Vertical uplift resistance of circular plate anchors in clays under undrained condition

The vertical uplift resistance of circular plate anchors, embedded horizontally in a clayey stratum whose cohesion increases linearly with depth, has been obtained under undrained ( = 0) condition. The axi-symmetric static limit analysis formulation in combination with finite elements proposed recently by the authors has been employed. The variation of the uplift factor (F_c) with changes in the embedment ratio (H/B) has been computed for several rates of increases of soil cohesion with depth. It is noted that in all the cases, the magnitude of F_c increases continuously with depth up to a certain value of H_cr/B beyond which the uplift factor becomes essentially constant. The proposed static limit analysis formulation is seen to provide acceptable results even for the two other simple chosen axi-symmetric problems.     

Stability of unsupported conical excavations in non-homogeneous clays

New plasticity solutions for the undrained stability of unsupported conical excavations in homogeneous and non-homogeneous clays were solved by axisymmetric finite element limit analysis. Three parametric studies were performed on excavated height ratios, slope inclinations and dimensionless strength gradients. In all cases, the exact stability factors were accurately bracketed by computed bound solutions within 0.6%. An accurate closed-form equation of the stability factor was proposed from nonlinear regression analysis of lower bound solutions. New conical stability factors for soil cohesion, strength gradient, and coupling effect of these components were deduced to conveniently and accurately predict a safe solution in practice.     

Stability numbers for an unsupported vertical circular excavation in c–ϕ soil

By using an axisymmetric lower bound finite element limit analysis formulation, the stability numbers (γH/c) for an unsupported vertical circular excavation in a cohesive–frictional soil have been generated. The numerical results are obtained for values of normalized excavation height (H/b) and friction angle (ϕ) greater than those considered previously in the literature. The results compare well with those available in literature. The stability numbers presented in this note would be beneficial from a design point of view.     

Lower bound limit analysis of unsupported vertical circular excavations in rocks using Hoek-Brown failure criterion

The stability of vertical unsupported circular excavations in rock media, obeying generalized Hoek-Brown yield criterion, has been investigated by using the lower bound finite elements limit analysis. An axisymmetric analysis, composed of a planar domain with a mesh of three-noded triangular elements, has been carried out. The optimization problem is dealt with by using the semidefinite programming technique avoiding the need of either smoothing the yield surface or making any assumption associated with the circumferential stress (σ_θ). A detailed parametric study has been executed, and the effects of different input material parameters, namely, geological strength index (GSI), yield parameter (m_i), and the disturbance factor (D) on the results have been studied. For different height to radius ratios of the excavation, the computed results are presented in the form of nondimensional stability numbers. Failure mechanisms have also been investigated for a few typical cases. The results from the analysis have been compared with that evaluated separately with the application of the software OptumG2.     

Comparison of two inverse analysis techniques for learning deep excavation response

Performance observation is a necessary part of the design and construction process in geotechnical engineering. For deep urban excavations, empirical and numerical methods are used to predict potential deformations and their impacts on surrounding structures. Two inverse analysis approaches are described and compared for an excavation project in downtown Chicago. The first approach is a parameter optimization approach based on genetic algorithm (GA). GA is a stochastic global search technique for optimizing an objective function with linear or non-linear constraints. The second approach, self-learning simulations (SelfSim), is an inverse analysis technique that combines finite element method, continuously evolving material models, and field measurements. The optimization based on genetic algorithm approach identifies material properties of an existing soil model, and SelfSim approach extracts the underlying soil behavior unconstrained by a specific assumption on soil constitutive behavior. The two inverse analysis approaches capture well lateral wall deflections and maximum surface settlements. The GA optimization approach tends to overpredict surface settlements at some distance from the excavation as it is constrained by a specific form of the material constitutive model (i.e. hardening soil model); while the surface settlements computed using SelfSim approach match the observed ones due to its ability to learn small strain non-linearity of soil implied in the measured settlements.     

Stability of a circular tunnel in cohesive-frictional soil subjected to surcharge loading

The stability of circular tunnels in cohesive-frictional soils subjected to surcharge loading has been investigated theoretically and numerically assuming plane strain conditions. Despite the importance of this problem, previous research on the subject is very limited. At present, no generally accepted design or analysis method is available to evaluate the stability of tunnels/openings in cohesive-frictional soils. In this study, continuous loading is applied to the ground surface, and both smooth and rough interface conditions are modelled. For a series of tunnel diameter-to-depth ratios and material properties, rigorous lower- and upper-bound solutions for the ultimate surcharge loading are obtained by applying finite element limit analysis techniques. For practical use, the results are presented in the form of dimensionless stability charts with the actual tunnel stability numbers being closely bracketed from above and below. As an additional check on the solutions, upper-bound rigid-block mechanisms have been developed and the predicted collapse loads from these are compared with those from finite element limit analysis. Finally, an expression that approximates the ultimate surcharge load has been devised which is convenient for use by practising engineers.     

Undrained stability of an active planar trapdoor in non-homogeneous clays with a linear increase of strength with depth

Finite element limit analysis was employed to determine the upper and lower bound solutions of the active failure of a planar trapdoor in non-homogeneous clays that have a linear increase of strength with depth. Influences of cover ratio, dimensionless strength gradient and trapdoor roughness on predicted failure mechanisms and stability factors were determined. In all cases, the exact stability factors were accurately bracketed by computed bound solutions within 1%. Accurate closed-form equations to predict the exact estimates of stability factors, trapdoor pressure and factor of safety using the new proposed factors for the cohesion and strength gradient are presented.     

Probabilistic analysis of the inverse analysis of an excavation problem

This study presents the probabilistic analysis of the inverse analysis of an excavation problem. Two techniques are used during two successive stages. First, a genetic algorithm inverse analysis is conducted to identify soil parameters from in situ measurements (i.e. first stage of the construction project). For a given tolerable error between the measurement and the response of the numerical model the genetic algorithm is able to generate a statistical set of soil parameters, which may then serve as input data to a stochastic finite element method. The second analysis allows predicting a confidence interval for the final behaviour of the geotechnical structure (i.e. second stage of the project). The tools employed in this study have already been presented in previous papers, but the originality herein consists of coupling them. To illustrate this method, a synthetic excavation problem with a very simple geometry is used.     

开挖卸荷状态下深基坑变形特性研究

深基坑开挖时因为卸荷作用会引起土体强度一定程度的降低,土体强度的降低会引起支护结构上土压力的变化,利用卸荷前土体强度指标进行土压力计算势必会小于实际情况,从而导致土体及支护结构变形计算值与实测值有一定的偏差。在深基坑开挖时,仅采用施工监测等手段进行事中控制是不够的,必须预先对变形值的发展规律做出模拟和预测。为探索深基坑开挖时,卸荷作用对基底土体和侧向土体强度特性和变形特性的影响规律,结合天津富力响锣湾大型基坑开挖,对开挖过程中土体基底回弹情况、支护结构以及周边土体的变形情况进行了全过程监测,利用试验结果数据计算出天津市富力响锣湾大型基坑开挖项目的卸荷强度参数,为后续数值模拟计算参数的选取提供了依据;利用ABAQUS有限元软件建立了三维数值模型,分别采用原状土的强度参数和卸荷参数对开挖过程中土体基底回弹、支护结构以及周边土体的变形情况进行了模拟,研究了两种情况下土体基底回弹、支护结构以及周边土体的变形规律,并将有限元模拟结果与监测结果进行了对比。研究发现,本工程土体卸荷后的扰动区在基底以下3～4 m范围,强度折减可达到20%～35%,根据卸荷比确定了周边土体强度折减为10%～15%;有限元模拟结果与实测值基本一致。通过分析可以看到,考虑基坑开挖卸荷作用是符合工程实际情况的,因此,建议在深基坑开挖设计时考虑土体的卸荷效应。该分析方法可为同类深基坑设计提供参考。     

The ultimate uplift capacity of multi-plate strip anchors in undrained clay

Soil anchors are commonly used as foundation systems for structures requiring uplift resistance such as transmission towers, or for structures requiring lateral resistance, such as sheet pile walls. Anchors commonly have more than one plate or bearing element and therefore there is a complex interaction between adjacent plates due to overlapping stress zones. This interaction will affect the failure mode and ultimate capacity. However, no thorough numerical analyses have been performed to determine the ultimate pullout loads of multi-plate anchors. By far the majority of the research has been directed toward the tensile uplift behaviour of single anchors (only one plate). The primary aim of this research paper is to use numerical modelling techniques to better understand plane strain multi-plate anchor foundation behaviour in clay soils. A practical design framework for multi-plate anchor foundations will be established to replace existing semi-empirical design methods that are inadequate and have been found to be excessively under or over conservative. This framework can then be used by design engineers to more confidently estimate the pullout capacity of multi-plate anchors under tension loading.     

Poromechanical response of borehole in excavation disturbed zone

This paper presents time-dependent response of a cylindrical borehole in a poroelastic medium with an excavation disturbed zone. The general solutions are derived based on Biot’s theory of poroelasticity by employing Laplace and Fourier transforms. Both shear modulus and permeability coefficient are assumed to be changed from their original values in the disturbed zone. The general solutions are employed to formulate boundary value problems corresponding to a borehole subjected to axisymmetric loading applied at its surface, and contact problems of a rigid cylindrical plug in a borehole. Selected numerical results are presented to portray the influence of poroelastic effects and the excavation disturbed zone.     

Vertical uplift capacity of two interfering horizontal anchors in sand using an upper bound limit analysis

The vertical uplift resistance of two interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. The analysis is performed by using an upper bound theorem of limit analysis in combination with finite elements and linear programming. It is specified that both the anchors are loaded to failure simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (ξ_γ) is determined. On account of interference, the magnitude of ξ_γ is found to reduce continuously with a decrease in the spacing between the anchors. The results from the numerical analysis were found to compare reasonably well with the available theoretical data from the literature.     

Bearing capacity factor Nc under ϕ=0 condition for piles in clays

Bearing capacity factor N_c for axially loaded piles in clays whose cohesion increases linearly with depth has been estimated numerically under undrained (?=0) condition. The study follows the lower bound limit analysis in conjunction with finite elements and linear programming. A new formulation is proposed for solving an axisymmetric geotechnical stability problem. The variation of N_c with embedment ratio is obtained for several rates of the increase of soil cohesion with depth; a special case is also examined when the pile base was placed on the stiff clay stratum overlaid by a soft clay layer. It was noticed that the magnitude of N_c reaches almost a constant value for embedment ratio greater than unity. The roughness of the pile base and shaft affects marginally the magnitudes of N_c. The results obtained from the present study are found to compare quite well with the different numerical solutions reported in the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

Three‐dimensional inverse analyses of a deep excavation in Chicago clays

Numerical models are commonly used to estimate excavation‐induced ground movements. Two‐dimensional (2D) plain strain assumption is typically used for the simulation of deep excavations which might not be suitable for excavations where three‐dimensional (3D) effects dominate the ground response. This paper adapts an inverse analysis algorithm to learn soil behavior from field measurements using a 3D model representation of an excavation. The paper describes numerical issues related to this development including the generation of the 3D model mesh from laser scan images of the excavation. The inverse analysis to extract the soil behavior in 3D is presented. The model captures the measured wall deflections. Although settlements were not sufficiently measured, the predicted settlements around the excavation site reflected strong 3D effects and were consistent with empirical correlations. Copyright © 2010 John Wiley & Sons, Ltd.     

Investigating the effect of soil models on deformations caused by braced excavations through an inverse-analysis technique

In this study, a series of inverse-analysis numerical experiments was performed to investigate the effect of soil models on the deformations caused by excavation by using the finite element method. The nonlinear optimization technique that was incorporated into the finite element code was used for the inverse-analysis numerical experiments. Three soil models (the hyperbolic model, pseudo-plasticity model, and modified pseudo-plasticity model) were employed in the intended numerical experiments on a well-documented excavation case history. The results indicate that wall deflection due to excavation can be accurately back-figured by each of the three soil models, while the ground surface settlement can be reasonably optimized only by the pseudo-plasticity model and the modified pseudo-plasticity model. Importantly, the modified pseudo-plasticity model can yield more reasonable simulations when the wall deflection and the ground surface settlement are simultaneously back-figured. The results show that selection of an adequate soil model that is capable of adequately describing the stress–strain-strength characteristics of the soils is essentially crucial when predicting the excavation-induced ground response.     

Assessment of strut forces for braced excavation in clays from numerical analysis and field measurements

One important consideration in the design of a braced excavation system is to ensure that the structural bracing system is designed both safely and economically. The forces acting on the struts are often determined using empirical methods such as the Apparent Pressure Diagram (APD) method developed by Peck (1969). Most of these empirical methods that were developed from either numerical analysis or field studies have been for excavations with flexible wall types such as sheetpile walls. There have been only limited studies on the excavation performance for stiffer wall systems such as diaphragm walls and bored piles. In this paper, both 2D and 3D finite element analyses were carried out to study the forces acting on the struts for braced excavations in clays, with focus on the performance for the stiffer wall systems. Subsequently, based on this numerical study as well as field measurements from a number of reported case histories, empirical charts have been proposed for determining strut loads for excavations in stiff wall systems.     

FAST台址巨石混合体边坡开挖稳定性分析

FAST台址巨石混合体的开挖稳定性对工程的建设和安全运营具有重要的意义。本文选取典型剖面,对FAST台址巨石混合体边坡在开挖后可能发生的坡体内部深层滑动和表层块体失稳两种破坏模式进行研究。结果表明:巨石混合体边坡沿最危险滑动面滑动的稳定系数约为2.8,不会发生坡体内部滑动。开挖后坡体上部较陡部位的表层块体由于失去支撑而发生失稳,再带动后方的块体运动。块体运动过程中重新堆积、咬合,体现出一定的自稳性。研究结果可为FAST台址巨石混合体及类似地质体的稳定性评价提供参考。     

Stability of long circular tunnels in sloping ground

Assessment of tunnel stability has become increasingly crucial as more and more tunnels are built in difficult terrains such as sloping ground. The required support pressure on the tunnel walls associates both tunnel stability and liner design considerations. The present analysis attempts to find a uniform internal pressure which can support a circular tunnel built in a sloping ground with a particular level of stability in cohesive-frictional soils. The lower bound finite element limit analysis has been applied to find the required minimum uniform internal support pressure presented as a non-dimensional term p/c; where p is the minimum normal internal pressure on the tunnel boundary to avoid collapse and c is the cohesion of soil. The variation of p/c is presented for a range of normalised embedment depth of tunnel (H/D), stability number (γD/c), internal friction angle of soil (?) and slope angle (β); where H is the crown depth of the tunnel, D is the tunnel diameter and γ is the unit weight of soil. Appropriate comparisons have been carried out with available literature. Failure patterns of the tunnel have also been studied to understand the extent and the type of failure zone which may generate during the collapse.     

Undrained lower bound solutions for end bearing capacity of shallow circular piles in non-homogeneous and anisotropic clays

The undrained bearing capacity of shallow circular piles in non-homogeneous and anisotropic clay is investigated by the lower bound (LB) finite element limit analysis (FELA) under two-dimensional (2D) axisymmetric condition using second-order cone programming, and the new solution of the problem is presented. Modified from the isotropic von Mises yield criterion, a cross-anisotropic undrained strength criterion of clays under the axisymmetric state of stress requiring three input shear strengths in triaxial compression, direct simple shear, and triaxial extension is employed in the 2D axisymmetric LB FELA. Parametric studies on the effects of pile embedment ratio, dimensionless strength gradient, anisotropic strength ratio, and pile roughness are investigated extensively, while the predicted failure mechanisms associated with these parameters are discussed and compared. Numerical results of undrained end bearing capacity of shallow circular piles are summarized in the form of design tables that are useful for design practice and represent a new contribution to the field of pile capacity considering the combined effects of undrained strength non-homogeneity and anisotropy.     

椭球形空洞地基稳定性分析

为了分析地基中的椭球形空洞的稳定性,利用叠加原理得到了线弹性各向同性无限大体中在远场三轴应力作用下椭球形空洞壁上出现极值的关键点应力精确解,为此又采用Matlab程序求解当s(短、长半轴之比)趋近于1时的极限而退化成球形空洞的应力精确解。最后利用摩尔-库仑准则判定椭球洞在三轴应力作用下的稳定性。分析结果表明,在远场应力状态相同的条件下,椭球洞相对于对应的椭圆孔不易失稳,指出土洞的三维椭球洞模型要比对应的二维椭圆孔模型和球形空洞更符合实际。