MODELLING OF NONLINEAR DYNAMIC BEHAVIOUR OF A SHALLOW STRIP FOUNDATION WITH MACRO-ELEMENT

A new nonlinear soil-structure interaction macroelement is presented. It models the dynamic behaviour of a shallow strip foundation under seismic action. Based on sub-structured methods, it takes into account the dynamic elastic effect of the infinite far field, and the material and geometrical nonlinear behaviour produced in the near field of the foundation. Effects of soil yielding below the foundation as well as uplift at the interface are considered. Through the concept of macro-element, the overall elastic and plastic behaviour in the soil and at the interface is reduced to its action on the foundation. The macro-element consists of a non linear joint element, expressed in the three degrees of freedom of the strip foundation, reflecting the limited bearing capacity of the foundation. This model provides a practical and efficient tool to study the seismic response of a structure in interaction with the surrounding soil medium. Applications to a bridge pier show the potentialities of this kind of model.     

Soil-Structure Interaction on a Shallow Rigid Circular Foundation: SH Wave Source from Near-Field Excitations

A closed-form wave function analytic solution is presented in this article regarding the two-dimensional scattering and diffraction of a flexible wall sitting on a rigid shallow circular foundation embedded in an elastic half-space that is activated by a nearby anti-plane line source such as a blast caused by underground construction or mineral exploration or a near-field fault rupture, using similar methodology as the other paper in a series [Lee and Luo, 2013]. These wave propagation influences, although often treated as a transient process, may be simulated as linear combinations of steady-simple harmonic responses as studied in this article. Ground surface displacements spectra for wide-band of incident wave frequencies are calculated. Based on the spectra obtained, the dependence of near-field ground displacements are shown with respect to the rise-to-span ratio of foundation profile, frequency of incident waves, distance of source from the foundation, and mass ratios of various media (foundation-structure-soil). The screening effect of rigid foundation upon ground motions behind grazing incident waves is also presented.     

Dynamic Interaction between Rigid Foundations on Multi-layered Stratum

This article concerns the cross-interaction problem among multi-foundations on a linearly viscoelastic medium at very small shear strains. In the analysis, the foundations are discretized into a number of sub square-elements. The dynamic response within each sub-element is described by the Green’s function, which is obtained by the Fourier-Bessel transform and the precise integration method. Incorporating the displacement boundary condition and the force equilibrium of the foundations, it obtains the dynamic impedance and compliance functions of the foundations. Extensive results for two rigid circular foundations placed at different separations are presented. Parametric studies are carried out on the dynamic interaction among adjacent foundations. Illustrative results for several closely spaced foundations are also illustrated.     

The Diffraction of Rayleigh Waves by Twin Circular Cavities in a Poroelastic Half-Space

The diffraction of Rayleigh waves by twin circular cavities in a poroelastic half-space is investigated using the indirect boundary integral equation method (IBIEM). To satisfy the boundary conditions on the free surface, Green’s functions of compressional and shear wave sources in a poroelastic half-space are derived based on Biot’s theory. It is verified that the IBIEM has great accuracy and numerical stability. Then, the influences of the drainage boundary condition, incident wave frequency, porosity, and cavity spacing on the dynamic responses are investigated by numerical examples. The results show that the amplification effect of the twin cavities is greater in the case of undrained boundary conditions, lower frequencies, and smaller cavity spacings. The porosity of the saturated medium also influences the dynamic responses because the velocity of the Rayleigh wave will change with the porosity of the saturated medium.     

Shaking table tests on a stone masonry building: modeling and identification of dynamic properties including soil-foundation-structure interaction

This article presents the identification of dynamic properties of a stone masonry building, followed by numerical simulation of its dynamic response accounting for soil-foundation-structure interaction. The first part regards numerical simulations of the earthquake response of a two-story building prototype with timber floors, made of three-leaf stone masonry without laces. This 1:2 scale prototype was tested on a shaking table in its as-built state and after strengthening, at the National Technical University of Athens. Afterward, the building prototype was modeled with flat shell elements and equivalent frames (common frames and macro-elements), for an investigation of its linear and nonlinear seismic response, assuming base fixity. Numerical results were compared to the experimental ones, which yielded conclusions on the considerations of each employed modeling strategy, as well as its efficiency and applicability. The second part considers the effect of soil-structure interaction using appropriately modified foundation stiffness values to account for the foundation soil flexibility. Comparison of the numerical results with and without SSI effects showed how the flexibility of the soil-foundation system and the soil-structure interaction modified the system’s modal characteristics and response within the elastic range, in terms of both seismic loads and deformations, and produced conclusions about its consequences on the overall structural stability.     

ELASTIC EARTH PRESSURES ON RIGID WALLS UNDER EARTHQUAKE LOADING

Elastic dynamic earth pressures induced by earthquakes are computed by analyzing a wall-foundation-backfill system. Both foundation and backfill are considered viscoelastic; the foundation is a semi-infinite space and the backfill, a uniform layer of constant thickness. A simple analytical solution is developed by assuming an approximate backfill-foundation interface condition and adopting the least squares method. The response functions computed indicate the large influence of the various system parameters on earth pressure, including the foundation characteristics,as well as wall geometry and mass. The transient response of the system is also studied by obtaining spectra for base shear. A large number of seismic records are analyzed to obtain average spectra and a total of three correction functions are used to take into account the foundation stiffness and density as well as wall inertia. A simple design method is proposed to estimate the maximum base shear.     

Experimental and Analytical Study of Seismic Soil-Pile-Structure Interaction in Layered Soil Half-Space

The dynamic interaction of pile foundations, embedded in a horizontally stratified soil profile, with superstructures under low to moderate earthquake excitation can be handled in different ways. In this article, the soil-pile-superstructure dynamic interaction problem has been investigated using the coupled finite element-boundary element method. Comparison with shaking table experiments of a small scale model pile shows a good correlation with the proposed method in terms of the kinematic response of pile foundations and the structural response. A parametric study of the proposed model has yielded important results essentially concerning the amplification factors of the pile foundation and the superstructure.     

NUMERICAL ANALYSIS OF EMBANKMENT FOUNDATION LIQUEFACTION COUNTERMEASURES

Computational simulations are presented for a unique series of centrifuge tests conducted to assess the performance of liquefaction countermeasure techniques. In these centrifuge tests, the dynamic response of an embankment supported on a liquefiable foundation (medium sand) is investigated. The experimental series included: (i) a benchmark test without a liquefaction countermeasure, (ii) foundation densiflcation below the embankment toe, and (iii) use of a sheet-pile containment enclosure below the embankment. This series of experiments documents a wide range of practical liquefaction response mechanisms (including countermeasure implementation). In order to numerically simulate the above centrifuge tests, a new calibrated soil stress-strain constitutive model is incorporated into a two-phase (solid-fluid) fully coupled Finite Element formulation. Comparison of the computational and experimental results demonstrates: (i) importance of post-liquefaction dilative soil behavior in dictating the dynamic response and deformation characteristics of the embankment-foundation system, and (ii) capabilities and limitations of the numerical modeling procedure.     

ANALYSIS OF PORE PRESSURE GENERATION AND DISSIPATION IN COHESIONLESS MATERIALS DURING SEISMIC LOADING

The earthquake loading of a shallow foundation resting on top of a cohesionless layer creates cyclic variations in the shear force and overturning moment acting on the supporting soil. These loads induce a tendency for volume change which, in turn, depending on the drainage conditions and material permeability, may cause in addition to a cyclic pore pressure variation a progressive pore pressure buildup. The paper develops an efficient and elegant way, based on a multiple time scale analysis, of solving this fully coupled problem. The theoretical solution is implemented in a finite element code and is applied to predict the pore pressure development and dissipation under a bridge pier foundation for which it was essential to limit the pore pressure increase.     

Nested Lumped-Parameter Model for Foundation with Strongly Frequency-dependent Impedance

A nested lumped-parameter model (LPM) consisting of frequency-independent springs and dashpots is proposed to represent the foundation-soil dynamic system with strongly frequency-dependent impedance in time domain. Due to the convergence and robustness of the complex Chebyshev polynomial, it is used to approximate the dynamic flexibility of the foundation by least-square curve-fitting technique. The comparisons with existing LPMs show that the present model can express the impedance by using a small number of elements and reduce oscillation of the solution appearing in simple polynomial approximations. Finally, several examples of foundations with irregular geometries are presented to show the application of nested LPMs.     

SIMPLE EXPRESSION OF THE DYNAMIC STIFFNESS OF GROUPED PILES IN SWAY MOTION

A simplified expression is derived for the dynamic stiffness of grouped piles subjected to lateral loading. A computer program, based on the Thin Layered Element Method, is used for this purpose. The results of the program are compared with rigorous solutions. The simplified expression of the dynamic stiffness of grouped piles, where the mass, damping and stiffness parameters are frequency invariant, will be particularly useful for an equivalent linear analysis of the interaction between nonlinear soil and grouped piles in real time.     

Evaluation of Side Boundary Effects on Dynamic Numerical Modeling for Centrifugal Model Tests

Four different boundary conditions consisting of fixed nodes, motion of roller only in the z or the x direction, and equivalent motion of two side boundaries were applied with a finite element code to simulate seismic behavior of two foundation conditions consisting of dry loose and dense sands. Comparing numerical results with physical model tests indicates that data obtained from the finite element code when considering soil nonlinearity with a sand model based on the tij concept have acceptable agreements with those from dynamic centrifuge tests regardless of the boundary conditions. The results from the boundary conditions of roller in the x direction and equivalent motion of two side boundaries agree well with the experimental data in wave peaks. The two side boundary conditions also keep the ground middle undisturbed and provide the results that are similar to those obtained from the wave amplification experimental data. For numerical simulations of centrifuge model tests, the side boundary condition with roller in the x direction is recommended because of low computation time and high simulation quality.     

COUPLED P-Y T-Z ANALYSIS OF SINGLE PILES IN COHESIONLESS SOIL UNDER VERTICAL AND/OR HORIZONTAL GROUND MOTION

Various approaches are currently used for the analysis of piles under vertical and lateral loading. Among these, the beam-on-a-nonlinear Winkler foundation (BNWF) approach using published P-y, T-z and Q-z curves is widely used in practice. In this approach, the P-y and T-z responses are generally uncoupled from each other. The objective of this paper is to investigate the influence that the coupling of the P-y and T-z responses has.on the cyclic and dynamic response of piles in cohesionless soil. A cyclic model is first developed and a parametric study is conducted to investigate the effect the initial confining pressure, angle of wall friction and effective vertical stiffness have on the lateral cyclic hysteretic response. A dynamic model is then developed, and used to study the response of a single pile in cohesionless soil under horizontal and/or vertical ground motion. Results from the parametric study showed that the three parameters did not have a significant influence on the lateral cyclic hysteretic response. Under horizontal and/or vertical ground motion, the horizontal ground motion was observed to dominate the inertial interaction response, and significantly affected both the horizontal and vertical displacement response, mainly due to second-order P-Δ and gapping effects.     

ON THE RELATIONSHIP BETWEEN SECTORAL AND SPATIAL MANAGEMENT IN THE ELECTRIC POWER INDUSTRY OF THE USSR

The management system of the electric power industry of the USSR operates at two technological levels: a lower level of 92 regional power systems, each encompassing one or more oblast-type civil divisions or a small union republic; an upper level in which regional systems are combined into 11 unified power systems, where peak loads can be more easily moved between time zones. In addition there are electric power administrations within the RSFSR and ministries within the union republics, concerned mainly with administrative functions. Power administrations often do not coincide with unified systems, creating problems of efficient electric power management. Furthermore, the boundaries of unified power systems and power administrations often do not conform to the boundaries of major economic regions, which are used for current and long-term planning of the Soviet economy. This does not necessarily mean that the power systems are out of step with the economic regions. Soviet economic regionalization theory has long stressed the important region-shaping role of electric power systems. It may well be that in some cases, the boundaries of economic regions, not the power systems, require adjustment.     

Real-Time Dynamic Hybrid Testing Coupling Finite Element and Shaking Table

In this article, a Simulink simulation block with the finite element function is developed on the basis of S-function and implemented as the numerical substructure of real-time dynamic hybrid testing. Thereby, a real-time dynamic hybrid testing system coupling finite element calculation and shaking table testing is achieved. Using the developed system, a shear frame mounted on the soil foundation is tested, in which the shear frame is simulated as the physical model and the foundation is simulated as the finite element model with 132 degrees of freedom. Several cases of the dynamic behavior of soil-structure interaction are studied.     

Shaking Table Test of the Taiwanese Traditional Dieh-Dou Timber Frame

This article attempts to explore the dynamic behavior of traditional Dieh-Dou timber structure under different combinations of structural forms and vertical loads. Using time-history record (TCU 084) from the Chi-Chi earthquake, two semi full-scale specimens (Symmetric and Asymmetric) were tested. Results showed that the Symmetric specimen tends to be damaged more easily and faster than the Asymmetric one. Damage pattern generally begins from the bottom Dou members and subsequently spreading upwards to the upper Dou, horizontal Gong members, and adjoining Shu members. Friction force between the contact surfaces is crucial towards the maintenance of overall structure. Increase vertical loadings have significant effect on the natural frequencies and global stiffness of the structure. Using the Single-Degree-Of-Freedom (SDOF) system, the derived stiffness is generally in good agreement with the dynamic results of both forms. This study suggests that the effects of increasing vertical loadings should be taken into consideration for future evaluation.     

Contact Dynamics of Masonry Block Structures Using Mathematical Programming

A simple variational formulation for contact dynamics is adopted to investigate the dynamic behavior of planar masonry block structures subjected to seismic events. The numerical model is a two-dimensional assemblage of rigid blocks interacting at potential contact points located at the vertices of the interfaces. A no-tension and associative frictional behavior with infinite compressive strength is considered for joints. The dynamic contact problem is formulated as a quadratic programming problem (QP) and an iterative procedure is implemented for time integration. Applications to analytical and numerical case studies are presented for validation. Comparisons with the experimental results of a masonry wall under free rocking motion and of a small scale panel with opening subjected to in-plane loads are also carried out to evaluate the accuracy and the computational efficiency of the formulation adopted.     

A SIMPLE METHOD FOR ANALYSIS OF SLIDING STRUCTURES CONSIDERING VARIATIONS OF FRICTION COEFFICIENT

In this paper, the responses of multidegree of freedom (MDOF) structures on sliding foundations, subjected to harmonic or random base motions, are investigated taking into consideration the variations of friction forces. The variation of friction force is a consequence of variation of friction coefficient, which depends on such parameters as relative velocity and the existing pressure. Modelling of the friction force under the foundation raft is accomplished by using a fictitious rigid link with a rigid-perfectly plastic material. This results in identical equations of motion for the sliding structure, both in the sliding and nonsliding (stick) phases and considerably decreases the required number of time steps for the nonlinear analysis. Since the force in the link is of constant value, to consider the varying friction force, a compensatory force, which is the difference between the exact friction force and the constant force in the rigid link, is applied to the foundation raft. A model of variable friction coefficient for Teflon-steel interfaces is used for the assessment of the method and the results are compared with existing literature, through which, the capability of the method is illustrated. It is shown that by using exact model of friction lower values for the superstructure responses are predicted compared with those obtained by using Coulomb friction model. Furthermore the effect of the stiffness of the structure on the differences between the results of the two models is also studied.     

Empirical Formulation for Estimating the Fundamental Frequency of Slender Masonry Structures

The fundamental frequency of a structure enables better assessment of its seismic demand for an efficient design and planning of its maintenance and retrofit strategy. The frequency is independent of the type of external loads, however, depends on structural stiffness, mass, damping and boundary conditions. In the case of slender masonry structures such as towers, minarets chimneys, and pagoda temples, it is influenced by mass and stiffness distribution, connection to adjacent structures, material properties, aspect ratio and slenderness ratio. In this present article, the data collected from various literature reviews on the slender masonry structures regarding dynamic, geometrical, and mechanical characteristics have been correlated to identify the major parameters influencing the fundamental frequency of such structures. The database has been used for developing an empirical formulation for predicting the fundamental frequency of such structures. The comparison between the experimental fundamental frequencies and the estimated fundamental frequencies are carried out in order to define reliability and accuracy of these empirical formulae.     

Dynamic Response of Saturated Soil - Foundation System Acted upon by Vibration

In this study, the response and behavior of machine foundations resting on dry and saturated sand was investigated experimentally. In order to investigate the response of soil and footing to steady state dynamic loading, a physical model was manufactured to simulate steady state harmonic load at different operating frequencies. Total of 84 physical models were performed. The footing parameters are related to the size of the rectangular footing and depth of embedment. Two sizes of rectangular steel model footing were tested at the surface and at 50 mm depth below model surface. Meanwhile the investigated parameters of the soil condition include dry and saturated sand for two relative densities 30% and 80%. The response of the footing was elaborated by measuring the amplitude of displacement by the vibration meter. The response of the soil to dynamic loading includes measuring the stresses inside the soil using piezoelectric sensors as well as measuring the excess pore water pressure using pore water pressure transducers. It was concluded that the maximum displacement amplitude response of the foundation resting on dry sand models is more than that on the saturated sand by about 5.0–10%. The maximum displacement amplitude of footing is reduced to half when the size of footing is doubled for dry and saturated sand. The final settlement (St) of the foundation increases with increasing the amplitude of dynamic force, operating frequency and degree of saturation. Meanwhile, it is reduced with increasing the relative density of sand, modulus of elasticity, and embedding inside soils. The excess pore water pressure increases with increasing the relative density of the sand, the amplitude of dynamic loading and the operating frequency. In contrast, the rate of dissipation of the excess pore water pressure during dynamic loading is more in the case of loose sand.