CALCULATING THE DYNAMIC STIFFNESS MATRIX OF 2-D FOUNDATIONS BY DISCRETE WAVE NUMBER INDIRECT BOUNDARY ELEMENT METHODS

Apart from some special cases, calculating the dynamic stiffness matrix of foundations on a layered half-space, especially for embedded foundations, is computationally expensive. An efficient method for two-dimensional foundations in a horizontally layered soil media is presented in this paper. This method is based on indirect boundary element methods and uses discrete wave number solution methods for calculating Green's functions for displacements and analytical methods for the integrations over the boundary. For surface foundations, the present method applies at all frequencies. For embedded foundations or for constructing energy transmitting boundaries, because the free-field part is modelled by boundary elements and the excavated part is modelled by finite elements, the present method applies only at low frequencies for the spring coefficients (the real parts of the dynamic stiffness matrix) but applies at all frequencies for the damping coefficients (the imaginary part of the dynamic stiffness matrix) for undamped sites. The novelty of the method can be used for three-dimensional foundations. © 1997 by John Wiley & Sons, Ltd.     

Seismic behaviour of confined masonry walls

The results of tests of plain and confined masonry walls with h/l ratio equal to 1·5, made at 1:5 scale, have been used to develop a rational method for modelling the seismic behaviour of confined masonry walls. A trilinear model of lateral resistance–displacement envelope curve has been proposed, where the resistance is calculated as a combination of the shear resistance of the plain masonry wall panel and dowel effect of the tie-columns’ reinforcement. Lateral stiffness, however, is modelled as a function of the initial effective stiffness and damage, occurring to the panel at characteristic limit states. Good correlation between the predicted and experimental envelopes has been obtained in the particular case studied. The method has been also verified for the case of prototype confined masonry walls with h/l ratio equal to 1·0. Good correlation between the predicted and experimental values of lateral resistance indicates the general validity of the proposed method. © 1997 John Wiley & Sons, Ltd.     

Spring-dashpot-mass models for foundation vibrations

The foundation on deformable soil, which, in general, radiates energy, can be represented in structural dynamics as a simple spring-dashpot-mass model with frequency-independent coefficients. For the two limiting cases of a site, the homogeneous half-space and the homogeneous layer fixed at its base, the coefficients are specified in tables for varying parameters such as ratios of dimensions and Poisson's ratio. Rigid foundations on the surface and with embedment are considered for all translational and rotational motions. In a practical analysis of soil–structure interaction this dynamic model of the foundation is coupled directly to that of the structure, whereby a standard dynamics program is used. © 1997 by John Wiley & Sons, Ltd.     

考虑尺寸效应的近海桥梁天然橡胶隔震支座力学性能老化时变规律研究

目前天然橡胶支座（NRB）的性能研究大多未考虑尺寸效应,在前期开展的近海桥梁隔震支座和材料老化时变规律研究的基础上,同时考虑支座直径尺寸变化和老化作用时间的影响对NRB的性能进行研究。首先采用ABAQUS有限元软件对不同直径尺寸NRB的性能进行分析,得到了NRB性能随直径尺寸的变化规律;然后结合前期老化作用对NRB及其橡胶材料性能时变规律的影响研究成果,分析了直径尺寸及老化作用时间共同作用下,NRB性能的变化规律,并通过ABAQUS有限元分析,验证了该变化规律的准确性。结果表明:NRB的水平刚度和竖向刚度均随其直径尺寸的增大呈正比例增大趋势;NRB水平刚度比和竖向刚度比均随老化作用时间的增长呈线性增大趋势;且直径为150mm的NRB在实际环境老化60a后,其水平刚度和竖向刚度的增长幅度分别为:30.8%和16.41%,由此可见老化作用时间对NRB水平刚度的影响较显著,对其竖向刚度的影响较小。研究内容可为隔震桥梁结构中支座缩尺模型试验的相关设计提供参考,并为将实验室缩尺橡胶隔震支座的相关成果较好地应用于实际工程计算及设计中提供依据。     

Seismic responses of postyield hardening single–degree-of-freedom systems incorporating high-strength elastic material

It is widely accepted that ductility design improves the seismic capacity of structures worldwide. Nevertheless, inelastic deformation allows serious damage to occur in structures. Previous studies have shown that a certain level of postyield stiffness may reduce both the peak displacement and residual deformation of a structure. In recent years, several high-strength elastic materials, such as fiber-reinforced polymer (FRP) and high-strength steel bars, have been developed. Application of these materials can easily provide a structure with a much higher and more stable postyield stiffness. Many materials, members, and structures that incorporate both high-strength elastic materials and conventional materials show significant postyield hardening (PYH) behaviors. The significant postyield stiffness of PYH structures can help effectively reduce both peak and residual deformations, providing a choice when designing resilient structures. However, the findings of previous studies of structures with elastic-perfectly plastic (EPP) behavior or small postyield stiffness may not be accurate for PYH structures. The postyield stiffness of a structure must be considered an important primary structural parameter, in addition to initial stiffness, yielding strength, and ductility. In this paper, extensive time history and statistical analyses are carried out for PYH single–degree-of-freedom (SDOF) systems. The mean values and coefficients of variation of the peak displacement and residual deformation are obtained and discussed. A new R-μ_p-T-α relationship and damage index for PYH structures are proposed. A theoretical model for the calculation of residual deformation is also established. These models provide a basis for developing the appropriate seismic design and performance evaluation procedures for PYH structures.     

EFFECT OF SLAB FLEXIBILITY ON INTERACTION BETWEEN TWO CIRCULAR FOUNDATIONS

The paper is aimed at investigating the effect of foundation rigidity on dynamic stiffness for two circular foundations on a viscoelastic medium. To generate the dynamic stiffness, a substructure technique is employed. For the substructure of a viscoelastic medium, the solution for wave motion reported in Reference 11 is used. For the substructures of two flexible foundations, classical plate theory with the inertial force neglected is employed to find the displacement fields of the foundation plates subjected to the interaction stresses. Then, the continuity condition for all the substructures is imposed implicitly by using the variational principle; then with the help of the reciprocal theorem the dynamic stiffness for the two flexible foundations can be obtained. For the numerical study, the boundary condition at the rims of both foundation plates is assumed to be a hinge connection to superstructures. Some numerical investigations are performed and the effect of foundation rigidity on dynamic stiffness is examined. Some discussions and conclusions are also made.     

SEQUENTIAL STIFFNESS DESIGN FOR SEISMIC DRIFT RANGES OF A SHEAR BUILDING–PILE–SOIL SYSTEM

A shear building supported by a prescribed pile–soil system is subjected to bedrock earthquake input. A new design procedure is presented for generating a sequence of stiffness designs satisfying the constraints on interstorey drifts. The mean peak interstorey drifts of the shear building subjected to a set of spectrum-compatible ground motions at the bedrock are evaluated by a modal combination rule. Tuning of the fundamental natural period of a shear building with a fixed base with that of a shear beam ground results in a non-monotonic sequence of stiffness designs with respect to a ground stiffness parameter and previous approaches cannot be applied to such a problem. This difficulty in finding such a non-monotonic sequence is overcome by utilizing the ground stiffness parameter and the superstructure stiffness parameter alternately in multiple design phases and by developing a new multi-phase perturbation technique. Fundamental characteristics of this sequence of stiffness designs and the effect of ground stiffnesses on the design of the shear building are disclosed. It is further shown that the stiffness contour method is also useful for the design procedure such that a scattering effect in the estimates of ground stiffnesses is taken into account. The usefulness of the proposed procedure of sequential stiffness design and contour line method is demonstrated through several sequential design examples.     

Experimental investigation of the vertical pullout cyclic response of bucket foundations in sand

A series of 1 g model tests was conducted to investigate the accumulated vertical pullout displacement and unloading stiffness of bucket foundations embedded in dry and saturated sands. The foundations were subjected to vertical pullout cyclic loading with different load amplitudes. Cyclic load was applied up to 10⁴ cycles. Test results showed that the accumulated vertical pullout displacement increased with the increase in the number of load cycles and cyclic load amplitudes. The unloading stiffness of the bucket foundations decreased with the increase in load amplitude and number of cycles. Empirical equations were proposed based on the test results to evaluate the accumulated vertical pullout displacement and unloading stiffness of the bucket foundations in saturated sand. These equations can be used for the preliminary design of single or tripod bucket foundations.     

系缆损伤对绷紧式系泊系统动力响应的影响

探究合成纤维系缆损伤对绷紧式系泊系统响应的影响,具有重要的工程意义。通过高强聚乙烯(HMPE)缆绳损伤动刚度实验,获得其动刚度随损伤的演变规律。在数值计算上,借鉴并合理简化了前人提出的动刚度经验公式,通过处理实验结果确定动刚度经验公式的参数并进行验证。在此基础上,以一座采用高强聚乙烯缆绳为主体系缆的FPSO为例,将所得动刚度经验公式导入系泊分析软件,结合水动力分析,计算得到在相同海洋环境中,系缆发生不同程度损伤时,各系缆张力和平台偏移响应的结果。通过处理、分析所得的计算结果,获得合成纤维缆绳损伤演变对绷紧式系泊系统响应的影响规律,并据此为系缆更换提供了建议。这些成果既有利于把握绷紧式系泊系统的非线性动力响应,也对安全、经济、合理地运用合成纤维系缆具有重要意义。     

Motion and Dynamic Responses of A Semisubmersible in Freak Waves

The present research aims at clarifying the effects of freak wave on the motion and dynamic responses of a semisubmersible. To reveal the effects of mooring stiffness, two mooring systems were employed in the model tests and time-domain simulations. The 6-DOF motion responses and mooring tensions have been measured and the 3-DOF motions of fairleads were calculated as well. From the time series, trajectories and statistics information, the interactions between the freak wave and the semisubmersible have been demonstrated and the effects of mooring stiffness have been identified. The shortage of numerical simulations based on 3D potential flow theory is presented. Results show that the freak wave is likely to cause large horizontal motions for soft mooring system and to result in extremely large mooring tensions for tight mooring system. Therefore, the freak wave is a real threat for the marine structure, which needs to be carefully considered at design stage.