Th. Triantafyllidis

Dynamic subsoil-coupling between rigid rectangular foundations

Abstract An analytical method to solve the mixed-boundary value problem of dynamic subsoil-coupling between a finite number of rigid, rectangular foundations is presented. The foundations are perfectly bonded to the surface of a linear-elastic, isotropic and homogeneous half-space and are subject to harmonic excitation. The mixed boundary-value problem of the dynamic subsoil-coupling has been formulated by a set of Fredholm integral equations of the first kind which are solved by the Bubnov-Galerkin method. Using this method the coupling between shear- and normal-stresses at the interface between foundation and half-space has been given full consideration. The method presented enables the description of the dynamic behaviour of a structure resting on a finite number of foundations as well as the solution of the problem of passive screening of vibrations by means of intermediate foundations.

Dynamic subsoil-coupling between rigid, circular foundations on the halfspace

On the surface of a homogeneous, isotropic and linear-elastic halfspace a number of rigid circular foundations are set to harmonic vibrations. The dynamic behaviour of this group of rigid foundations is being described by means of influence functions. These influence functions are gained from the solution of a system of integral equations describing the mixed-boundary value problem. In order to solve the system of integral equations the stress-distributions acting in the contact area between foundation and halfspace are approximated by a system of orthogonal polynomials. This procedure is suitable for the determination of the dynamic behaviour of a group of foundations as well as for the solution of problems of passive screening if the frequency of the excitation is known.

Rigid circular foundation: Dynamic effects of coupling to the half-space

An analytical method is presented to calculate, the dynamic lumped parameter of a circular rigid foundation resting upon a homogeneous, isotropic, linear-elastic half-space subjected to harmonic excitation. The mixed boundary-value problem is formulated by means of a system of integral equations. The unknown stress distributions in the contact area are approximated by a complete polynomial system. Finally, frequency depending stiffness functions are given for all degrees of freedom, different Poissons ratios of the half-space, and perfect as well as partial bonding between foundation and half-space. The method presented is a simple means to calculate the dynamic behaviour of inert rigid foundations subject to harmonic excitation.

Ein analytisches Verfahren zur Berechnung der Untergrundkopplung von mehreren starren, auf der Halbraumoberfläche liegenden Streifenfundamenten bei harmonischer Erregung

ÜbersichtEin gemischtes ebenes Randwertproblem der Elastokinetik ist gelöst worden. Der linear elastische, homogene und isotrope Halbraum wird an seiner Oberfläche mit starren Laststreifenflächen harmonisch verformt, und die dadurch entstehenden Reaktionsspannungen des elastischen Mediums unterhalb der Lastflächen werden ermittelt. Das gemischte Randwertproblem führt zu einem Gleichungssystem von gekoppelten Fredholmschen Integralgleichungen erster Art, wobei die Kerne den Reaktionsspannungen des Halbraumes entsprechen, die aufgrund einer erzwungenen harmonischen Verschiebungserregung an einem bestimmten Teilbereich der Oberfläche hervorgerufen werden. Das Integralgleichungssystem wird approximativ mit Hilfe des verallgemeinerten Bubnov-Galerkin-Verfahrens gelöst. Schließlieh wird gezeigt, wie aus den Ergebnissen dieser Arbeit die Verschiebungen von mehreren starren benachbarten Streifenfundamenten bei einer harmonischen Belastung errechnet werden können.SummaryA finite number of dynamically coupled rigid strip foundations is considered, which are perfectly bonded to the surface of a linear-elastic isotropic and homogeneous half space, representing a mixed two-dimensional boundary value problem. The resulting loads between the rigid inertialess strip foundations and the half space due to harmonic displacement excitation are calculated. The mixed boundary value problem is transformed into a system of coupled Fredholm integral equations of the first kind, the kernels being the unknown surface stresses under the foundations. An approximate solution of the integral equations is obtained using the generalized Bubnov-Galerkin method. It is demonstrated that the results provide a simple means for studying the motions of a finite number of adjacent foundations with varying inertia properties.

Effects of Soil Deposition on the Initial Stress State in Model Tests: Experimental Results and FE Simulation

The knowledge of the initial soil state (stress and density distribution) in geotechnical model tests is indispensable, particularly with regard to FE back calculation of experimental results. Usually, so-called \(K_{0}\)-conditions are assumed, which for many cases do not describe the soil stress state before the experiment begins adequately. Using an exemplary test device we present and discuss different measurement techniques for the interpretation of soil deposition procedures and the evaluation of the initial state. By means of stress and bearing force measurements, the stress state is captured representatively. The soil deformations during the filling of the test device are evaluated with Digital Image Correlation (DIC) methods and the initial density distribution is examined by cone penetration tests (CPT). Afterwards, a simple FE simulation method is presented, which models the soil deposition procedure by a weight increase layer-by-layer. It is shown that the method is suitable to provide a realistic initial soil state. The methods presented can be easily transferred to other geotechnical test devices and can in many cases ensure a better comparability of tests with their simulations.

On Soil Deformation and Stress Redistribution Around Pressed-in and Vibrated Displacement Pile Tips

The experimental study compares soil displacement trajectories around model pile tips obtained from Digital Image Correlation (DIC) for different penetration modes. Monotonic and cyclic quasi-static penetration under plane strain-resembling conditions in dry sand and vibratory model pile penetration in saturated sand are investigated. The comparison results agree well although the penetration mode and the degree of saturation differ considerably. In the experiments, the soil below the pile tip is first pushed downwards as the pile approaches and is then moved more and more sidewards. A slight uplift of the grains is observed when the pile tip has passed. Subsequently, a clear trend of the soil adjacent to the pile shaft to move towards the pile is measured in the case of quasistatic cyclic and vibratory penetration. This trend is considered to be an indicator for \(``{\textit{friction~fatigue}}\)”, the degradation of shaft friction at a certain depth as the pile penetrates further. A discussion on the comparability with numerical results and on the influence of disturbing boundary effects concludes this contribution.

The causality of the boundary element method in elastodynamics

The conventional application of the Boundary Element Method in elastodyanmics using ‘shadow zones’ within the domain under consideration violates a particular type of causality constraint. Thus the problems associated with the propagation of waves within the domain under definition are not calculated correctly. In this paper the problems associated with the non-causal region are explored and a way to avoid the difficulties is presented.

Demonstrator Experiments on Significant Effects During Pile Installation

Benchmark tests for the numerical simulation of pile installation require clearly defined boundary value problems with corresponding experimental data. These experiments have to provide quantitative information on the soil deformations and stresses. Large scale model tests in dry, granular soil were carried out for this purpose. The interface testing device, that is used for the tests, allows the investigation of selected aspects of pile penetration. The normal and shear forces on the pile structure are measured. The displacements in the surrounding soil zone can be evaluated via Digital Image Correlation (DIC). The test results concentrate on the interface behavior between the soil and the pile and the evolution of stresses and deformations around the pile tip. For rough pile surfaces the occurrence of dilatancy effects in the pile-soil interface is shown. The localization of deformations in the post-peak phase is analyzed for monotonic and cyclic test paths. The influence of the pile driving mode on the evolution of stresses around the pile tip is demonstrated.

Settlements And Pore Pressure Generation In Sand During Earthquakes – Physical Phenomena And Their 1-D Description

This paper discusses the pore water pressure generation due to earthquake shaking. Moreover a method of settlement prediction during the reconsolidation phase is presented. The cumulative effects are calculated with an explicit (N-type) constitutive model.

Horizontale Stoßbelastung von Pfählen ‐ Modellversuche in der geotechnischen Großzentrifuge in Bochum

Es werden Modellversuche zum Tragverhalten von vertikalen Pfahlen unter horizontaler Stosbelastung vorgestellt, welche in der geotechnischen Groszentrifuge im Bochumer Zentrifugenzentrum durchgefuhrt wurden. Bei einem Beschleunigungsniveau von 50 g wird hierbei ein Prototyppfahl mit einem Durchmesser von 1,5 m und einer eingebundenen Pfahllange von 30 m modelliert. Die Modellpfahle werden mittels eines Schusmechanismus stosartig belastet, wobei zwei verschiedene Stoskraftamplituden verwendet werden. Fur die Pfahlkopflagerung werden die Systeme des freien und des starr eingespannten Pfahlkopfes untersucht. Mit Hilfe einer entsprechend abgestimmten, schnellen Meswerterfassung kann das Tragverhalten des Pfahls wahrend des gesamten Stosverlaufs untersucht werden. Aufgrund der hieraus gewonnenen Erkenntnisse konnen zum einen die dynamischen Effekte bei der horizontalen Anprallbelastung von Pfahlen genauer beschrieben werden als dies bisher der Fall war, und zum anderen konnen fundierte Angaben zur Bemessung von stosbelasteten Pfahlen gemacht werden.