Estimation of static earth pressures for a sloping cohesive backfill using extended Rankine theory with a composite log-spiral failure surface

The Rankine earth pressure theory is extended herein to an inclined c–? backfill. An analytical approach is then proposed to compute the static passive and active lateral earth pressures for a sloping cohesive backfill retained by a vertical wall, with the presence of wall–soil interface adhesion. The proposed method is based on a limit equilibrium analysis coupled with the method of slices wherein the assumed profile of the backfill failure surface is a composite of log-spiral and linear segments. The geometry of the failure surface is determined using the stress states of the soil at the two boundaries of the mobilized soil mass. The resultant lateral earth thrust, the point of application, and the induced moment on the wall are computed considering global and local equilibrium of forces and moments. Results of the proposed approach are compared with those predicted by a number of analytical models currently adopted in the design practice for various combinations of soil’s frictional angles, wall–soil interface frictional angles, inclined angles of backfill and soil cohesions. The predicted results are also verified against those obtained from finite element analyses for several scenarios under the passive condition. It is found that the magnitude of earth thrust increases with the backfill inclination angle under both the passive and active conditions.

     

轴向荷载对斜桩水平承载特性影响试验及理论研究

斜群桩受水平荷载作用时,群桩中的基桩受到径向荷载、轴向荷载和弯矩的共同作用。为研究轴向荷载对斜桩水平承载特性的影响,完成了3根单桩以及1组1×2斜桩的大尺寸模型试验。试验结果表明：轴向拉力作用会降低斜桩的水平刚度和极限承载力;而轴向压力作用则会使其水平刚度和极限承载力提高。基于桩侧浅层土体楔形破坏假定,推导了考虑轴向荷载影响的斜桩水平极限土抗力计算公式,提出了桩侧土抗力的p-y曲线方法,并通过模型试验及现场试验验证其合理性。     

柱下独立基础稳健性设计与分析

岩土工程随机参数统计特征的不确定性,使得岩土工程可靠度设计存在一定风险。岩土工程稳健性设计能够充分考虑随机参数的不确定性结合结构安全性、稳健性和经济性实现最优设计。针对随机参数统计特征的不确定性对柱下独立基础设计的影响,基于可靠度理论和岩土工程稳健性设计方法,考虑岩土参数、混凝土和钢筋材料力学参数统计特征不确定性的影响,以独立基础几何尺寸作为可控设计参数进行设计分析。将独立基础地基承载力、地基变形、基础结构冲切破坏和基础弯曲破坏4种失效模式视为串联系统,进行多失效模式下的结构体系稳健性设计,分析了多失效模式下结构几何参数与结构体系可靠度的关系。结合稳健性和经济性,进行了独立基础多目标优化设计,确定柱下独立基础设计的最优解。     

A generalized surrogate response aided-subset simulation approach for efficient geotechnical reliability-based design

This paper aims to develop an efficient geotechnical reliability-based design (RBD) approach using Monte Carlo simulation (MCS). The proposed approach combines a recently developed MCS-based RBD approach, namely expanded RBD approach, with an advanced MCS method called “Subset Simulation (SS)” to improve the computation efficiency at small probability levels that are often concerned in geotechnical design practice. To facilitate the integration of SS and expanded RBD, a generalized surrogate response f is proposed to define the driving variable, which is a key parameter in SS, for expanded RBD of geotechnical structures (e.g., soil retaining structures and foundations). With the aid of the proposed surrogate response, failure probabilities of all the possible designs in a prescribed design space are calculated from a single run of SS. Equations are derived for integration of the surrogate response-aided SS and expanded RBD, and are illustrated using an embedded sheet pile wall design example and two drilled shaft design examples. Results show that the proposed approach provides reasonable estimates of failure probabilities of different designs using a single run of the surrogate response-aided SS, and significantly improves the computational efficiency at small probabilities levels in comparison with direct MCS-based expanded RBD. The surrogate response-aided SS is able to, simultaneously, approach the failure domains of all the possible designs in the design space by a single run of simulation and to generate more complete design information, which subsequently yields feasible designs with a wide range of combinations of design parameters. This is mainly attributed to the strong correlation between the surrogate response and target response (e.g., factor of safety) of different designs concerned in geotechnical RBD.     

Effect of sampling plan and trend removal on residual uncertainty

ABSTRACT

The ground is one of the most highly variable of all engineering materials. As a result, geotechnical designs depend upon a site investigation to estimate the ability of the ground to perform acceptably. For example, when a shallow foundation is being proportioned to avoid a bearing capacity failure under a certain applied load, the frictional and cohesive properties of the ground under the foundation must first be estimated through a site investigation. Questions which arise are: How does the quality and intensity of the site investigation affect the design? Is more investigation cost effective? If the site is sampled at one location and the foundation placed at a different location, how does this mismatch affect the target design and the reliability of the final foundation? By modelling the ground as a spatially variable material, questions such as the above can be investigated through Monte Carlo simulation and sometimes theoretical probabilistic models. Using such tools, this paper looks specifically at how the intensity (frequency and spatial distribution) of a site sampling plan, and how the samples are used, affects the understanding of the ground properties under a foundation. Interestingly, it is found that removing the sample mean outperforms removing the best linear unbiased estimate (BLUE) when the actual field correlation length is small but the BLUE correlation length is assumed equal to the field size. Recommendations are made regarding number of samples and the type of trend to best characterise the field.

Abbreviations: BLUE: best linear unbiased estimate; MCS: Monte Carlo simulation; LAS: local average subdivision     

基于有限元的弯矩计算中若干问题探讨

在岩土工程的数值计算中,除了将岩土材料本身划分为实体单元外,设置在岩土体中,与岩土材料相互作用的其他材料也常常划分为实体单元,比如桩基、堤坝防渗墙和面板等。由于对桩基、防渗墙等往往需要利用内力和弯矩进行设计,这就提出了如何利用有限元得到的应力和位移信息计算结构弯矩的问题。通过对一悬臂梁的计算分析就这一问题进行探讨,发现用应力计算弯矩为提高精度需要划分较多单元。用位移计算可以减少单元划分的工作量,但计算易出现振荡,结果不可靠。同时,对剪切闭锁现象等进行了探讨。     

Effect of soil variability on the bearing capacity of clay and in slope stability problems

Site-specific geotechnical data are always random and variable in space. In the present study, a procedure for quantifying the variability in geotechnical characterization and design parameters is discussed using the site-specific cone tip resistance data (q_c) obtained from static cone penetration test (SCPT). The parameters for the spatial variability modeling of geotechnical parameters i.e. (i) existing trend function in the in situ q_c data; (ii) second moment statistics i.e. analysis of mean, variance, and auto-correlation structure of the soil strength and stiffness parameters; and (iii) inputs from the spatial correlation analysis, are utilized in the numerical modeling procedures using the finite difference numerical code FLAC 5.0. The influence of consideration of spatially variable soil parameters on the reliability-based geotechnical deign is studied for the two cases i.e. (a) bearing capacity analysis of a shallow foundation resting on a clayey soil, and (b) analysis of stability and deformation pattern of a cohesive-frictional soil slope. The study highlights the procedure for conducting a site-specific study using field test data such as SCPT in geotechnical analysis and demonstrates that a few additional computations involving soil variability provide a better insight into the role of variability in designs.     

基于能量法的轴横向荷载作用下单桩受力变形分析

轴向和横向荷载作用下单桩的受力变形分析是桩基研究的重点内容之一。单桩在水平荷载作用下会产生一定的水平位移与弯矩,而此时作用轴向荷载会使得桩体出现一定的压曲与附加弯矩,以致轴横向荷载作用下的单桩受力变形与单独作用水平荷载或轴向荷载的单桩存在较大的区别。故本文基于能量法,首先分别建立轴横向荷载作用下单桩的受力变形能量方程以及桩周土体能量方程,然后考虑桩土变形协调与一定的桩土相互作用,基于最小势能原理得到单桩变形控制微分方程,并采用幂级数法进行求解,最终得到轴横向荷载作用下单桩受力变形分析的幂级数解答。通过编程计算,将本文方法计算结果与试验结果、数值分析结果、规范法计算结果进行对比分析,验证了本文方法的合理性和可行性。在此基础上,基于本文解答进行了影响参数分析,结果表明:桩体长径比、桩土弹性模量比、桩周土模量深度变化系数均对轴横向受荷单桩的桩身水平位移与最大弯矩值有一定的影响,其中桩周土模量深度变化系数以不小于0.6为宜。     

Combined loading of caisson foundations in cohesive soil: Finite element versus Winkler modeling

The undrained response of massive caisson foundations to combined horizontal, vertical and moment loading is parametrically investigated through a series of 3D finite element analyses. The parameters are: (a) the embedment ratio (D/B), (b) the factor of safety against initial vertical loading (FS_V) and (c) the ratio of the overturning moment to the horizontal force applied at the top of the caisson (M/Q). Emphasis is given on: (i) the identification of all possible failure mechanisms in M–Q–N space, (ii) the developed stress distributions along the caisson walls for various load levels up to complete failure conditions. The results are then used as a feedback for calibrating the parameters of a generalized four-type spring model, originally proposed by Gerolymos and Gazetas (2006), through a genetic algorithm-based optimization procedure. The predictions of the Winkler model compare very well with the FE results, not only at the local response level (in terms of stress distributions along the caisson shafts), but at a global response level (in terms of force–displacement curves and M–Q–N failure envelopes at the top of the caisson) as well. Contrary to established lateral soil resistance theories, it is shown that both the ultimate horizontal soil reaction and resisting moment per unit depth do not solely depend on the strength properties of soil and geometry of the caisson but are also functions of the applied load ratio M/Q and initial soil yielding due to vertical loading. Interesting conclusions are also drawn regarding the transition from the elastic to the ultimate limit state (hardening). Quantifying through analytical expressions the contribution of each of the two basic lateral resisting mechanisms to the response of the caisson, a classification method for embedded foundations is then proposed. The capabilities of the Winkler model are further demonstrated through comparison with FE analysis of the caisson cyclic lateral response.     

Improved performance-based seismic coefficient for gravity-type quay walls based on centrifuge test results

Verifying the seismic performance of port structures when the force balance limit is exceeded is important for the performance-based seismic design of gravity-type quay walls. Over the last three decades, performance verification methods have been developed that consider the effects of the design earthquake motion, geotechnical conditions, and structural details on the deformation of a quay wall to accurately predict earthquake-induced damage. In this study, representative performance verification methods (i.e., simplified dynamic analysis methods extending from the Newmark sliding block method and performance-based seismic coefficients developed in Japan) were quantitatively assessed with actual cases of earthquake-damaged quay walls and the results of dynamic centrifuge tests previously conducted under various conditions (i.e., different wall heights, earthquake motions and the thickness of subsoil). The dynamic centrifuge test results suggested directions for improving the performance-based seismic coefficients of the representative methods, while their field applicability and reliability were confirmed according to the actual earthquake records.

     

Discussion on the Multi-Solution of Three-Dimensional Slope Safety Factor

The limit equilibrium method cannot yield a unique value of safety factor in three-dimensional (3D) analysis of slope. However, the calculated value of safety factor according to limit equilibrium method directly determines the design of slope engineering. So, the study of multi-solution of three-dimensional slope safety factor may help people to judge further the reasonableness of the computation results and select the range of safety factor’s possible values. In this paper, the initial distribution of normal stresses over the sliding surface is assumed, which is then modified by a function involving four parameters to satisfy force and moment equilibrium conditions of the sliding body. Then, according to a series of assumed safety factors, the corresponding minimum value of the normal stress of sliding surface is calculated by force and moment equilibrium conditions of the sliding body. Then the reasonable range of slope safety factor is justified according to the reasonableness of the normal stress distribution over the sliding surface. The calculation results of engineering examples show that the reasonable range of safety factor for symmetric slopes is between 8 and 12% and that the reasonable range of safety factor for asymmetric slope is over 30%. Therefore, it is necessary to further verify the rationality of normal stress for the safety factor of three-dimensional asymmetric slope in order to further apply it to engineering.

     

基于FELA的随机场方法在考虑降雨入渗的边坡开挖稳定性分析中的应用

黑山共和国南北高速公路项目部分路段处于复理石地区,降雨集中、空间变异性显著且分层分布的岩土体给道路边坡施工带来了挑战。条分法、常规有限元法等确定性分析方法不能考虑岩土材料的不确定性,给出的具有唯一性、确定性的结果不能反映边坡稳定的不确定性。以该工程某边坡为例,采用有限元极限分析方法（FELA）,考虑岩土材料强度的空间变异性,利用上下限解法得出安全系数的分布区间。由勘察资料得到材料均值、标准差和空间相关长度并重建描述抗剪强度指标的二维随机场,同时考虑开挖岩层的节理分布,分析边坡在分级开挖过程中,各施工步骤的稳定性和破坏模式。与有限元分析结果相比,随机场条件下,部分情况开挖阶段安全系数低于限值,并出现局部破坏和整体破坏两种形式。结合不饱和土理论,模拟暴雨情况下雨水的入渗深度并在饱和区采用降低后的强度参数重新计算。通过蒙特卡洛模拟,得到各工况下安全系数、滑动体体积、挡墙弯矩和锚杆内力的概率密度分布函数。挡墙结构约束土体的变形,使得破坏模式趋向于整体破坏,安全系数分布区间变小。锚杆能带动更多土体进入工作状态,同样约束安全系数分布区间。旱季施工与雨季施工边坡破坏区域不同,同等支护条件下,雨季边坡安全系数分布区间更大,且均值明显降低。      

A method for designing the longitudinal spacing of slope-stabilising shafts

The work at hand deals with the design of the longitudinal spacing among rows of closely spaced large-diameter shafts used to stabilise a precarious slope. The problem under consideration is idealised through a conceptual framework where an unstable mass of an infinitely long slope pushes a stable portion of soil adjacent to shafts, leading to failure along a slip surface passing through the upper end of the reinforcement elements. By exploiting the upper bound theorem of plastic collapse, a closed-form solution is derived for the load required for the failure of the stable mass as a function of geometrical and mechanical parameters of the slope and the soil. Results are validated through physical model tests by means of geotechnical centrifuge. Given the satisfactory agreement between analytical and experimental results, the model is extended to evaluate the safety conditions of the reinforced slope.     

黏土中桶式基础的宏单元模拟

本研究旨在对黏土中的桶式基础进行从完整的有限元分析到简化的宏单元的建模。首先通过有限元方法分析了在不同单调组合荷载作用下的黏土中吸力桶基础。为保证模拟结果的可靠性,采用了硬化土模型（HS）对正常固结黏土地基进行模拟。通过对比离心试验验证了使用HS模型的有限元分析的有效性,并通过径向位移试验进一步延伸到V-H-M（竖向力-水平力-弯矩）空间的破坏模式研究,并在此基础上,提出了的V-H-M空间三维破坏包络面公式。接着,应用此三维破坏包络面公式,采用亚塑性框架提出了黏土中桶式基础的宏单元设计模型。通过与试验结果的比较,验证了宏单元模型在模拟单调和循环荷载条件下桶式基础的强度与变形响应的有效性。所提的宏单元模型对于海洋岩土工程设计实践将很有帮助。     

A lateral soil resistance model for XCC pile in soft clay considering the effect of the geometry of cross section

In this paper, a series of well-calibrated finite-element analyses are performed to quantify the influence of the geometry of cross section on the load transfer mechanism of X-section Cast-in-place Concrete (XCC) pile under lateral load, aiming to propose a lateral soil resistance model for XCC pile in soft clay. Based on the results of the numerical parametric analysis, the failure mechanism of soil flow and the ultimate lateral soil pressure are investigated to reveal the underlying mechanism that controls the cross-section geometry-dependency response. Finally, a general p-y formula for XCC pile, which can well capture the lateral behavior of XCC pile considering the various cross section geometries, is developed. In addition, compared with the traditional circular cross section pile with the same area, the XCC pile is more effective in terms of resistance to lateral load.

     

复合加载条件下沉箱基础稳定性的三维效应

联合采用swipe加载模式与固定位移比加载模式,对于吸力式沉箱基础在水平荷载H与力矩M的复合加载条件下的稳定性进行比较系统的三维有限元分析,主要探讨了基础埋深与直径之比、地基土不排水强度的非均质性对于基础在H-M荷载空间内的破坏包络轨迹的影响,揭示了地基在不同荷载分量组合条件下的失稳破坏机制,并与平面应变假定下得到的结果进行了比较。计算结果表明：平面应变与三维情况下基础的破坏包络面形状有较大差异,分析基础稳定性时,必须考虑其三维效应。在三维情况下,非均质土中埋深与直径之比较小的基础的破坏包络面仍然会向负方向倾斜,已有的包络面方程明显高估这种情况下沉箱基础在正向水平荷载与力矩联合作用下的承载力,从而导致基础设计偏于不安全。     

Robust geotechnical design of shield-driven tunnels

This paper presents a fuzzy set-based robust geotechnical design (RGD) methodology for the design of shield-driven tunnels. Here, uncertain geotechnical parameters required for analysis of tunnel performance (referred to herein as the structure safety and serviceability performance of tunnel cross section) are represented as fuzzy sets. Given fuzzy input parameters, the performance of a shield-driven tunnel will be uncertain, which is expressed in this study as a fuzzy factor of safety, according to the analysis of vertex method. Then, the fuzzy factor of safety for a given design is used to evaluate the failure probability and design robustness, which are, in turn, employed in the proposed RGD framework. Note that a design is considered robust if the performance of the shield-driven tunnel is insensitive to the variation of its uncertain geotechnical parameters. Within the RGD framework, each candidate design in the design space is analyzed for its safety state (in terms of failure probability), design robustness, and cost. The goal of the RGD of a shield-driven tunnel is to bring the safety state to an acceptable level, while maximizing the robustness and cost efficiency simultaneously. To this end, a multi-objective optimization is performed and a Pareto front is obtained, which provides a trade-off that may be used to select the most preferred design. Through an illustrative case, the effectiveness and significance of this new robust design methodology is demonstrated.     

Micro-mechanical analysis of soil–structure interface behavior under constant normal stiffness condition with DEM

The mechanical behavior at soil–structure interface (SSI) has a crucial influence on the safety and stability of geotechnical structures. However, the behavior of SSI under constant normal stiffness condition from micro- to macro-scale receives little attention. In this study, the frictional characteristics of SSI and the associated displacement localization under constant normal stiffness condition are investigated at both macro- and microscales by simulating a series of interface shear tests with discrete element method. The algorithm to achieve a constant normal stiffness is first developed. The macroscopic mechanical response of the interface shear tests with both loose and dense specimens at various normal stiffness is discussed in terms of shear stress, normal stress, vertical displacement, horizontal displacement and stress ratio. Then, the microscopic behaviors and properties, including shear zone formation, localized void ratio, coordination number, force chains and soil fabric, are investigated. The effect of normal stiffness is thus clarified at both macro- and microscales.

     

Evaluation of the Instability Risk of the Dam Slopes Simulated with Monte Carlo method (Case Study: Alborz Dam)

Embankment dams are one of the most important geotechnical structures that their failures can lead to disastrous damages. One of the main causes of dam failure is its slope instability. Slope Stability analysis has traditionally been performed using the deterministic approaches. These approaches show the safety of slope only with factor of safety that this factor cannot take into account the uncertainty in soil parameters. Hence, to investigate the impact of uncertainties in soil parameters on slope stability, probabilistic analysis by Monte Carlo Simulation (MCS) method was used in this research. MCS method is a computational algorithm that uses random sampling to compute the results. This method studies the probability of slope failure using the distribution function of soil parameters. Stability analysis of upstream and downstream slopes of Alborz dam in all different design modes was done in both static and quasi-static condition. Probability of failure and reliability index were investigated for critical failure surfaces. Based on the reliability index obtained in different conditions, it can be said that the downstream and upstream slope of the Alborz dam is stable. The results show that although the factor of safety for upstream slope in the state of earthquake loading was enough, but the results derived from probabilistic analysis indicate that the factor of safety is not adequate. Also the upstream slope of the Alborz dam is unstable under high and uncontrolled explosions conditions in steady seepage from different levels under quasi-static terms.

     

液化型路堤边坡动力数值模拟分析

液化型路堤边坡动力稳定性问题涉及岩土工程与工程地震两个学科领域,是边坡工程与砂土液化的交叉课题。采用天然地震记录为输入条件,应用Finn本构关系模型,运用有限差分法,对填土+砂土+卵砾土地层组合的路堤边坡进行了全时程动力分析,探讨了地震作用下路堤边坡的液化初步规律和稳定性。数值模拟结果表明:地震作用引起了路基饱和砂土有效应力急剧减小,并导致路基砂土液化,引起路堤变形破坏。孔隙水压力的积累与消散不仅与地震记录序列存在对应关系,也与砂土所处的位置和深度有密切关系。地表变形破坏主要表现为路堤顶面发生震陷和拉裂破坏,坡底面产生挤压隆起变形。地面以下的变形破坏主要包括土体剪切破坏和深部砂土液化引起的侧向流动破坏。