Rectangular footing on soil with depth-degrading stiffness: Vertical and rocking impedances under conditional existence of surface waves

The response of rectangular rigid footings resting on an elastic soil of shear modulus decreasing monotonically with depth is studied. Such profiles are typically encountered after ground improvement. The propagation characteristics of SV/P surface waves are investigated, showing the appearance of cut-off frequencies above which surface waves do not exist. The semi-analytical method of the subdivision of the footing/soil contact area is then used for solving the boundary value problem, whereby the influence functions for the sub-regions are determined by integration of the corresponding surface-to-surface Green׳s functions. Impedance functions are presented over a wide range of frequencies for typical values of the non-homogeneity parameters, the Poisson׳s ratio and the foundation geometry. The salient features that are associated with the non-homogeneity and the appearance of cut-off frequencies are elucidated.     

Simplified discrete systems for dynamic analysis of structures on footings and piles

A simplified discrete system in the form of a simple oscillator is developed to simulate the dynamic behavior of a structure founded through footings or piles on compliant ground, under harmonic excitation. Exact analytical expressions for the fundamental natural period and the corresponding damping coefficients of the above system are derived, as function of geometry and the frequency-dependent foundation impedances. In an effort to quantify the coupling between swaying and rocking oscillations in embedded foundations such as piles, the reference system is translated from the footing–soil interface to the depth where the resultant soil reaction is applied, to ensure a diagonal impedance matrix. The resulting eccentricity is a measure of the coupling effect between the two oscillation modes. The amounts of radiation damping generated from a single pile and a surface footing are evaluated. In order to compare the damping of a structure on a surface footing and a pile, the notion of static and geometric equivalence is introduced. It is shown that a pile may generate significantly higher radiation damping than an equivalent footing, thus acting as an elementary protective system against seismic action.     

Embedded foundation in layered soil under dynamic excitations

The critical step in the substructure approach for the soil–structure interaction (SSI) problem is to determine the impedance functions (dynamic-stiffness coefficients) of the foundations. In the present study, a computational tool is developed to determine the impedance functions of foundation in layered soil medium. Cone frustums are used to model the foundation soil system. Cone frustums are developed based on wave propagation principles and force-equilibrium approach. The model is validated for its ability to represent the embedded foundation in layered medium by comparing the results with the rigorous analysis results. Various degrees of freedom, such as, horizontal, vertical and rocking are considered for this study.     

A practical method for estimating dynamic soil stiffness on surface of multi‐layered soil

It is important to estimate the influence of layered soil in soil–structure interaction analyses. Although a great number of investigations have been carried out on this subject, there are very few practical methods that do not require complex calculations. In this paper, a simple and practical method for estimating the horizontal dynamic stiffness of a rigid foundation on the surface of multi‐layered soil is proposed. In this method, waves propagating in the soil are traced using the conception of the cone model, and the impulse response function can be calculated directly and easily in the time domain with a good degree of accuracy. The characteristics of the impedance, that is the transformed value to the frequency domain of the obtained impulse response, are studied using two‐ to four‐layered soil models. The cause of the fluctuation of impedance is expressed clearly from its relation to reflected waves from the lower layer boundary in the model. Copyright © 2005 John Wiley & Sons, Ltd.     

A method for nonlinear dynamic response analysis of semi-infinite foundation soil

This paper presents development of a special finite difference method for the nonlinear dynamic response analysis of semi-infinite foundation soil. Semi-infinite domain is mapped into the finite domain using special mapping. For the region of engineering interest, mapping is isometrical, and for far field, shrink mapping which transforms an infinite interval into a finite interval is adopted. Using linear and nonlinear constitutive models, the responses of semi-infinite foundation soil are computed using a proposed method with a small mesh model and an extensive mesh model. Surface loadings or incident earthquake waves are applied to the models in the computations. Good agreements were obtained among the theoretical and computed results of the two models and the effectiveness of the proposed method was demonstrated.     

A numerical and experimental study of hollow steel pile in layered soil subjected to lateral dynamic loading

The present study aims at investigating the nonlinear behavior of single hollow pile in layered soil subjected to varying levels of horizontal dynamic load. A finite element model has been developed using commercially available FEM based software. Mohr–Coulomb plasticity model is used to simulate the soil plasticity whereas the pile-material is idealized as elastic. Numerical results are validated comparing with the experimental results. The experimental investigations were carried out in the field located at IIT Kharagpur. Two types of motion: horizontal and rocking are studied. The effects of various influencing parameters, namely, exciting moment, length and diameter of the pile etc. on the nonlinear dynamic response of piles are investigated. It is found that separation of pile from the surrounding soil considerably affects the resonance frequency and amplitude of the pile foundations.     

埋地管线-土横向动力相互作用等效弹簧系数解析解

基于一维柱面弹性波动理论,推导了埋地管线-土横向动力相互作用等效弹簧系数解析表达式,并对该表达式的影响因素,诸如频率(ω)、管线埋深(d)、管线半径(b)、场地波速(VP)、泊松比(μ)的影响程度进行了分析。分析结果表明,无量纲频率bω/VP取较小值时(<0.1),弹簧系数取值随着管线埋深与管线半径之比γ的增加而增大,但总是限制在2.0G～4.0G(G为土体剪切模量)之间,且泊松比对其影响很小,对于工程实际情况,弹簧系数可在该范围内取值。     

Cyclic shearing and liquefaction of soil under irregular loading: an incremental model for the dynamic earthquake-induced deformation

The paper presents a mathematical model for the deformation of soil under irregular cyclic loading in the simple-shear conditions. The model includes the possible change in the effective pressure in saturated soil due to the cyclic shearing, the reciprocal influence of the effective pressure on the response of the soil to the shear loading, and the pore pressure dissipation due to the seepage of the pore fluid. The hysteresis curves for the strain–stress relationship are constructed in such a way that they produce both the required backbone curve and the required damping ratio as functions of the strain amplitude. At the same time, the approach enables the constitutive functions involved in the model to be specified in various ways depending on the soil under study. The constitutive functions can be calibrated independently of each other from the conventional cyclic shear tests. The constitutive model is incorporated in the boundary value problem for the dynamic site response analysis of level ground. A numerical solution is presented for the dynamic deformation and liquefaction of soil at the Port Island site during the 1995 Hyogoken-Nambu earthquake.     

Generalized failure envelope for caisson foundations in cohesive soil: Static and dynamic loading

The response of massive caisson foundations to combined vertical (N), horizontal (Q) and moment (M) loading is investigated parametrically by a series of three-dimensional finite element analyses. The study considers foundations in cohesive soil, with due consideration to the caisson-soil contact interface conditions. The ultimate limit states are presented by failure envelopes in dimensionless and normalized forms and the effects of the embedment ratio, vertical load and interface friction on the bearing capacity are studied in detail. Particular emphasis is given on the physical and geometrical interpretation of the kinematic mechanisms that accompany failure, with respect to the loading ratio M/Q. Exploiting the numerical results, analytical expressions are derived for the capacities under pure horizontal, moment and vertical loading, for certain conditions. For the case of fully bonded interface conditions, comparison is given with upper bound limit equilibrium solutions based on Brinch Hansen theory for the ultimate lateral soil reaction. A generalized closed-form expression for the failure envelope in M–Q–N space is then proposed and validated for all cases examined. It is shown that the incremental displacement vector of the caisson at failure follows an associated flow rule, with respect to the envelope, irrespective of: (a) the caisson geometry, and (b) the interface conditions. A simplified geometrical explanation and physical interpretation of the associativity in M-Q load space is also provided. Finally, the derived failure envelope is validated against low (0.67 Hz) and high frequency (5 Hz) dynamic loading tests and the role of radiation damping on the response of the caisson at near failure conditions is unraveled.     

Development of pedotransfer functions for soil hydraulic properties in the critical zone on the Loess Plateau,China

Soil hydraulic properties (SHPs) including the soil water retention curve and saturated soil hydraulic conductivity (Ks) are crucial input data for simulations of soil water and solute transport in the Earth's critical zone. However, obtaining direct measurements of SHPs at a wide range of scales is time consuming and expensive. Pedotransfer functions (PTFs) are employed as an alternative method for indirectly estimating these parameters based on readily measured soil properties. However, PTFs for SHPs for the deep soil layer in the Earth's critical zone are lacking. In this study, we developed new PTFs in the deep soil profile for Ks and soil water retention curve on the Loess Plateau, China, which were fitted with the van Genuchten equation. In total, 206 data sets comprising the hydraulic and basic soil properties were obtained from three typical sites. Samples were collected from the top of the soil profile to the bedrock by soil core drilling. PTFs were developed between the SHPs and basic soil properties using stepwise multiple linear regression. The PTFs obtained the best predictions for Ks (R_adj² = 0.561) and the worst for van Genuchten α (R_adj² = 0.474). The bulk density and sand content were important input variables for predicting Ks, α, and θs, and bulk density, clay content, and soil organic carbon were important for n. The PTFs developed in this study performed better than existing PTFs. This study contains the first set of PTFs of SHPs to be developed for the deep profile on the Loess Plateau, and they may be applicable to other regions.     

Monitoring soil erosion on agricultural land: results and implications for the Rother valley,West Sussex,UK

Monitoring has played a key role in understanding the rates, extent and frequency of erosion on agricultural land and this includes projects in Switzerland, Germany and the UK. In this case we focus on highly erodible soils in the Rother valley, West Sussex, southern England on which grow a range of arable crops throughout the year. Erosion rates and extent are high, particularly in response to exceptionally wet periods in the early winter. In the monitored period, rates on summer crops were relatively low due to an absence of intense summer storms. In the years 2015–2020, erosion was localized to where limited areas of bare ground coincided with heavy winter rainfall. Issues of river pollution, associated with excessive sedimentation, off-site flooding and a high degree of connectivity between arable fields and the river, are of increasing concern. Mitigation measures need to be expanded to protect freshwater systems and properties. This study has implications for similar programmes in intensely farmed regions. © 2020 John Wiley & Sons, Ltd.