A numerical model for the transient analysis of offshore foundations under cyclic loading

A comprehensive numerical model for the analysis of offshore foundations under a general transient loading is presented here. The theoretical basis of the model lies on the Swansea formulation of Biot’s equations of dynamic poroelasticity combined with a constitutive model that reproduces key aspects of cyclic soil behaviour in the frame of the theory of generalised plasticity. On the practical side, the adoption of appropriate finite element formulations may prevent the appearance of spurious numerical instabilities of the pore pressure field. In this respect, the use of a coupled enhanced-strain element is here proposed. On the other hand, the practicality of the presented model depends ultimately on its computational efficiency. Some practical recommendations concerning the solution strategies, the matrix storage/handling procedures and the parallel multi-processor computation are here provided. Finally, the performance of the model with a benchmark study case and its practical application to analyse the soil–structure interaction of an offshore monopile under a realistic transient storm loading are discussed.     

强夯法加固地基的多重耦合分析

强夯法加固地基的机理非常复杂,影响因素众多,且涉及到多重耦合现象。笔者综合考虑地基士的流、固、动力耦合和地基与夯锤接触表面的动力耦合情况,给出了基于三维有限单元法的计算方法和迭代格式,并对一具体算例进行了耦合数值分析,总结了地基位移、应力及接触反力等在强夯作用时间内的变化规律和在空间上的分布特征。经与实际工程资料对比,结果令人满意。说明所建立的耦合方法可用于强夯加固法求解,并提出了适宜动力分析的有效方法,可应用于其它同类问题的分析计算中。     

Multiphase model for inclusion‐reinforced geostructures: Application to rock‐bolted tunnels and piled raft foundations

A multiphase model is proposed to describe the mechanical behaviour of geomaterials reinforced by linear inclusions. This macroscopic approach considers the reinforced soil or rock mass as the superposition of continuous media. Equations of motion and constitutive laws of the model are first derived. Its implementation in a finite element computer code is then detailed. A modified implicit algorithm for elastoplastic problems is proposed. The model and its implementation are fully validated for rock‐bolted tunnels (comparison with scale model experiments) and piled raft foundations (comparison with the classical ‘hybrid method’). The Messeturm case history is finally presented to assess the handiness of the approach for real structures. Copyright © 2001 John Wiley & Sons, Ltd.     

A semi‐analytical approach for modelling heat transfer during salt‐cavern leaching process

The use of gas‐storage caverns in salt formations is a growing industry that continues to gain momentum because it allows gas to be injected and withdrawn at high rates compared with other underground gas‐storage systems such as porous rock systems. In order to predict cavern production performances, cavern thermodynamics behaviour must be studied by higher accuracy approaches. This behaviour is extremely related to the temperature distribution in the surrounding formations. During the leaching process, the thermal equilibrium of the rock salt surrounding the cavern is extensively disrupted. The purpose of this paper is to study the heat transfer problem during the leaching process and to develop a thermal model that can be easily used in field applications. The results of this work will be the input data for the prediction of the gas temperature and pressure during cavern gas‐storage operation phase. Moreover, the developed model can find its use in the design of salt caverns since it can be coupled with geometrical modelling of salt dissolution codes. Copyright © 2008 John Wiley & Sons, Ltd.     

倒T型导管墙桩基防波堤稳定性简化计算方法

倒T型导管墙桩基防波堤是一种重力式和桩基式混合而成的新型防波堤,具有复杂的承载机制和破坏模式。建立倒T型导管墙桩基防波堤稳定性分析的三维弹塑性有限元模型,分析极限状态下结构的位移场分布,得出其失稳模式为绕底板下且偏离桩基轴线一定距离的某点发生转动失稳。结合有限元法和极限平衡法,建立该新型防波堤的抗滑稳定性、抗倾稳定性计算的简化方法。与有限元计算结果的比较表明,建立的简化计算方法是可靠的。     

Numerical modelling of seepage beneath skirted foundations subjected to vertical uplift

This study reports the results of small strain finite element analyses undertaken to determine the rate of displacement of skirted foundations subjected to uplift loading, due to combined swelling and seepage. Compatibility of foundation movement with cumulative seepage of water into the skirt compartment is modelled using a layer of soft poroelastic material immediately below the foundation top plate. Performance of the model is first assessed for a range of stiffness values for the soft layer. The model is then used to investigate the rate of displacement for skirt depths ranging from 0.1 to 1 times the foundation diameter. The results are compared with available theoretical solutions and experimental results, and expressions are provided for calculating the equivalent seepage lengths and resulting uplift velocities. The effect on the seepage behaviour of the presence of a gap down the external skirt–soil interface is also discussed.     

Three‐dimensional finite element analysis of the interaction between tunneling and pile foundations

This paper concerns analysis of the impact of construction of urban tunnels on adjacent pile foundations. It is carried out using an elastoplastic three‐dimensional finite element modelling. Numerical simulations are performed in two stages, which concern, respectively, the application of the pile axial loading and the construction of the tunnel in presence of the pile foundations. Analysis is carried out for both single piles and groups of piles. Results of numerical simulations show that tunneling induces significant internal forces in adjacent piles. The distribution of internal forces depends mainly on the position of the pile tip regarding the tunnel horizontal axis and the distance of the pile axis from the centre of the tunnel. Analysis of the interaction between tunneling and a group of piles reveals a positive group effect with a high reduction of the internal forces in rear piles. Copyright © 2002 John Wiley & Sons, Ltd.     

A three‐dimensional staggered finite element approach for random parametric modeling of thermo‐hygral coupled phenomena in porous media

The aim of this paper is to present a three‐dimensional (3D) finite element modeling of heat and mass transfer phenomena in partially saturated open porous media with random fields of material properties. Randomness leads to transfer processes within the porous medium that naturally need a full 3D modeling for any quantitative assessment of these processes. Nevertheless, the counterpart of 3D modeling is a significant increase in computations cost. Therefore, a staggered solution strategy is adopted which permits to solve the equations sequentially. This appropriate partitioning reduces the size of the discretized problem to be solved at each time step. It is based on a specific iterative algorithm to account for the interaction between all the transfer processes. Accordingly, a suitable linearization of mass convective boundary conditions, consistent with the staggered algorithm, is also derived. After some validation tests, the 3D numerical model is used for studying the drying process of a cementitious material with regard to its intrinsic permeability randomness. Copyright © 2011 John Wiley & Sons, Ltd.     

Discrete element method simulations of the seismic response of shallow foundations including soil‐foundation‐structure interaction

A novel three‐dimensional particle‐based technique utilizing the discrete element method is proposed to analyze the seismic response of soil‐foundation‐structure systems. The proposed approach is employed to investigate the response of a single‐degree‐of‐freedom structure on a square spread footing founded on a dry granular deposit. The soil is idealized as a collection of spherical particles using discrete element method. The spread footing is modeled as a rigid block composed of clumped particles, and its motion is described by the resultant forces and moments acting upon it. The structure is modeled as a column made of particles that are either clumped to idealize a rigid structure or bonded to simulate a flexible structure of prescribed stiffness. Analysis is done in a fully coupled scheme in time domain while taking into account the effects of soil nonlinear behavior, the possible separation between foundation base and soil caused by rocking, the possible sliding of the footing, and the dynamic soil‐foundation interaction as well as the dynamic characteristics of the superstructure. High fidelity computational simulations comprising about half a million particles were conducted to examine the ability of the proposed technique to model the response of soil‐foundation‐structure systems. The computational approach is able to capture essential dynamic response patterns. The cyclic moment–rotation relationships at the base center point of the footing showed degradation of rotational stiffness by increasing the level of strain. Permanent deformations under the foundation continued to accumulate with the increase in number of loading cycles. Copyright © 2011 John Wiley & Sons, Ltd.     

基于软化特性的三维边坡强度折减有限元分析

基于现有边坡强度折减有限元的基本原理,建立了一套新的强度折减算法。该算法把强度参数降低的过程看成脆塑性应力跌落的过程,并设置一折减增量 ,当 充分小时认为系统达到收敛条件而退出循环,最终的折减系数就是边坡的安全系数。该算法很容易扩展到三维边坡的稳定性分析,得到边坡滑动面滑动和破坏的发展趋势。通过2个算例,分析了进行三维模型计算的重要性,建议当地质条件复杂时宜从三维角度分析计算边坡,不能简单地将问题当作平面应变处理。     

Three‐dimensional responses of buried corrugated pipes and ANN‐based method for predicting pipe deflections

This study investigated localized responses, such as circumferential stresses, on corrugation and pipe deflections. Also, this study examined the effect of corrugation geometry on the overall and localized response of corrugated pipes with refined three‐dimensional modeling of the entire soil–pipe interaction system, including corrugation. To investigate the availability of the traditional two‐dimensional method, the results from the three‐dimensional finite element method (FEM) were compared with those from the two‐dimensional FEM. The soil–pipe modeling techniques of this study were verified by comparing the FEM results by Utah State University and analytical results. An artificial neural network (ANN)‐based model to predict vertical deflections of buried corrugated pipes was developed to overcome the shortcomings of existing methods and obtain results that are close to the level of accuracy of FEM results. In order to train an ANN, analyses on a large amount of data were executed with various standardized pipe geometries and burial depths regulated by the Korea Highway Corporation using the two‐dimensional FEM verified in this study. The widely used back propagation algorithm was adopted. The ANN‐based model developed in this study was shown to be an effective tool by comparing the results with test data and sensitivity analyses were executed based on the data from the developed ANN. Copyright © 2010 John Wiley & Sons, Ltd.     

A simplified analysis method for piled raft foundations in non‐homogeneous soils

A simplified method of numerical analysis based on elasticity theory has been developed for the analysis of axially and laterally loaded piled raft foundations embedded in non‐homogeneous soils and incorporated into a computer program “PRAB”. In this method, a hybrid model is employed in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. The interactions between structural members, pile–soil–pile, pile–soil–raft and raft–soil–raft interactions, are approximated based on Mindlin's solutions for both vertical and lateral forces with consideration of non‐homogeneous soils. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups and capped pile groups in non‐homogeneous soils. Thereafter, the solutions from this approach for the analysis of axially and laterally loaded 4‐pile pile groups and 4‐pile piled rafts embedded in finite homogeneous and non‐homogeneous soil layers are compared with those from three‐dimensional finite element analysis. Good agreement between the present approach and the more rigorous finite element approach is demonstrated. Copyright © 2002 John Wiley & Sons, Ltd.     

浅基础沉降可靠性的摄动随机有限元法

将二阶非线性摄动随机有限元理论和土性参数随机场的离散技术相结合,可以处理岩土工程中由多种不确定因素带来的结果的不确定性。与一阶摄动随机有限元相比,二阶摄动随机有限元具有较高的计算精度。笔者探讨了这一方法,考虑土性分布参数和荷载变异性,用二阶摄动随机有限元法进行了浅地基沉降的概率分析。     

Displacement‐controlled method and its applications to material non‐linearity

For the analysis of non‐linear problems, the displacement‐controlled method (DCM) has a more extensive application scope and more powerful abilities than the load‐controlled method (LCM). However, difficulties of the DCM's procedure not amenable to most finite element implementations of the conventional LCM have restricted its applications in geomechanics. By means of Sherman–Morrison's theorem, the solution of DCM is improved. The improved procedure is characterized by high efficiency, good numerical stability and a programme structure similar to LCM. Two aspects of applications of DCM are illustrated. The first application is to compute the response of a structure under a given load level like the conventional finite element analysis. The second application is to trace the equilibrium path of a structure under a given load distribution type. A simple but effective algorithm is presented for automatically adjusting the step length in tracing the equilibrium path. Examples illustrate that the proposed procedures are suited for modelling complicated non‐linear problems in geomechanics. Copyright © 2005 John Wiley & Sons, Ltd.     

A multiphase approach for evaluating the horizontal and rocking impedances of pile group foundations

This paper advocates the use of a multiphase model, already developed for static or quasi‐static geotechnical engineering problems, for simulating the behaviour of piled raft foundations subject to horizontal as well as rocking dynamic solicitations. It is shown that such a model, implemented in a FEM code, yields appropriate predictions for the foundation impedance characteristics, provided that shear and bending effects in the piles are taken into account, thus corroborating the findings of the asymptotic homogenization theory. Besides, it is notably pointed out that such a multiphase‐based computational tool makes it possible to assess the dynamic behaviour of pile groups in a much quicker way than when using direct numerical simulations, which may face oversized problems when large pile groups are concerned. Copyright © 2016 John Wiley & Sons, Ltd.     

A high strain‐rate constitutive model for sand and its application in finite‐element analysis of tunnels subjected to blast

The paper presents a constitutive model for simulating the high strain‐rate behavior of sands. Based on the concepts of critical‐state soil mechanics, the bounding surface plasticity theory and the overstress theory of viscoplasticity, the constitutive model simulates the high strain‐rate behavior of sands under uniaxial, triaxial and multi‐axial loading conditions. The model parameters are determined for Ottawa and Fontainebleau sands, and the performance of the model under extreme transient loading conditions is demonstrated through simulations of split Hopkinson pressure bar tests up to a strain rate of 2000/s. The constitutive model is implemented in a finite‐element analysis software Abaqus to analyze underground tunnels in sandy soil subjected to internal blast loads. Parametric studies are conducted to examine the effect of relative density and type of sand and of the depth of tunnel on the variation of stresses and deformations in the soil adjacent to the tunnels. Copyright © 2012 John Wiley & Sons, Ltd.     

A multidirectional semi‐analytical method for analysis of laterally loaded pile groups in multi‐layered elastic strata

A semi‐analytical method for calculating the response of single piles and pile groups subjected to lateral loading is developed in this paper. Displacements anywhere in the soil domain are tied to the displacements of the piles through decay functions. The principle of virtual work and the calculus of variations are used to derive the governing differential equations that describe the response of the piles and soil. The eigenvalue method and the finite difference technique are used to solve the system of coupled differential equations for the piles and soil, respectively. The proposed method takes into account the soil surface displacement along and perpendicular to the loading direction and produces displacement fields that are very close to those produced by the finite element method but at lower computational effort. Compared with the previous method that considered only the soil displacement along the loading direction, accounting for the multi‐directional soil displacement field produces responses for the piles and soil that are closer to those approximated by the finite element method. Copyright © 2016 John Wiley & Sons, Ltd.     

极限分析有限元法讲座—— Ⅰ岩土工程极限分析有限元法

经典岩土工程极限分析方法一般采用解析方法，有些还要对滑动面作假设，且不适用于非均质材料，尤其是强度不均的岩石工程，从而使极限分析法的应用受到限制。随着计算技术的发展，极限分析有限元法应运而生，它能通过强度降低或者荷载增加直接算得岩土工程的安全系数和滑动面，十分贴近工程设计。为此，探讨了极限分析有限元法及其在边坡、地基、隧道稳定性计算中的应用，算例表明了此法的可行性，拓宽了该方法的应用范围。随着计算机技术与计算力学的发展，岩土工程极限分析有限元法正在成为一门新的学问，而且有着良好的发展前景。     

A high‐frequency open boundary for transient seepage analyses of semi‐infinite layers by extending the scaled boundary finite element method

A high‐frequency open boundary has been developed for the transient seepage analyses of semi‐infinite layers with a constant depth. The scaled boundary finite element equation of pore water pressure is formulated first in the frequency domain. With the eigenvalue problem, the equation can be decoupled into modal equations whose modal dynamic permeability equation can be determined. The continued fraction technique is adopted to formulate the continued fraction solution in the frequency domain. All constants in the solution are determined recursively at the high‐frequency limit. By introducing auxiliary variables and the continued fraction solution to the relationship between the prescribed seepage flow and the pore water pressure in the frequency domain, the open boundary condition is obtained. After transformed to the time domain, the open boundary condition is expressed as a system of fractional differential equations. No convolution integral is required. The accuracy of the analysis results increases with the increasing orders of continued fraction. Copyright © 2015 John Wiley & Sons, Ltd.