Analytical solutions to the axisymmetric consolidation of a multi-layer soil system under surcharge combined with vacuum preloading

Surcharge combined with vacuum preloading is a common technique for accelerating the consolidation process in ground improvement. A unit cell model for the axisymmetric consolidation of a soft soil using a prefabricated vertical drain (PVD) under a surcharge, combined with vacuum preloading, is investigated in this study. Based on this model, analytical solutions for a multi-layer soil system are put forward and the explicit expressions for two-layer and one-layer systems are presented. The accuracy of the proposed solution is verified using an analytical solution available in the literature. In the parametric study, the influencing factors on the consolidation process, such as, the smear zone, the PVD spacing, the hydraulic conductivity in the radial direction, the coefficient of vacuum decrease, are taken into account. The water flow in the radial direction plays an important role in the consolidation process while the impact of the vertical flow mainly develops around the interfaces between two adjacent layers. In addition, the proposed analytical solution is applied in a case history with three different layers and the results are reasonable.     

恒荷载作用下复合地基非线性分析

从桩周土体径竖向渗流方程出发,采用土体e–logσ和e–logk半对数模型,对于排水桩桩体仅考虑竖向渗流并考虑涂抹区影响,建立恒荷载作用下复合地基非线性固结方程。通过与已有解的对比,证明此解析解的正确性。根据对复合地基非线性固结分析发现:复合地基固结速率随土体非线性参数Cc/Ck和荷载增量σ0/σsi的增大而减小,但相比Cc/Ck,荷载增量σ0/σsi对固结速率影响很小;随着桩土模量比增大,复合地基固结速率加快,且非线性参数Cc/Ck对固结速率的影响程度减小;排水桩复合地基固结速率受kh/kc即桩体渗透性影响很大。     

General solutions for consolidation of multilayered soil with a vertical drain system

A quasi-analytical method is newly introduced to solve the equal-strain consolidation problem of multilayered soil with a vertical drain system. Both vertical and radial drainage conditions are considered, together with the effects of drain resistance and smear. By using the method of Laplace transform with respect to time, a general explicit analytical solution for the consolidation in transformed space is obtained. Numerical inversion of the Laplace transform in the time domain is then applied to obtain the solution for calculating excess pore-water pressure. This solution is explicitly expressed and conveniently coded into a computer program for ease and efficiency of practical use. Its validity and accuracy are verified by comparing the special cases of the proposed solution with a finite-element solution and an available analytical solution. Moreover, the consolidation behavior of a four-layered soil with a vertical drain is investigated. The order of soil layers is shown to have a significant effect on the behavior of consolidation. This highlights that caution should be exercised when weighted average consolidation parameters of multilayered soil are used to analyze the consolidation behavior.     

考虑井阻随时间变化下砂井地基的非线性固结解

针对砂井地基固结过程中砂井的渗透系数会逐渐降低这一特性,通过引入e-lg??和e-lgk对数模型来描述土体的非线性固结特性,同时考虑井阻随时间变化和涂抹区径向渗透系数变化等因素,推导砂井地基非线性固结的控制方程,并采用分离变量法求得该方程的固结解。通过退化研究并与已有的解析解进行对比分析,对该解答的正确性进行验证。基于该解答,对砂井地基的非线性固结性状进行分析。分析表明:砂井地基的固结速率随井阻因子的增大而减小,井阻的变化主要对砂井地基后期固结速率的影响较大;在涂抹区径向渗透系数变化的3种模式中,抛物线变化模式固结速率最快,线性变化模式次之,常数变化模式固结速率最慢;压缩指数与渗透指数的比值越大,砂井地基的固结速率越慢;在非线性压缩关系下,砂井地基固结过程中的平均孔压固结度始终慢于平均沉降固结度。     

堆载预压径竖向固结等体积应变解答

现有的含竖向排水体地基固结问题的解析解答大都是在传统的等竖向应变假设基础上建立的,而且在考虑涂抹区土体的渗流和压缩作用方面,还没有真实地体现出涂抹区土体的竖向渗透系数和体积压缩系数,其对地基固结的影响也尚不明确。为此,针对含竖向排水体地基径竖向同时固结的轴对称问题,采用等体积应变假设,考虑井阻作用、涂抹作用、随时间线性堆载预压以及地基附加球应力任意分布,推导了完整的径竖向固结微分方程的解答,给出了超静孔隙水压力和固结度的显式表达式,分析了侧向变形即泊松比效应以及涂抹区土体的竖向渗透系数和三维体积压缩系数对地基整体平均固结度的影响。结果表明,泊松比效应较为明显,基于传统的等竖向应变假设的解答高估了地基的固结速率;不考虑涂抹区土体体积压缩的解答虽然也高估了地基的固结速率,但影响有限;而涂抹区土体的竖向渗透系数对于地基固结的影响则几乎可忽略不计。     

A new contribution to the finite line-source model for geothermal boreholes

Heat transfer around vertical ground heat exchangers is a common problem for the design and simulation of ground-coupled heat pump (GCHP) systems. Most models are based on step response of the heat transfer rate, and the superposition principle allows the final solution to be in the form of the convolution of these contributions. The step response is thus a very important tool. Some authors propose numerical tabulated values while others propose analytical solutions for purely radial problem as well as axisymmetric problems. In this paper we propose a new analytical model that yields results very similar to the tabulated numerical ones proposed in the literature. Analytical modeling offers better flexibility for a parameterized design.     

遗传算法与自适应粒子群算法耦合的大坝安全预警评价模型

改变应用最小二乘法求解大坝统计预警模型的传统方式,利用粒子群算法随机搜索的优化能力确定统计模型的回归系数。针对粒子群算法收敛速度较慢等问题,提出一种新的自适应策略,能够依据粒子个体和种群的优化信息,调整学习因子,并将该策略与遗传算法的交叉、变异算子相结合。通过工程算例表明,该方法具备较好的搜索多样解能力,自适应地调整粒子飞行的步长,提高了粒子群算法的收敛速度;基于该方法的大坝预警评价模型与最小二乘法、基本粒子群算法相比,数据挖掘能力强,预警评价结果与大坝的实际运行状态更加吻合,有效地提高了统计模型的预测精度。     

Consolidation of a composite foundation with soil–cement columns and prefabricated vertical drains

A new ground improvement method is proposed for embankment foundation on soft soils, involving the use of both soil–cement columns and prefabricated vertical drains (PVDs) to improve the shear strength and accelerate the pre-consolidation process. An analytical solution was derived for calculating the consolidation process of this composite foundation under time-dependent loading by considering the PVDs as cylindrical drain wells. The equivalent coefficient of permeability was acquired by matching the average degree of consolidation of a unit cell model. The analytical expression of consolidation was established according to the axi-symmetric analytical model, and its theoretical solution under time-dependent loading was achieved through the variable separation method. The analytical solution under ramp loading was verified by comparing the calculated results with the three-dimensional finite-element analysis. The influence of replacement ratio of the soil–cement column, column-soil modulus ratio, improvement depth and column-soil permeability ratio were explored. Field experiments on the Huai-Yan Highway indicated the calculated settlements agreed well with the field measurements.     

饱和半空间表面无限长梁的沉降变形

采用解析方法研究了饱和半空间表面无限长欧拉梁的沉降变形特性。假定梁与地基的竖向接触应力沿梁截面均匀分布、梁的挠度与梁截面下地基表面的位移均值相等,分别考虑地基表面完全透水及完全不透水情况,基于Fourier及Laplace联合变换获得了问题的解析解,并通过已有研究结果及ABAQUS~(TM)有限元分析模型对比验证了解的正确性。分析结果表明,梁的弯曲刚度、地基的排水及不排水泊松比以及地基表面的透水条件对梁的沉降变形有明显影响。     

Modelling the Effects of Surcharge to Reduce Long Term Settlement of Reclamations over Soft Clays: A Numerical Case Study

Long-term settlement of reclamations constructed over soft soils may be reduced by the use of temporary pre-loading, although there is often uncertainty over how much surcharge to use, and how long it should be maintained. An elastic visco-plastic constitutive model is described and its application in assessing surcharging strategy for reclamation schemes is discussed. The model is incorporated in a one-dimensional finite difference consolidation analysis with vertical and radial drainage of a multi-layer soil profile. The analysis allows the inclusion of vertical drain resistance, a zone of peripheral smear around the drain, permeabilities that vary with void ratio, and creep both during and after primary consolidation. Drawing on data from the Bothkennar soft clay research site, the model is used to predict settlements beneath a hypothetical test fill, including the creep settlement behaviour when a surcharge is removed after different time periods. The behaviour during primary consolidation is back-analysed using Asaoka’s and the hyperbolic observational methods, and both are found to under-predict the magnitude of the settlement.     

A simple solution for prefabricated vertical drain with surcharge preloading combined with vacuum consolidation

Prefabricated vertical drains (PVDs) with the surcharge preloading and vacuum consolidation has become considerably popular for ground improvement projects. A simple solution that incorporates the fundamental embankment features, such as the average degree of consolidation and excess pore pressure, are essential for the design of soft ground improvements by PVDs with vacuum preloading. However, most of the solutions for vertical drains with vacuum consolidation require numerical simulations, whose implementation tends to be laborious. In contrast, a simple solution for vacuum consolidation under time-dependent loading has not yet been proposed. In this study, a simple solution that can be easily incorporated into a conventional spreadsheet is derived for PVDs with vacuum preloading by applying the Laplace transform technique. The proposed solution accounts for several actual construction conditions, such as initial surcharge load, vacuum pump trial period, variations of radial permeability, and time-dependent loading. The results obtained from this proposed approach were validated with those from the finite element method and field data from the case study of the Cai Mep International Terminal project in southern Vietnam. The derived solutions, including the excess pore pressures and average degrees of consolidation, were in good agreement with the predicted and observed data.     

水平向渗透系数变化条件下散体材料桩复合地基固结理论研究及分析

 建立考虑排水影响区土体水平向渗透系数因施工扰动影响而逐渐变化的散体材料桩复合地基的固结定解问题,并求出其一般解。基于实际工程中桩体施工对扰动区土体水平向渗透系数影响的复杂性,选择排水影响区土体水平向渗透系数沿径向分布的3种特殊情况,给出相应特解。根据解析解结果,通过编程计算,绘制出主要因素对复合地基固结过程的影响曲线图,分析排水影响区土体水平向渗透系数变化对散体材料桩复合地基固结性状的影响。研究结果表明：土体渗透性变化对复合地基固结影响显著,桩体施工对周围土体扰动越大,复合地基固结会越慢;考虑土体水平向渗透系数变化的散体材料桩复合地基固结理论较现有的复合地基固结理论更接近实际情况。     

排水板真空度损耗的排水固结解析解

无砂真空预压吹填软土在国内造地工程中广泛应用,但实践表明传统固结解析解已不足以预测其加固性状和加固效果。从固结方程出发,在原有的等应变假设基础上,在定解条件中增加了吹填土特有的高度欠固结特性和无砂真空预压特别明显的真空度损耗,重新推导得到径向和竖向完全协调的新的等应变解析解——JJJ解答,以解决无砂真空预压吹填软土的排水固结设计理论问题。JJJ法作为固结方程的原生解答,兼容以往所有该类解析解的同时,增加了针对高度欠固结土类和排水板真空度损耗严重的排水固结问题的解决能力。经现场和试验验证,JJJ解析解可相当精确预测无砂真空预压吹填软土的复杂固结过程和加固土体超孔压分布和孔压消散分布,该解答同时也适用于堆载和真空预压的工况。     

考虑软黏土结构性损伤的圆柱孔扩张弹塑性分析

针对天然沉积软黏土中施工扰动导致原位土结构性损伤和强度降低的特征,根据圆孔扩张过程中产生的塑性剪切应变以及实测的渗透系数与不排水强度随径向距离的变化规律,提出对数式的原位扰动度函数以描述塑性损伤区的屈服强度变化;基于结构性剑桥模型屈服准则,采用屈服应力比和灵敏度分别表征初始结构稳定性和结构强度可变性大小,并与扰动函数相结合,推导了考虑土结构性损伤的软黏土柱孔扩张弹塑性解,表达式中灵敏度值为1时退化为不考虑结构损伤的传统解。进而通过竖井和沉桩施工引起的超静孔隙水实测结果与理论计算值的对比,验证了本文理论解的有效性;并分析了土结构及其损伤对柱孔扩张效应的影响,结果表明：屈服应力比越大,塑性区半径越小,径向应力越大,超静孔压随径向距离先增大后减小;灵敏度越大,径向应力越小,超静孔压越大。分析推导结果对准确预测挤土效应与合理揭示孔压静力触探等原位试验测试机理具有实用价值。     

Nonlinear consolidation analysis of soft soil with vertical drains considering well resistance and smear effect under cyclic loadings

In this paper, the nonlinear consolidation behavior of soft soil with vertical drains considering well resistance and smear effect under cyclic loadings was investigated. Using the variables separation method, a series of analytical solutions were derived to calculate the excess pore water pressure and the average degree of consolidation of the soil subjected to various cyclic loadings including trapezoidal cyclic loading, rectangular cyclic loading, triangular cyclic loading and haversine cyclic loading. The correctness of the proposed solutions was verified through degenerating into the existing solutions. Finally, the effects of different parameters on the nonlinear consolidation behavior of soil with vertical drains under cyclic loadings were analyzed.     

Effects of temperature circulation on dredged sludge improved by vacuum preloading

Vacuum preloading is an effective and common method used for clay soil improvement. However, the smear zone generated by the installation of prefabricated vertical drain (PVD) hinders additional efficiency improvements. PVD combined with heat is applied to overcome this problem. This study presents a series of model tests conducted on clayey soil improved by vacuum preloading with different rectangular-wave temperature circulation modes to investigate the effects of cyclic temperature on vacuum consolidation. During the test, the settlement, pore-water pressure, and drainage were monitored. The degree of consolidation was analyzed to evaluate the effectiveness of this method, and the coefficient of energy consumption was used to quantify the energy consumption at different cyclic temperature modes. The results indicated that the rectangular-wave temperature circulation mode of 30–75–30 °C was the most effective. The results of this study contribute substantially to the state of knowledge regarding the cyclic temperature effects on dredged slurry performance subjected to vacuum preloading. Concurrently, a novel approach is introduced for the determination of the optimal soil consolidation.     

Radial consolidation characteristics of soft undisturbed clay based on large specimens

In recent years, reconstituted small samples have often been used to assess the performance of radial consolidation due to prefabricated vertical drains (PVDs), but the permeability and compressibility of samples of undisturbed soil often differ from those of the remoulded ones. The problem seems more complex in marine environment due to the presence of random coarse particles including gravels, shells and natural partings. Performing small-scale laboratory experiment with reconstituted samples, especially in marine environment, cannot predict the exact soil behaviour in the field. This paper describes an experimental programme that measures radial consolidation using a conventional Rowe cell and a large-scale consolidometer, where the samples of undisturbed soil obtained from a site along the Pacific Highway (north of Sydney) were compared using measured settlements and excess pore pressures. Moreover, this paper highlights the implications of the smear effect and sample size influence, which are imperative in translating the laboratory testing practices to actual real-life behaviour. The effect of vacuum pressure on the coefficient of radial consolidation of a large-scale undisturbed test specimen is also discussed. The paper demonstrates that the extent of smear zone in the field can be very similar to the large-scale laboratory consolidation test using a scaled-down drain and mandrel, but considerably different from the data obtained for small laboratory specimens.     

基于粒子群算法和广义回归神经网络的岩爆预测

 岩爆是岩石深部开挖中一种常见的工程地质灾害。为评价岩爆发生的可能性,提出一种基于粒子群算法和广义回归神经网络模型(PSO-GRNN模型)的岩爆预测方法。该方法利用已有岩爆数据,通过神经网络技术建立回归模型,采用粒子群算法对模型参数进行优化,减少人为因素对神经网络设计的影响。据此方法,在能量理论的基础上,选取洞壁围岩最大切向应力、岩石单轴抗压强度、抗拉强度和弹性能量指数作为主要影响因素,利用国内外26组已有工程数据建立岩爆预测的PSO-GRNN模型。通过对苍岭隧道和冬瓜山铜矿岩爆预测的工程实例分析验证该方法的可行性和适用性。所提方法可为类似工程的岩爆预测提供参考。     

Reliability-based design optimization with discrete design variables and non-smooth performance functions: AB-PSO algorithm

The purpose of reliability-based design optimization (RBDO) is to find a balanced design that is not only economical but also reliable in the presence of uncertainty. Practical applications of RBDO involve discrete design variables, which are selected from commercially available lists, and non-smooth (non-differentiable) performance functions. In these cases, the problem becomes an NP-complete combinatorial optimization problem, which is intractable for discrete optimization methods. Moreover, the non-smooth performance functions would hinder the use of gradient-based optimizers as gradient information is of questionable accuracy. A framework is presented in this paper whereby subset simulation is integrated with a new particle swarm optimization (PSO) algorithm to solve the discrete and non-smooth RBDO problem. Subset simulation overcomes the inefficiency of direct Monte Carlo simulation (MCS) in estimating small failure probabilities, while being robust against the presence of non-smooth performance functions. The proposed PSO algorithm extends standard PSO to include two new features: auto-tuning and boundary-approaching. The former feature allows the proposed algorithm to automatically fine tune its control parameters without tedious trial-and-error procedures. The latter feature substantially increases the computational efficiency by encouraging movement toward the boundary of the safe region. The proposed auto-tuning boundary-approaching PSO algorithm (AB-PSO) is used to find the optimal design of a ten-bar truss, whose component sizes are selected from commercial standards, while reliability constraints are imposed by the current design code. In multiple trials, the AB-PSO algorithm is able to deliver competitive solutions with consistency. The superiority of the AB-PSO algorithm over standard PSO and GA (genetic algorithm) is statistically supported by non-parametric Mann-Whitney U tests with the p-value less than 0.01.     

非瞬时加载下土工袋装砂石桩复合地基固结解析解

 针对土工袋装砂石桩复合地基,推导非瞬时加载情况下土工袋装砂石桩复合地基固结度的解析解。该解析解不仅同时考虑了桩体和土体的径向和竖向变形,而且考虑了桩体和土体的径向和竖向渗流。在通解的基础上,给出了附加应力线性施加并沿深度梯形分布情况下的固结度计算公式,并通过将土工袋装砂石桩复合地基退化为普通砂石桩复合地基与已有固结理论的计算结果做比较。结果表明,由于采用了桩土体积应变的完整解答,本文计算的固结速度要比已有固结理论的计算结果小。