Probabilistic Analysis and Design of a Strip Footing on Layered Soil Media

In the present paper, the analysis of a strip footing resting on a layered soil system has been carried out considering the elastic moduli of soil layers as random variables. Three layers of soil have been considered and the analysis employs Monte Carlo simulation. The modulus of elasticity has been considered as random variable having lognormal distribution. Factors of safety with respect to settlement of footing and the interfacial stresses have been determined and have been related to the associated risk factor and coefficient of variation of the random variable. A detailed parametric study revealed that for a given risk level, the factors of safety is strongly dependent on the coefficient of variation of elastic modulus and only mildly upon other parameters of the soil?Cfoundation system. This facilitated the development of closed form equations for the upper bounds on factors of safety only in terms of allowable risk of failure and the coefficient of variation of elastic modulus.     

Fuzzy finite element analysis of a foundation on an elastic soil medium

One of the important factors that lead to errors in settlement predicitions is the degree of precision in obtaining the soil parameters. Most mathematical methods for reliability modelling offered to date in the area of geomechanics are based on the classical probabilistic approach, in which soil properties are treated as random variables. In this paper, a model based on the theory of fuzzy sets is presented to take account of the uncertainty in the soil behaviour. This proposed method considers the elastic modulus and Poisson's ratio as two fuzzy numbers in the elastic matrix. An example is given to show the possibility distributions of the displacements and the stresses at some locations in the soil medium. By means of a fuzzy inference scheme, the total possibility distributions or total membership functions of the finite element results may be obtained by considering the estimated error resulting from the mesh discretization.     

Revisiting the effect of foundation embedment on elastic settlement: A new approach

The effect of foundation embedment on settlement calculation is a widely researched topic in which there is no scientific consensus regarding the magnitude of settlement reduction. In this paper, a non-linear three dimensional Finite Element analysis has been performed with the aim of evaluating the aforementioned effect. For this purpose, 1800 models were run considering different variables, such as the depth and dimensions of the foundation and the Young’s modulus and Poisson’s ratio of the soil. The settlements from models with foundations at surface level and at depth were then compared and the relationship between them established. The statistical analysis of this data allowed two new expressions, with a mean maximum error of 1.80%, for the embedment influence factor of a foundation to be proposed and these to be compared with commonly used corrections. The proposed equations were validated by comparing the settlements calculated with the proposed influence factors and the true settlements measured in several real foundations. From the comprehensive study of all modelled cases, an improved approach, when compared to those proposed by other authors, for the calculation of the true elastic settlements of an embedded foundation is proposed.     

An analytical continuum model for axially loaded end-bearing piles in inhomogeneous soil

An approximate static solution is derived for the elastic settlement and load-transfer mechanism in axially loaded end-bearing piles in inhomogeneous soil obeying a power law variation in shear modulus with depth. The proposed generalised formulation can handle different types of soil inhomogeneity by employing pertinent eigenexpansions of the dependent variables over the vertical coordinate, in the form of static soil “modes”, analogous to those used in structural dynamics. Contrary to available models for homogeneous soil, the associated Fourier coefficients are coupled, obtained as solutions to a set of simultaneous algebraic equations of equal rank to the number of modes considered. Closed-form solutions are derived for the (1) pile head stiffness; (2) pile settlement, axial stress, and side friction profiles leading to actual, depth-dependent Winkler moduli, (3) displacement and stress fields in the soil; and (4) average, depth-independent Winkler moduli to match pile head settlement. The predictive power of the model is verified via comparisons against finite element analyses. The applicability to inhomogeneous soil of an existing regression formula for the average Winkler modulus is explored.     

复合地基沉降计算的复合本构有限元法适应性研究

复合本构有限元法是一种新型的复合地基沉降数值计算方法.采用复合本构有限元和传统三维有限元两种计算模型,通过不同桩土模量比、置换率和桩长条件下复合地基沉降计算结果的比较,对复合本构有限元法的适应性进行了探讨.     

考虑加筋与遮帘效应计算群桩沉降的相互作用系数法

群桩中各基桩在地基土中的加筋与遮帘效应是客观存在的,然而,在目前的桩基沉降理论与实践中,相关的研究仍显不足。基于剪切变形法理论,考虑桩的加筋与遮帘效应,求得各基桩在自身桩顶荷载作用下产生的沉降以及其引起相邻桩的附加沉降量,由此提出群桩中任两桩的相互作用系数简化公式,同时,也得到各基桩桩侧及桩端桩-土接触等效弹簧刚度,并基于荷载传递法原理,建立了成层地基条件下各基桩在自身桩顶荷载作用下的桩身位移平衡方程,推导出各土层层顶处桩身沉降、轴力与层底处桩身沉降、轴力之间的递推关系,进而将公式推广到高、低承台群桩基础计算中。工程算例分析表明,用该方法计算有较高的精度,求得的荷载-沉降曲线及两桩相互作用系数与实测值吻合较好;相互作用系数要明显小于弹性理论计算结果。     

基于饱和渗透系数空间变异结构的斜坡渗流及失稳特征

以往研究一般采用单随机变量方法（SRV）或基于水平或垂直方向波动范围生成的空间变异随机场来模拟岩土参数的空间变异性,对具有倾斜定向特征的空间变异随机场未有涉及.基于条件模拟相关理论和非侵入式随机有限元的理论框架,提出了利用序贯高斯模拟方法进行斜坡参数条件随机场模拟并运用有限元方法进行斜坡渗流和稳定性分析的方法.针对理想边坡,对各向同性和几何各向异性的共7种空间变异结构的饱和渗透系数（K_s）各进行了200次条件随机场模拟,基于条件随机场模拟结果进行了有限元渗流和稳定性计算,对每种空间变异结构多次计算结果进行了统计分析.结果表明:本文所提出的方法不仅再现了研究区域参数的空间二阶统计特性,通过设定变异函数参数进行不同空间变异类型、变异程度、变异定向性的随机场模拟,同时利用现场观测数据对随机场模拟结果进行条件限制,从而提高了随机场的赋值精度;K_s的空间变异结构对孔隙水压力的分布规律、地下水位线变化范围、稳定性系数和最危险滑动面分布特征均有一定程度的影响.本研究为库岸斜坡稳定性评价提供方法支撑.      

Prediction of probabilistic settlements via spectral stochastic meshless local Petrov–Galerkin method

This study introduces the prediction of probabilistic settlements with the uncertainty in the spatial variability of Young’s modulus to illustrate the preliminary development of a spectral stochastic meshless local Petrov–Galerkin (SSMLPG) method. Generalized polynomial chaos expansions of Young’s moduli and a two-dimensional meshfree weak–strong formulation in elasticity are combined to derive the SSMLPG formulation. Because of the local and truly meshless nature, the SSMLPG method is more computationally efficient than available stochastic numerical methods. Two examples further show that SSMLPG-based predictions remain sufficiently accurate even in case of scattered nodes. Therefore, the SSMLPG method can be a valuable alternative for solving stochastic boundary-value problems.     

Consolidation in spatially random unsaturated soils based on coupled flow‐deformation simulation

This paper integrates random field simulation of soil spatial variability with numerical modeling of coupled flow and deformation to investigate consolidation in spatially random unsaturated soil. The spatial variability of soil properties is simulated using the covariance matrix decomposition method. The random soil properties are imported into an interactive multiphysics software COMSOL to solve the governing partial differential equations. The effects of the spatial variability of Young's modulus and saturated permeability together with unsaturated hydraulic parameters on the dissipation of excess pore water pressure and settlement are investigated using an example of consolidation in a saturated‐unsaturated soil column because of loading. It is found that the surface settlement and the pore water pressure profile during the process of consolidation are significantly affected by the spatially varying Young's modulus. The mean value of the settlement of the spatially random soil is more than 100% greater than that of the deterministic case, and the surface settlement is subject to large uncertainty, which implies that consolidation settlement is difficult to predict accurately based on the conventional deterministic approach. The uncertainty of the settlement increases with the scale of fluctuation because of the averaging effect of spatial variability. The effects of spatial variability of saturated permeability k_sat and air entry parameters are much less significant than that of elastic modulus. The spatial variability of air entry value parameters affects the uncertainties of settlement and excess pore pressure mostly in the unsaturated zone. Copyright © 2016 John Wiley & Sons, Ltd.     

Analysis of creep settlement of pile groups in linear viscoelastic soil

This paper presents the analysis of creep settlement of pile groups for line pile groups, square pile groups, and rectangular pile groups undergoing creep settlements over a period of time. The soil is treated as a viscoelastic material and is modeled using a three-parameter viscoelastic model. The damping component (dashpot) takes care of the permanent time-dependent deformations in three-parameter viscoelastic model. An approach suggested by Mindlin has been employed to calculate the stress distribution along the pile length in a group. The viscoelastic problem is converted into an elastic problem by the application of Laplace transform. Results in the form of variation of interaction factors for parameters such as pile length to diameter ratio, pile spacing, Poisson's ratio, and modulus ratio have been presented. Comparison has been made between interaction factors for piles groups undergoing immediate settlements and creep settlements. Finally, a typical predictive example has been presented for a 3 × 3 pile group showing creep settlement. The load rearrangement due to creep settlements causes about 5% to 35% increase in base resistance over time. Interaction factors for pile groups (2 × 1, 3 × 1, 2 × 2, and 3 × 2) undergoing creep settlement is about 15% to 55% higher than the interaction factors considering only the immediate settlements for pile group spacing less than or equal to 5d.     

Response of Euler–Bernoulli beam on spatially random elastic soil

A new method is developed for analysis of flexible foundations (beams) on spatially random elastic soil. The elastic soil underneath the beams is treated as a continuum, characterized by spatially random Young’s modulus and constant Poisson’s ratio. The randomness of the soil Young’s modulus is modeled using a two-dimensional non-Gaussian, homogeneous random field. The beam geometry and Young’s modulus are assumed to be deterministic. The total potential energy of the beam-soil system is minimized, and the governing differential equations and boundary conditions describing the equilibrium configuration of the system are obtained using the variational principles of mechanics. The differential equations are solved using the finite element and finite difference methods to obtain the beam and soil displacements. Four different beam lengths, representing moderately short, moderately long and long beams are analyzed for beam deflection, differential settlement, bending moment and beam shear force. The statistics of the beam responses are investigated using Monte Carlo simulations for different beam-soil modulus ratios and for different variances and scales of fluctuations of the soil Young’s modulus. Suggestions regarding the use of the analysis in design are made. A novelty in the analysis is that the two-dimensional random heterogeneity of soil is taken into account without the use of traditional two-dimensional numerical methods, which makes the new approach computationally efficient.     

Prediction of settlement trough induced by tunneling in cohesive ground

Surface settlements of soil due to tunneling are caused by stress relief and subsidence due to movement of support by excavation. There are significant discrepancies between empirical solutions to predict surface settlement trough because of different interpretations and database collection by different authors. In this paper, the shape of settlement trough caused by tunneling in cohesive ground is investigated by different approaches, namely analytical solutions, empirical solutions, and numerical solutions by the finite element method. The width of settlement trough was obtained by the finite element method through establishing the change in the slope of the computed settlement profile. The finite element elastic-plastic analysis gives better predictions than the linear elastic model with satisfactory estimate for the displacement magnitude and slightly overestimated width of the surface settlement trough. The finite element method overpredicted the settlement trough width i compared with the results of Peck for soft and stiff clay, but there is an excellent agreement with Rankin’s estimation. The results show that there is a good agreement between the complex variable analysis for Z/D = 1.5, while using Z/D = 2 and 3, the curve diverges in the region faraway from the center of the tunnel.     

用双曲线切线模量方程计算地基非线性沉降

提出了一种利用原位试验成果求解非均质非线弹性地基最终沉降的新方法。对分层原状土载荷试验或螺旋板试验成果进行双曲线拟合,建立分层原状土切线模量与竖向附加应力的关系方程;在沉降计算公式中引入附加应力修正系数,以考虑基础埋深、地基非均质非线性特征等因素对应力分布的影响;利用双曲线切线模量方程及附加应力弹性解,可准确求解地基的总沉降。通过对几个压板载荷试验成果的拟合分析,得出了各土类的双曲线切线模量方程,用于求解地基在各级荷载下的沉降。计算结果表明,计算值与实测值吻合得很好。该方法原理简单、参数可靠、结果准确,为地基沉降计算开辟了一条新途径。     

Settlements and stresses of multi‐layered grounds and improved grounds by equivalent elastic method

The investigation of equivalent elastic method is made to predict settlements and stresses of multi‐layered grounds and improved grounds. Analytical models to represent the heterogeneous elastic properties of layers in vertical and horizontal directions for multi‐layered grounds and improved grounds are proposed in taking into account the equivalent elastic modulus and the equivalent thickness. By introducing the equivalent thickness derived from Terzaghi's formula of the vertical stress, the equivalent elastic method of using the equivalent elastic modulus and the equivalent thickness is applied to the formulations concerning immediate settlements and vertical stresses in multi‐layered grounds and improved grounds. Comparison is performed between rigorous solutions and simulations for immediate settlements and vertical stresses in multi‐layered grounds and improved grounds. It is found that the proposed method is able to describe properly the characteristics of distributions for settlements and vertical stresses in multi‐layered grounds and improved grounds. Copyright © 2007 John Wiley & Sons, Ltd.     

A probabilistic analysis of foundation settlements

This paper deals with a settlement analysis of shallow foundations resting on a layered subsoil. Three basic sources of randomness are discussed: random shape of the subsoil (location of an interface between two strata), random material parameters and random loads. The numerical analysis is based on the finite element method coupled with stochastic versions of the perturbation and the Neumann expansion methods. Both methods lead to a simple evaluation of the response variability in terms of the mean value and the covariance matrix for foundation settlements. More sophisticated analyses introduce the probability of failure as a measure of safety. In this context, failure means either exceeding the bearing capacity or exceeding allowable displacements. The probability of failure is usually evaluated by means of FEM-oriented gradient algorithms or some versions of the Monte Carlo simulation techniques. Numerical examples are presented for a raft foundation resting on an elastic subsoil. The obtained results compare the scale of random fluctuations of soil properties or loading with the scale of foundation settlement fluctuations.     

柔性基础下复合地基下卧层沉降特性的数值分析

采用复合本构有限元和传统有限元两种计算模型,通过不同桩土模量比和置换率条件下复合地基、双层地基、人工均质地基下卧层沉降与天然地基相应计算结果的比较,系统地研究了复合地基下卧层的沉降特性,并在此基础上建立了相应的计算方法。     

岩石抗剪强度参数的理论概率分布形态研究

岩石抗剪强度参数的概率分布形态是岩石工程可靠度分析和设计的基础。在考虑完整岩石压缩强度为服从正态分布随机变量的条件下,针对Mohr-Coulomb和Drucker-Prager屈服准则的线性系数形式,基于随机变量函数分布理论推导出岩石抗剪强度参数内摩擦角 和黏聚力 的概率密度函数。 和 概率密度函数显示：不仅岩石压缩强度和抗剪强度参数概率分布具有非一致性,而且根据不同屈服准则计算得出的岩石抗剪强度参数概率分布也具有非一致性。在进一步分析屈服准则系数具有不同变异系数和相关系数时的抗剪强度参数概率密度函数特征的基础上,提出根据概率分布的偏度和峰度确定一般情况下抗剪强度参数概率分布形态的方法,从理论上解决岩石压缩强度与抗剪强度参数分布的协调性问题。最后,对大理岩常规三轴压缩试验得出的抗剪强度参数进行大样本统计分析,验证了其概率密度函数理论推导的正确性以及概率分布形态确定方法的合理性。该研究为实际岩石强度概率分析时选择抗剪强度参数合理概率分布形式提供了理论指导。     

Prediction of Probabilistic Settlements by the Perturbation-Based Spectral Stochastic Meshless Local Petrov–Galerkin Method

Originating an attempt of understanding the reliability and serviceability of foundations, an interest of comparing the difference between settlements predicted with and without considering the uncertainty in such as the spatial variability of soil properties is born. This study selectively compares between settlements predicted with and without considering the uncertainty in the spatial variability of Young’s modulus. The tool is a coupling of perturbation expansions of Young moduli and a two-dimensional meshfree weak-strong form in elastostatics. Two further examples show that the spatial variability of Young’s modulus causes apparent difference between probabilistic and deterministic settlement components along the direction of a surcharge. We can derive an autocorrelation function to describe the spatial variability of Young’s modulus and understand how it affects predicted settlements depending upon autocorrelation function values. In addition, the spectral stochastic meshless local Petrov–Galerkin method is a time-saving tool for predicting probabilistic settlements with the uncertainty in the spatial variability of soil properties.     

盾构施工引起地表固结沉降问题的研究

将隧道周围土体视为均质连续各向同性的饱和弹性介质,采用保角变换的方法将含有隧道的半无限平面映射为同心圆环计算域。根据Terzaghi-Rendulic二维固结理论,建立隧道在不透水的情况下周围土体超孔隙水压力分布的控制方程。然后,采用分离变量法计算得到土体超孔隙水压力分布的解析解,最后,根据弹性理论计算得出隧道中线上方地表固结沉降的计算公式。结合算例,分析盾构施工扰动程度、土体渗透系数、土体弹性模量及隧道埋深等因素对隧道中心上方地表处固结沉降的影响。研究结果表明,地表固结沉降的增加值与隧道外侧初始超孔隙水压力值C0的变化量成正比例关系,施工扰动程度越大所引起的固结沉降越大;土体的渗透系数越大固结沉降速度越快,但土体的渗透系数与最终的地表固结沉降量无关;土体的弹性模量越大,最终的地表固结沉降量越小;隧道埋深越深,地表固结沉降所需时间越长,最终的地表固结沉降量也越大。     

碎石垫层强度与变形特性试验研究和有限元分析

碎石垫层已广泛应用于土木工程各个领域,但碎石垫层的强度与变形特性尚不十分清楚,需要进一步研究。通过对5种不同厚度碎石垫层在高应力下的室内模型试验和有限元分析,揭示了不同厚度碎石垫层的强度特性和变形特征。通过有限元分析与试验结果的对比分析,得出了不同厚度的碎石垫层荷载与沉降变形、竖向应力与侧向约束力都近似呈线性变化。碎石垫层的厚度对沉降大小有一定影响,在其他条件相同的情况下,碎石垫层越厚,沉降越大。在一定荷载作用下,碎石垫层在较短的时间内自身压缩变形已基本趋于稳定,而后随时间的增加,其压缩变形量很小。提出了一种测定碎石类土侧压力系数、泊松比及变形模量的试验测定方法,以期为测定其他类别土的侧压力系数、泊松比及变形模量提供参考。