is a soil-structure interaction problem as the lateral capacity of pile depends on the soil strength and stiffness parameters and its reaction to the lateral load on pile. The common approach to determine the lateral load analysis of piles is the Beam on Lateral Springs Method also known as “p-y” method. In this method the pile is modelled as a beam and supporting soil is modelled as lateral springs. This study is focused on the comparison of output obtained from three geotechnical softwares namely FB-MultiPier, L- Pile and Wallap. L-Pile Software is based on Finite Difference Method, Wallap on Horizontal Subgrade Modulus Method and FB MultiPier on Finite Element Method. Pile response in terms of deflection, shear force and bending moments under vertical and horizontal loads from above three software are compared and concluded.

Sep 1, 2022

By J. D. Findlay

The demands on development in London in recent years has led to the increasing use of top down construction methods in which there is a requirement to place steel columns to high tolerances into large diameter bored piles with deep cut-offs. A number of different proposals for the sequence of construction are being suggested. The tolerances requires for the steel columns are becoming increasingly stringent. This review examines a number of basic construction proposals and comments on the problems and solutions used by foundation contractors to provide the required foundations.

Jan 1, 1989

By Y. C. Han

The advances in seismic design considering soil-structure interaction or soil-pile-structure interaction are described using a substructure approach. The nonlinearity of soil is considered approximately using a boundary zone model with non-reflective interface, and computer programs are available for practical applications. The validation of model is confirmed with dynamic tests on piles in the field, and the results for a single pile are used to compare with the predictions in this study. The liquefaction for sand soil layer can be accounted for, and a case of liquefaction is discussed. Two practical examples are examined, a vacuum tower structure supported on foundation of steel pile group and a table top structure supported on foundation of concrete pile group. To illustrate the effects of soil-pile-structure interaction on the seismic response of vacuum structure, different base conditions are considered, rigid base, i.e. no deformation of the foundation; linear soil-pile system; and nonlinear soil-pile system. The method introduced can be applied to the design of tall buildings, bridges, industrial structures and offshore platforms with soil-pile-structure interaction under seismic or dynamic loads.

Jan 1, 2010

By W. G. K. Fleming

The general history of piling is traced up to the present time with regard to the evolution of methods and materials. The processes have been strongly influenced by developments in basic equipment and industrial change. It is noticeable that in the twentieth century more progress has taken place than in the many previous centuries. It has been strongly influenced by the general development of Soil Mechanics. Test loading is probably the most effective way to assess the success of designs and many empirical relationships have been challenged through it. As we approach a new century it appears that it will be an age of rapid equipment development, with much enhancement of understanding of what has been done. Processes of automatic construction and testing will becoming commonplace. These changes will narrow the limits of conventional scatter that have come to be accepted and to a large extent will be driven by political efforts to curtail energy consumption, to raise standards of quality and reliability, and to conserve the environment. 1. Ancient history. Piling is an ancient art. Its first mention in history is from Herodotus, the first person to commit an account of his times to the written word in the years 557 to 479 BC. He evidently had a strong interest in engineering matters because he wrote of building, brick making, reinforced brickwork, river training, canal building, bridge construction, tunnelling and its acoustic detection and piling. The piling reference comes from Book 5 at paragraph 16.

Jan 1, 1999

By K. Mallikarjuna Rao

There are several methods available to estimate deflection and ultimate Capacity of laterally loaded piles. In this investigation an attempt has been made to verify the existing methods for prediction of ultimate lateral resistance and deflection with the laboratory and field test results reported in the literature. A 75 pile loading test data obtained from the literature was used to evaluate two methods designed to predict the ultimate lateral resistance of rigid piles and three methods designed to predict the lateral deflections of rigid piles and four methods designed to predict the lateral deflection of flexible piles subjected to lateral loads. The accuracy and precision of each method is quantified statistically. The statistical results of the overall analysis indicate that the mean values of the ratios of predicted to measured lateral capacities vary from 0.62 to 1.14 with an average of 0.88. However, the settlement predictions were much more widely scattered than the ultimate load predictions and in general all the methods have a tendency to under predict the deflections. A new method is proposed by modifying the Broms's method to estimate the lateral deflections of free headed rigid and flexible piles separately. The proposed modified methods were found to be reasonably good in comparison to existing methods and to overestimate deflections.

Jan 1, 1996

By Arash Saeidi-Rashk-Olia, Dunja Peric

Energy piles are gaining increased popularity due to a growing demand for clean energy. To further advance the understanding of soil-structure interaction in energy piles, recently-derived analytical solutions have been implemented to investigate the impact of stratigraphy on the soil-structure interaction. This was accomplished by comparing the measured and predicted head displacements, axial strains and stresses in an energy pile embedded in the actual homogeneous and layered soil profiles, as well as into synthetic homogeneous soil profiles. The analytical solutions for homogeneous soil profile captured the smooth experimentally observed response versus depth very well. In the case of a layered soil profile, the corresponding analytical model was capable of capturing nuances in trends of axial stress and strain versus depth at the interface of different layers. The analytical predictions for the layered profile appear to be slightly less accurate than for the homogenous profile. The experimental data obtained from the layered profile appear to be a bit more scattered than those from the homogeneous profile. In the former case, the interplay of the individual soil layers with the pile occurs while maintaining the continuity of the pile stress and displacement at the interface of different layers. The response throughout each layer of the layered profile is quantitatively different than the corresponding homogeneous response. Nevertheless, qualitatively the response throughout each layer of the layered profile is similar to the response of the pile embedded in the corresponding homogeneous layer.

Sep 8, 2021

By Hennie F. T. Barnard

Where geotechnical designs are governed by settlement requirements, soil and rock moduli are important parameters for design. This paper reports on a method that was used to utilize dynamic modulus measurements in the field toward pile settlement designs for the proposed Square Kilometer Array (SKA) Project to be located near Carnarvon, South Africa. The project will comprise of over 3000 No. movement sensitive satellite dish structures. The method described in the paper utilizes strain-related modulus degradation across the complete ground profile, starting from measurements of peak particle velocity (and inference to dynamic modulus at small strain) as measured using Continuous Surface Wave (CSW) testing at individual dish positions. This is required due to the very small allowable foundation rotation of 5 arc seconds under the dishes? operational conditions. The strategy of analysis was to conduct an iterative process starting from the measured small strain modulus profile of the ground. The likely maximum pile force for a specific piled foundation option was estimated and a single pile finite element analysis was performed using Plaxis 2D (Version 2010) to estimate the expected ground strain developing along the length of the pile. By assuming the shape of the shear modulus degradation curve with increasing shear strain, the iteration process then converged on a likely degraded modulus profile associated with the single pile and maximum load assumed. This process enabled identifying the pile cap size, pile configuration, pile sizes and pile lengths that would meet the operational movement limits. The chosen pile group configuration was then analyzed using the Repute 1.5 pile group analysis software. The design process and typical results are discussed in this paper.

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

A common type of deep foundation used in Norway to support bridge structures is the drilled pipe piles (piles) filled with concrete reinforcement after installation. The standard installation practice is the use of down-hole hammers. Complex geology and difficult subsoil conditions in Norway causes a high variability of soil and rock layers which in turn make for differences between actual subsurface conditions and those expected from geotechnical exploratory borings. This situation is strongly noted when the foundations are not fully socketed, and the rock layer is sloped. In this particular case, special testing procedures are required to assess the drilled pile base material and evaluate the rock-socket to ensure full contact between the foundation base and the rock surface. The local standard practice to verify the latter condition, consists of coring and visually evaluating the material recovered at the bottom of the drilled pile. This paper presents a case where the coring and visual inspection were not possible and alternatively the geological material encountered at the base of the deep foundations was evaluated using force-displacement measurements. Two 1016-mm (40in) diameter open-end drilled piles identified as P02-04 and P02-05 were tested and evaluated using in-situ force-displacement data prior to filling the piles with concrete. Test results showed an average displacement of 7mm (0.28in) corresponding to 35MPa (5.1ksi) stress level for P02-04, and 7.2mm (0.28in) corresponding to a stress level of 38MPa (5.5ksi). Based on testing results, both drilled piles were within the established material assessment criterion presented by the local authorities. INTRODUCTION This paper presents a case study in Norway where the material encountered at the base of an open- end drilled pipe pile (pile) was evaluated using force-displacement data. In the deep foundation industry in Norway, it is a common practice to install piles to support transportation structures. Once the piles reach the embedment elevation, and the pile base is assessed, these are filled with concrete. In projects where sloping rock is the supporting layer, and all nominal loads are supported by the pile base resistance, assessing the material encountered at the pile base to ensure full contact with the rock becomes critical. The local practice to make this assessment consists of the use of weighted tape, coring, or inspection cameras. However, similar to any other testing and evaluation methods, these come with their own limitations. The variability associated with the use of the weighted tape, accessibility for the coring equipment to complete a coring process, or the conditions at the foundation base such as murky water or thick drilling fluids could significantly impact the photo or video quality taken at the pile base. In such conditions, it is important to consider alternate testing methods to evaluate the material at the foundation base.

Jan 1, 2018

By David C. Kraft

A major manufacturer and user of machine tools had the need to install a screw press machine at its plant site with the following design load requirements: (1) Vertical Compression Live Load = 2000 kip (8896 kN) and Dead Load = 1000 kip (4448 kN), (2) Rotational Moment = 6600 ft-kip (8950 kN'm). The screw press machine was to be located within an existing manufacturing building. The bottom of the footing base was located 15 ft (4.6 m) below existing floor slab. A geotechnical investigation of the site indicated a 17 ft (5.2 m) thick initial stratum of stiff to very stiff clay underlain by a 14 ft (4.3 m) thick stratum of loose to medium dense sand. Beneath the sand stratum was soft rock described as weathered shale. Obvious concern was raised on the possible effects of the dynamic motion of the screw press and potential resulting settlement within the loose sand stratum. This combination of large loads and dynamic motion resulted in the selection of a helical pile and tieback system to support the concrete foundation. The helical pile foundation system consisted of a group of vertical helical piles installed into the shale rock and a group of inclined helical tiebacks set into the remaining portion of the clay stratum. Four load tests were conducted on the vertical helical piles in order to establish compression load capacity. The results of these load tests as reported herein, led to the addition of a limited number of tubular steel push piles in order to meet the project required Factor of Safety on the design loads. All of the helical piles, push piles and inclined helical tiebacks were successfully installed and the screw press is now installed and operational.

Jan 1, 2003

By Hennie F. T. Barnard, Theodore E. B. Vorster

Where geotechnical designs are governed by settlement requirements, soil and rock moduli are important parameters for design. This paper reports on a method that was used to utilize dynamic modulus measurements in the field toward pile settlement designs for the proposed Square Kilometer Array (SKA) Project to be located near Carnarvon, South Africa. The project will comprise of over 3000 No. movement sensitive satellite dish structures. The method described in the paper utilizes strain-related modulus degradation across the complete ground profile, starting from measurements of peak particle velocity (and inference to dynamic modulus at small strain) as measured using Continuous Surface Wave (CSW) testing at individual dish positions. This is required due to the very small allowable foundation rotation of 5 arc seconds under the dishes’ operational conditions. The strategy of analysis was to conduct an iterative process starting from the measured small strain modulus profile of the ground. The likely maximum pile force for a specific piled foundation option was estimated and a single pile finite element analysis was performed using Plaxis 2D (Version 2010) to estimate the expected ground strain developing along the length of the pile. By assuming the shape of the shear modulus degradation curve with increasing shear strain, the iteration process then converged on a likely degraded modulus profile associated with the single pile and maximum load assumed. This process enabled identifying the pile cap size, pile configuration, pile sizes and pile lengths that would meet the operational movement limits. The chosen pile group configuration was then analyzed using the Repute 1.5 pile group analysis software. The design process and typical results are discussed in this paper.

Jan 1, 2017

By R. J. Folic

Investigations of the vibrations of a pile in soil are performed on a dynamic model in the form of a prismatic bar of finite axial and flexural stifnesses with a discrete mass at its free end representing the cap. The soil is represented by a system of springs of constant and variable stiffnesses. Oscillation differential equations are derived by means of the Hamiltonian principle for non-conservative systems. The problem is reduced to a coupled system of two non-linear partial differential equations with corresponding initial-boundary conditions. Frequency equations of longitudinal and lateral linearized equations are formed. The paper determines natural frequenc­ies and oscillation modes. It separately examines longitudinal vibrations excitated by a hermonic force acting upon the pile cap, and lateral vibrations excitated by an impulse acting upon the cap. The results of the numerical processing are presented in respective diagrams in dimensionless form.

Jan 1, 2010