成层多孔粘弹性地基在轴对称荷载作用下的解

给出一种有效的解析方法求解成层多孔粘弹性地基在轴对称荷载作用下的固结问题，通过关于时间t的拉普拉斯变换和关于半径r的亨克尔变换，将控制偏微分方程转化为常微分方程，从而得到用常微分短阵方程形式表示的控制方程，基于矩阵常微分方程的解以及拉普拉斯，亨克尔逆变换，可得到该固结问题的解，该方法理论及计算简捷，通过算例比较了该方法的精度，并研究了地基的粘弹性特性对固结过程的影响。     

三维横观各向同性成层地基的传递矩阵解

通过解耦变换推导出三维直角坐标系下横观各向同性地基的非耦合状态方程;利用双重Fourier变换以及Cayley-Hamilton定理得到了单层地基的传递矩阵;结合边界条件和层间连续条件进而得其传递矩阵解。编制了相应程序并进行了数值计算与分析,结果表明：数值结果与已有文献结果十分吻合,地基的横观各向同性性质与成层性质对受荷地基中竖向位移和应力的影响较为显著。     

多层横观各向同性地基轴对称固结的传递矩阵解

从横观各向同性地基轴对称Biot固结的基本方程出发,通过关于t的Laplace变换和关于r的Hankel变换,得到关于z的一阶常微分方程组。然后,对变换域内的基本未知量进行线性化处理,建立了变换域内的基本状态变量在z = 0处和任意深度处z的显式关系。利用传递矩阵法,结合层间连续性条件和边界条件,得到了多层横观各向同性地基的Biot固结轴对称问题的解答。该解答能避免随着层数增加而需要求解大型方程组的困难,明显地提高了计算效率。     

双层广义Gibson地基轴对称问题求解

假定双层地基土体为弹性、不可压缩、剪切模量随深度线性变化的广义Gibson地基,在两层土体剪切模量表达式常数项与一次项系数之比相同条件下,采用Hankel变换,得到了表面分布轴对称荷载时地基土体应力、位移的积分形式解,讨论了下层深度、剪切模量等对位移的影响。获得的解可退化到半空间情况。     

多层地基非轴对称Biot固结的理论解

提出了一种新方法来推导多层地基非轴对称Biot固结问题的传递矩阵,相应的理论推导工作量较少。基于柱坐标系下非轴对称Biot固结的基本方程,通过引入中间变量,并对坐标 进行Fourier级数展开,对时间 和坐标 进行Laplace-Hankel变换,得到了6×6阶和2×2阶的两组常微分方程;然后,两组常微分方程进行关于 的Laplace变换和逆变换,得到了单层地基非轴对称Biot固结问题的传递矩阵;结合边界条件和连续条件,运用传递矩阵法得到多层地基非轴对称Biot固结问题在Laplace-Hankel变换域内的解,通过Laplace-Hankel逆变换得到了该问题物理域的真实解答。编制了计算程序,并进行了数值计算与分析。该方法具有计算速度较快的特点,方便工程应用。     

考虑成层弹性地基固结的污染物运移模型

文章在多层地基固结理论与污染物运移理论相结合的基础上,提出了污染物在成层弹性地基中运移的一维数学模型,其最大特点是考虑了土体受力变形对污染物运移的影响,然后给出了所建模型的解析解,并将计算结果与太湖疏浚污染底泥堆场的实测结果作了比较分析。结果表明堆场的地基土层对太湖疏浚底泥中的污染物具备足够的阻隔能力,在堆场的使用年限内不会对周围环境造成二次污染。实际天然防渗层中以成层土居多,故推导出的污染物在成层土中运移模型具有重要的工程价值和现实意义。     

考虑成层土路堤荷载下复合地基加固区沉降计算

考虑土的成层性,假定桩周成层土弹性模量的不同不影响桩中性点位置,应用弹性理论和桩土位移协调条件及边界条件,推导了路堤荷载下复合地基加固区桩及桩周土压缩量计算的解析式,同时得到了各层土范围内桩、桩周土竖向应力及桩侧剪应力的表达式,并利用有限元分析了桩周土弹性模量的变化对桩中性点位置的影响规律,验证了假定。结果表明:使用该计算方法分析路堤荷载下复合地基加固区内桩和桩周土的变形,计算结果与有限元及实测结果比较接近,满足工程计算精度要求,能为类似地基土成层分布工程沉降分析提供有益参考。     

弹性矩形板下横观各向同性多层地基分析

利用弹性矩形板与多层地基表面的竖向位移协调条件与光滑接触条件,由横观各向同性多层地基应力与位移非耦合的传递矩阵解,推导出弹性矩形板下竖向应力和位移的解析解。在此基础上,编制了相应的程序,并进行了数值计算。计算结果表明：矩形板刚度对板底竖向位移及板中心下的竖向应力有着较为显著的影响;板底竖向位移及板中心下的竖向应力随着板刚度的增加而减小,相同荷载作用下横观各向同性地基与均匀各向同性地基模型的计算结果差异较大,实际工程中很有必要采用更符合土体性质的横观各向同性地基模型     

多层可压缩性地基非轴对称固结解耦分析

采用Schiffman和Fungaroli提出的位移函数,从非轴对称可压缩地基固结的基本控制方程出发,引入中间变量,通过对坐标θ的Fourier级数展开,关于坐标t、r的Laplace-Hankel变换,得到了6×6阶和2×2阶两组非轴对称固结问题的非耦合传递矩阵,然后利用传递矩阵法,结合层间连续性条件和边界条件,得到了多层可压缩地基非轴对称固结问题在积分变换域内的解耦解。最后应用Laplace-Hankel逆变换技术,得到了该问题在物理域内的理论解。编制了相应的计算程序,并进行了数值计算与分析,讨论了可压缩性对地基固结过程的影响。     

双层地基位移和应力场求解

通过对半无限弹性体的通解进行Hankel数值逆变换,得到两层地基内部受有轴对称荷载下的位移和应力解,通过改变参数进行了大量的数值计算,计算结果表明与文献中的研究结果一致,可用于设立于层状地基的桩基沉降计算。     

MODFLOW procedure to simulate axisymmetric flow in radially heterogeneous and layered aquifer systems

A procedure is outlined to simulate axisymmetric groundwater flow in radially heterogeneous and layered aquifer systems using the unmodified version of MODFLOW. The procedure is straightforward, as it only requires correction of some of the input parameters. In contrast to other MODFLOW procedures to simulate axisymmetric flow, no restrictions are imposed on the type of flow, the discretization of radial distance, or the parameter values. Hence, the method can deal with both confined and unconfined flow, wellbore storage, and axisymmetric aquifer inhomogeneities including effects of finite-thickness skin and gravel pack. Several test cases are presented, which compare the calculated results with existing analytical solutions, the analytic element solver TTim, and the axisymmetric, finite-difference model MAxSym. It is concluded that the MODFLOW procedure is capable of simulating accurately axisymmetric flow in radially heterogeneous multi-aquifer systems.     

Approximate up-scaling of geo-spatial variables applied to deep foundation design

We present a series of simple approximate methods for up-scaling the cumulative distribution function of spatially correlated variables by using an effective number n _e of independent variables. Methods are based on the property of distribution permanence of the gamma and inverse Gaussian distributions under averaging, bootstrap sampling and expansions about the normal and gamma distributions. A stochastic simulation study is used to validate each method, and simple parameters are defined to identify respective ranges of applicability. A practical example is presented where core sample rock strength data are up-scaled to shaft size for probabilistic (risk-based) deep foundation design. Supplemental material is available online.     

成层地基在轴对称荷载下的稳态振动分析

基于Biot动力固结方程,考虑了土体和水体的惯性力以及水-土耦合作用的影响,采用Hankel积分变换求解耦联合方程组,得到动荷载下饱和土Lamb问题的解答。根据下边界为不透水基岩的边界条件,获得了地基表面作用圆形轴对称周期荷载时土层应力、位移等的一般积分形式解,并利用矩阵传递法完成了对多层地基和Gibson地基的计算。通过算例研究了层厚和激振频率等对竖向位移的影响。     

层状地基群桩沉降研究

考虑了桩的加筋与遮帘效应,通过剪切位移法依据力与位移的协调条件得出桩的柔度系数。在此基础上建立土的成层性模型,根据桩顶与桩底的物理关系推导了桩顶沉降与荷载关系的解析解。通过工程算例进行比较,结果表明, 以土层状模型建立的群桩沉降计算方法是可行的。分析表明, 加固区土层不同分布对桩沉降有所影响,浅部土模量的提高有利于减小沉降。     

A theoretical estimate of the tilt of a surface foundation due to an inclined anchor load applied at the interior of the soil medium

This paper examines the problem of the interaction between a loaded rigid circular foundation located at the surface of an isotropic elastic halfspace and an inclined concentrated anchor load which is located at a finite depth along the axis of symmetry. Such inclined loads can be induced by, for example, anchor regions supporting earth retaining structures. The loaded rigid circular foundation resting in smooth contact with the elastic soil mass experiences a displacement and a tilt due to the action of the inclined anchor load. The magnitude of the rotational settlement is evaluated in exact closed form.     

Practical second‐order reliability analysis applied to foundation engineering

A practical and efficient approach of implementing second‐order reliability method (SORM) is presented and illustrated for cases related to foundation engineering involving explicit and implicit limit state functions. The proposed SORM procedure is based on an approximating paraboloid fitted to the limit state surface in the neighborhood of the design point and can be easily carried out in a spreadsheet. Complex mathematical operations are relegated to relatively simple user‐created functions. The failure probability is calculated automatically based on the reliability index and principal curvatures of the limit state surface using established closed‐form SORM formulas. Four common foundation engineering examples are analyzed using the proposed method and discussed: immediate settlement of a flexible rectangular foundation, bearing capacity of a shallow footing, axial capacity of a vertical single pile, and deflection of a pile under lateral load. Comparisons with Monte Carlo simulations are made. In the case of the laterally loaded pile, the friction angle of the soil is represented as a one‐dimensional random field, and pile deflections are computed based on finite element analysis on a stand‐alone computer package. The implicit limit state function is approximated via the response surface method using two quadratic models. Copyright © 2011 John Wiley & Sons, Ltd.     

Relevance vector machine applied to settlement of shallow foundation on cohesionless soils

The settlement of shallow foundation on cohesionless soil is a key parameter in the design of shallow foundation. The recently introduced relevance vector machine (RVM) technique is applied to predict the settlement of shallow foundation on cohesionless soils. RVM allows computation of the prediction intervals, taking into account the uncertainties of both the parameters and the data. It provides much sparser regressors without compromising performance, and kernel bases give a small but worthwhile improvement in performance. It also estimates the prediction variance. This study shows that compared to the available methods, RVM is better at determining the settlement of shallow foundation on cohesionless soil.     

深基坑降水中不同的地质模型有限元应用研究

分析水-土耦合场相互作用时,将岩土视作弹塑性材料。在非线性本构关系下,考虑渗透作用,得出岩土体有限元方程,建立了基坑降水的三维水-土耦合的数学模型。对基坑降水中不同的地质模型潜水、承压水及有越流补给和实际工程条件井管、过滤管、止水帷幕分别进行了计算处理,并以武汉国际证券大厦降水工程为实例,对其降水过程进行了三维有限元计算。应用三维数值模拟方法,能很好地模拟基坑防渗帷幕、非均质和各向异性、承压-无压等一些解析法难以处理的实际工程条件和地质模型。     

恒载作用下轴对称圆巷围岩的流变变形方程求解

建立围岩-支护相互作用流变变形机制的数学力学模型是解决岩石地下工程支护问题的有效途径,其关键问题是,在围岩产生流变变形的过程中支护是如何对围岩进行作用的。根据基于Levy-Mises本构关系及D-P屈服准则的轴对称圆巷的理想弹塑性解、一维蠕变曲线的等时曲线相似的假设以及三维流变试验结果,推导出了原岩应力和被动支护反力均为恒载,且巷道围岩为三维应力状态下的蠕变方程及轴对称圆巷围岩的非线性黏弹塑性流变变形计算公式。与前人的工作相比,文中推导的公式中含有对围岩流变变形起决定作用的2个参数,即原岩应力 和岩石材料的单轴塑性屈服应力 ,因此公式推导的理论基础更加完备、可信度更高。