Application of nonlinear optimization technique to back analyses of deep excavation

This study presents a nonlinear optimization technique (NOT) for conducting the back analyses of geotechnical engineering problems based on the field observations. Additional auxiliary techniques are incorporated to enhance the convergence and stability of the NOT. The developed NOT and additional auxiliary techniques are incorporated into a finite element code and then applied to the back analysis of excavation-induced wall deflection. A number of hypothetical excavation cases with various scenarios of stratigraphy and two quality excavation case histories are used to validate the developed NOT, in which the dominant soil parameters are treated as target parameters. Results show that the wall deflections of all hypothetical and actual excavation cases at each stage can be accurately and efficiently back-figured. The developed NOT has a potential to be an useful tool for preventing the building damage through accurately and efficiently predicting the excavation-induced deformations at subsequent stages.     

Modeling small-strain behavior of Taipei clays for finite element analysis of braced excavations

We examine the small-strain behavior of Taipei clays in braced excavation through a detailed analysis of a well-documented case history. Specifically, we analyze the case of the Taipei National Enterprise Center (TNEC) excavation using two soil models, the Modified Cam-clay model (MCC) and the three-Surface Kinematic Hardening model (3-SKH). Our finite element analysis includes a consideration of the over-consolidated stress state and the high initial shear modulus of the clay. Results show that the observed wall deflection and surface settlement can be satisfactorily predicted simultaneously using the 3-SKH model. This is an improvement on the MCC model, for which only wall deflection, not ground settlement, can be accurately predicted. This study re-confirms the importance of considering small-strain non-linear behavior for the over-consolidated stress state in finite element analyses of braced excavation responses.     

Evaluation of deformation parameter for deep excavation in sand through case histories

This study back analyzed deformation parameters of in situ sand through two excavation case histories in Kaohsiung, Taiwan. Two main features are highlighted; deformation prediction based on monitoring data at the first excavation stage and in situ Young’s modulus evaluation for sand considering monitoring data at the overall excavation stages. The former tends to establish a reliable method to predict the wall deflection at the critical stage based on the data at the first stage and the latter to enrich the limited database of Young’s modulus correlation for sand, specifically applicable for deep excavations analysis. The two constitutive models, linear elastic perfectly plastic and non-linear stress–strain constitutive models, were selected. The stiffness parameters of the models were discretely distributed along the subdivided soil body mesh to reflect the effect of overburden pressure on the in situ soil. In addition, relationship between Standard Penetration Test value (SPT-N value) and Young’s modulus and relationships for estimating the in situ Young’s modulus of the Kaohsiung sand as a function of depth were evaluated. The results greatly enhanced a framework for estimating the in situ Young’s modulus of sand.     

砂土地层圆形深基坑三维分析与测斜仪测量

介绍了铁皮坑开挖中测斜仪监测和三维有限元反分析的结果。所研究的铁皮坑为深度27 m、总直径26 m的圆形深基坑,最终开挖面以上土层以砂土为主。每个开挖阶段采用腰梁加固的咬合桩作为挡土墙对基坑进行支护。采用硬化土模型作为土体本构模型,反分析结果表明,桩墙位移的趋势与测斜仪测量的结果接近,最大位移为5.1mm。案例中胶结土的有效黏聚力c′取决于胶结砂层的厚度,约为50～200kPa。NSPT为标准贯入试验中分离式取样器打入土体30cm的锤击数。模拟结果表明,砂土模量约为1 400NSPT～2 000NSPT（单位：k Pa）,而对于胶结砂,其模量为7 000NSPT。还研究了腰梁和外部荷载对咬合桩变形和受力的影响。结果表明,外部荷载对桩墙位移具有主导作用;同时,腰梁对减少桩墙位移没有明显作用。     

Probabilistic Inverse Analysis of Excavation-Induced Wall and Ground Responses for Assessing Damage Potential of Adjacent Buildings

This paper presents an approach for the probabilistic inverse analysis of braced excavations based on the maximum likelihood formulation. Here, the soil parameters are updated using the observations of the maximum ground settlement and/or the maximum wall deflection measured in a staged excavation. The updated soil parameters are then used to refine the predicted wall and ground responses in the subsequent excavation stages, as well as to assess the building damage potential at the final excavation stage. Case study shows that the proposed approach is effective in improving the predictions of the excavation-induced wall and ground responses. More-accurate predictions of the wall and ground responses, in turn, lead to a more accurate assessment of the damage potential of buildings adjacent to the excavation. The proposed approach offers an effective means for a probabilistic inverse analysis of braced excavations.     

An efficient probabilistic back-analysis method for braced excavations using wall deflection data at multiple points

This paper presents an efficient Bayesian back-analysis procedure for braced excavations using wall deflection data at multiple points. Response surfaces obtained from finite element analyses are adopted to efficiently evaluate the wall responses. Deflection data for 49 wall sections from 11 case histories are collected to characterize the model error of the finite element method for evaluating the deflections at various points. A braced excavation project in Hang Zhou, China is chosen to illustrate the effectiveness of the proposed procedure. The results indicate that the soil parameters could be updated more significantly for the updating that uses the deflection data at multiple points than that only uses the maximum deflection data. The predicted deflections from the updated parameters agree fairly well with the field observations. The main significance of the proposed procedure is that it improves the updating efficiency of the soil parameters without adding monitoring effort compared with the traditional method that uses the maximum deflection data.     

软土地区深基坑连续墙最大变形简易计算方法

采用有限单元法研究了影响软土地区地下连续墙最大侧向变形的主要参数。针对基坑开挖深度H、基坑开挖宽度B、单位宽度地下连续墙系统刚度S、支撑结构的轴向刚度 及黏土归一化的不排水抗剪强度 为不排水抗剪强度, 为有效垂直应力）5个参数进行分析研究,通过回归分析研究结果,给出地下连续墙最大侧向变形的简易计算方法。利用简易计算方法,计算实际工程中基坑案例的地下连续墙最大侧向变形,并与现场监测结果进行对比,验证了计算方法的准确性,可为以后预估地下连续墙最大侧向变形及检查设计提供参考。     

Influence of diaphragm wall installation on the numerical analysis of deep excavation

This paper presents a numerical analysis of the influence of initial stress state on the response of deep excavation supported by retaining wall. Indeed, the influence of diaphragm wall installation prior to excavation works may affect the soil response and lateral wall deflection induced by excavation process. The first part of this paper gives a short review of the numerical methods aimed to reproduce the retaining wall installation. Numerical analysis of a deep excavation in two‐dimensional and three‐dimensional conditions is then performed according to the methods previously presented. In three‐dimensional conditions, diaphragm wall installation is performed considering a sequence of panels, described by their number and length. Results of three‐dimensional calculations confirm that stress state is disturbed by wall installation, which has a sensitive effect on the ground response induced by soil excavation. It is also noted that these results are not easily reproduced in two‐dimensional conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

软土地区采用灌注桩围护的深基坑变形性状研究

根据上海软土地区80个钻孔灌注桩围护的深基坑工程案例有关数据,系统地分析了基坑开挖引致的灌注桩变形性状。所有基坑的灌注桩最大侧向位移介于0.1 %～1.0 %倍的开挖深度之间,平均值为开挖深度的0.44 %。钢筋混凝土支撑和钢支撑在控制墙体的变形上没有明显差别,最大侧向位移一般位于开挖面上下5 m的范围内。无量纲化最大侧向位移随着支撑系统刚度的增大而减小,随着墙底以上软土层厚度的增加而增大,但与灌注桩插入比及坑底抗隆起稳定系数之间并无明显的关系。墙顶侧向位移随着首道支撑位置深度的增加而呈现出指数增长的趋势,而灌注桩最大侧向位移与首道支撑的深度位置无明显关系。     

Efficiency of excavations with buttress walls in reducing the deflection of the diaphragm wall

Installation of buttress walls against diaphragm walls has been used as an alternative measure for the protection of adjacent buildings during excavation, but their mechanism in reducing movements has not yet been fully understood. This study performs three-dimensional finite element analyses of two excavation case histories, one in clay with T-shape buttress walls and another in dominant sand with rectangular buttress walls, to establish analysis model. Then, a series of parametric study were performed by varying soil types, types and length of buttress walls based on the above-mentioned excavations. Results show that the mechanism of buttress walls in reducing wall deflections mainly came from the frictional resistance between the side surface of buttress wall and adjacent soil rather than from the combined bending stiffness from diaphragm and buttress walls. The buttress wall with a length <2.0 m had a poor effect in reducing the wall deflection because the soil adjacent to the buttress wall had almost the same amount of movement as the buttress wall, causing the frictional resistance little mobilized. Since the frictional resistance of buttress walls in a deep excavation has fully been mobilized prior to the final excavation depth, the efficiency of buttress walls in reducing the wall deflection in a deep excavation was much less than that in a shallow excavation. Rectangular shape of buttress walls was of a better effect than T-shape in the shallow excavation because frictional resistance between buttress walls and adjacent soil played a major role in reducing the wall deflection rather than bearing resistance of the flange. When the excavation went deeper, the difference in reducing the wall deflection between the R-shape and T-shape became small.     

基于多重响应面法的基坑位移反分析

基坑变形的反分析涉及数值模型与优化方法的耦合,常具有计算量大、使用不方便的特点。为此,提出1种可用于基坑变形反分析的多重响应面法,该方法在基坑地下连续墙不同深度处分别采用二次多项式表示地下连续墙水平位移与土层弹性模量之间的隐式关系,在此基础上利用位移观测对基坑土层弹性模量进行反分析。该方法可以解开数值模型和优化算法的耦合,从而具有较高的计算效率。工程应用实例表明,多重响应面法对基坑土层弹性模量进行反分析具有使用方便、计算效率高、计算结果准确的优点,非常适合求解基坑工程的位移反演问题。     

基于圆弧主应力迹线的黏性土主动土压力分析

墙背粗糙导致墙后土体应力方向发生偏转,目前,黏性土中考虑土体应力方向偏转对土压力影响的研究较少。为此,本文首先在探讨墙后土体主应力偏转规律的基础上,采用沿主应力迹线分层形成曲线薄层单元。然后,通过分析曲线薄层单元的受力情况,建立曲线薄层单元的静力平衡方程,推导出平动模式下黏性土体土压力沿墙高分布的公式,进而获得黏性土土压力分析新方法。最后,将本文方法与实测结果和现有理论进行对比验证和参数分析,验证本文方法的可靠性和合理性。研究结果表明:考虑墙土摩擦效应的计算结果更能准确反映黏性土体土压力沿墙高的分布规律;土压力大小随黏聚力增大而减小;随着墙土摩擦角的增大,土压力合力逐渐减小,作用点高度缓慢升高。     

Finite element analysis of excavation

The finite element method has often been used to simulate excavation. When the soil is linearly elastic, the results of excavation should be independent of the number of stages in the excavation process, and lack of such independence indicates an incorrect procedure. The simple direct method described in this paper provides the required independence in the case of linearly elastic materials, and hence can be used for multi-stage excavation in non-linear problems without excessive errors. However methods whose errors increase with the number of stages of excavation are quite unsuitable for non-linear problems. Alternative methods of analysis, errors arising from the inability of the elements to model adequately the stress gradients near the toe of the excavation and excavation adjacent to a diaphragm wall are discussed.     

基坑围护结构最大侧移深度对周边环境的影响

围护结构最大侧移所在深度是衡量基坑变形的重要指标之一,而目前鲜有关于其对周边环境变形影响的研究。基于工程实测数据分析和有限元数值模拟,系统地研究了基坑围护结构最大侧移深度对邻近桩基础建筑物不均匀沉降和坑外深层土体位移场的影响。经研究发现：围护结构最大侧移的下移会导致坑外土体位移场扩大,进而降低相应区域的桩基础承载力,导致邻近桩基础建筑物发生显著的不均匀沉降。不同深度的土体经历复杂的竖向位移,且位移形态与围护结构最大侧移深度密切相关。随围护结构最大侧移深度的逐渐下移,坑外土体位移场向深层土体发展,且主要影响范围相应地扩大。在实际工程中,根据基坑周边环境合理地控制围护结构最大侧移所在深度,可有效降低基坑开挖对周边环境的不利影响。     

Inverse analysis for geomaterial parameter identification using Pareto multiobjective optimization

An inverse analysis method that combines the back propagation neural network (BPNN) and vector evaluated genetic algorithm (VEGA) was proposed to identify mechanical geomaterial parameters for a more accurate prediction of deformation. The BPNN is used to replace the time‐consuming numerical calculations, thus enhancing the efficiency of the inverse analysis. The VEGA is used to find the Pareto‐optimal solutions to multiobjective functions. Unlike traditional back‐analysis methods which are based on only 1 type of field measurement and a single objective function, this proposed method can consider multiple field observations simultaneously. The proposed method was applied to the Shapingba foundation pit excavation located in Chongqing city, China. Two types of measurements are considered in the method simultaneously: the displacements in the x‐direction (north orientation) and those in the y‐direction (east orientation). Five deformation modulus parameters for artificial backfill soil, silty clay, siltstone, sandstone, and mudstone were selected as the inversion parameters. Compared with the weighted sum approach, the proposed method was demonstrated as an efficient multi‐objective optimization tool for back calculating undetermined parameters. After performing a forward‐calculation using the optimized parameters obtained by the inverse analysis, the predicted results were well consistent with the practical deformation in magnitude and trend.     

Investigation of the integrated retaining system to limit deformations induced by deep excavation

A series of three-dimensional finite element analyses of deep excavations with the integrated system between buttress walls and diaphragm walls was conducted to investigate the effect of the buttress wall intervals, treatments, locations, height, and thickness on limiting deformations induced by deep excavation. The integrated retaining system was formed by maintaining buttress walls when soil was excavated. The wall deflection control mechanism of the integrated retaining system mainly came from the combined stiffness between the buttress wall and the diaphragm wall. In addition, the ground settlement control mechanism came from the combined stiffness between the buttress wall and the diaphragm wall, and the frictional resistance between the buttress wall and the surrounding soil. For achieving 50% reduction in the wall deflection and the ground surface settlement, the length and intervals of buttress walls that were applied to the integrated retaining system were at least 4 and 8 m, respectively. When the deflection at the diaphragm wall head was well restrained, for example, by the floor slab, the position of the buttress wall head could be located at a depth the diaphragm wall starts to bulge out. In such a case, the performance between the full height and limited height of buttress walls was quite close. Furthermore, a new well-documented excavation project was analyzed to verify the performance of the integrated retaining system. Results showed that the integrated retaining system worked excellently if the joints between buttress walls and diaphragm walls were constructed properly.     

Finite-element modeling of a complex deep excavation in Shanghai

The excavation of the north square underground shopping center of Shanghai South Railway Station is a complex deep excavation using the top-down construction method. The excavation has a considerable size and is close to the operating Metro Lines. In order to predict the performance of the excavation more accurately, 3D finite-element analyses are conducted to simulate the construction of this complex excavation. The effects of the anisotropic soil stiffness, the adjacent excavation, and zone excavation on the wall deformation are investigated. It is shown that the numerical simulation with anisotropic soil stiffness yields a more reasonable prediction of the wall deflection than the case with isotropic soil stiffness. The deformation of the shared diaphragm wall between two excavations is influenced by the construction sequence of the two excavations. The zoned excavation can greatly reduce the diaphragm wall deformation. However, only the zoned excavation at the first excavation stage affects the deformation of the walls significantly. When the depth of the excavation increases, the zoned excavation has minor effect on the deformation of diaphragm walls.     

位移正反分析在地铁施工变位分配控制中的应用

采用浅埋暗挖法施工的城市地铁车站,开挖将不可避免地扰动土层引起地表沉降,从而对周围建构筑物的安全造成危害。由于地铁车站洞室的断面较大,大多采用分步开挖的方式施工,采用变位分配的方法通过预测每一步施工造成的地表沉降将最终的地表沉降分解到各个施工步序中,从而建立起各个阶段的地表沉降控制标准。这样,就可以通过加强对各个阶段的地表沉降的控制来实现对地表沉降进行整体控制的目的。而通过地质勘测所得的参数往往不能满足变位分配所依赖的数值模拟的要求,因此,反分析作为一种有效地补充手段来获得适合岩土工程数值模拟的力学参数。详细介绍了位移正反分析的特点、模型的建立条件和分析步骤,并通过工程实例验证了位移正反分析在预测地表沉降,从而提出变位分配控制标准的可行性。     

Intelligent model selection with updating parameters during staged excavation using optimization method

Various constitutive models have been proposed, and previous studies focused on identifying parameters of specified models. To develop the smart construction, this paper proposes a novel optimization-based intelligent model selection procedure in which parameter identification is also performed during staged excavation. To conduct the model selection, a database of seven constitutive models accounting for isotropic or anisotropic yield surface, isotropic or anisotropic elasticity, or small strain stiffness for clayey soils is established, with each model numbered and deemed as one additional parameter for optimization. A newly developed real-coded genetic algorithm is adopted to evaluate the performance of simulation against field measurement. As the process of optimization goes on, the soil model exhibiting good performance during simulation survives from the database and model parameters are also optimized. For each excavation stage, with the selected model and optimized parameters, wall deflection and ground surface settlement of the subsequent unexcavated stage are predicted. The proposed procedure is repeated until the entire excavation is finished. This proposed procedure is applied to a real staged excavation with field data, which demonstrates its effectiveness and efficiency in engineering practice with highlighting the importance of anisotropic elasticity and small strain stiffness in simulating excavation. All results demonstrate that the current study has both academic significance and practical significance in providing an efficient and effective approach of adaptive optimization-based model selection with parameters updating in engineering applications.