盾构管片设计改进惯用法模型及其内力解析解

管片设计一直是地铁设计中亟待解决的难题之一。管片计算模型的建立主要是考虑接头和土层抗力两种因素对结构的影响。对现有管片计算模型的接头简化进行了改进,推导了改进惯用法模型的内力和位移求解公式;并结合北京地铁10号线工程实例资料,对惯用法模型及改进模型进行了对比分析,与数值计算结果进行了综合验证分析。研究结果表明,推导的公式是可靠的,对地铁管片的设计和施工具有理论和实践意义。     

An analytical solution for rainfall infiltration into an unsaturated infinite slope and its application to slope stability analysis

Surficial slope failures in residual soils are common in tropical and subtropical regions as a result of rainfall infiltration. This study develops an analytical solution for simulating rainfall infiltration into an infinite unsaturated soil slope. The analytical solution is based on the general partial differential equation for water flow through unsaturated soils. It can accept soil–water characteristic curve and unsaturated permeability function of the exponential form into account. Numerical simulations are conducted to verify the assumptions of the analytical solution and demonstrate that the proposed analytical solution is acceptable for the coarse soils with low air entry values. The pore‐water pressure (pwp) distributions obtained from the analytical solution can be incorporated into a limit equilibrium method to do infinite slope stability analysis for a rain‐induced shallow slip. The analysis method takes into account the influence of the water content change on unit weight and hence on factor of safety. A series of analytical parametric analyses have been performed using the developed model. The analyses indicate that when the residual soil slope, consisting of a completely decomposed granite layer underlain by a less permeable layer, is subjected to a continuous heavy rainfall, the loss of negative pwp and the reduction in factor of safety were found to be most significant for the shallow soil layer and during the first 12 h. The antecedent and subsequent rainfall intensity, depth of a less permeable layer and slope angle all have a significant influence on the pwp response and hence the slope stability. Copyright © 2012 John Wiley & Sons, Ltd.     

多结构面三维块体极限稳定新方法探讨

对复杂块体进行简单切分后,根据块体基本理论与刚体分块极限平衡原理,探讨多结构面三维复杂块体稳定分析新方法,研制适应性较强的三维极限稳定分析程序,在龙滩水电站右岸坝肩高边坡等工程中取得成功应用。     

隧洞边界超欠挖的摄动法解析分析

钻爆法施工常造成隧道边界不平整,隧道分析模型一般将开挖界面光滑处理,忽略了边界不平整对围岩应力的扰动作用。将隧道超欠挖值当作中心偏量小参数,利用摄动法得到了静水压力下圆形隧道的弹性应力解。计算分析表明:超欠挖改变了隧道洞壁附近围岩的应力状态,围岩应力随超欠开挖曲线呈波浪状变化,应力变化量与超欠挖曲线幅值及曲线斜率有关;环向应力变化最大值在洞壁处,其应力集中系数分别在超挖及欠挖顶点达到局部极大与极小值,径向应力变化最大值靠近洞壁表面,切应力变化最大值位于超挖与欠挖表面相交处;扰动应力在径向衰减较快,影响范围约为1~2倍的隧道半径。     

A new stereo‐analytical method for determination of removal blocks in discontinuous rock masses

The paper provides a new stereo‐analytical method, which is a combination of the stereographic method and analytical methods, to separate finite removable blocks from the infinite and tapered blocks in discontinuous rock masses. The methodology has applicability to both convex and concave blocks. Application of the methodology is illustrated through examples. Addition of this method to the existing block theory procedures available in the literature improves the capability of block theory in solving practical problems in rock engineering. Copyright © 2003 John Wiley & Sons, Ltd.     

An analytical solution for a jointed shield‐driven tunnel lining

This paper presents an analytical solution for the prediction of internal forces and displacements of a jointed segmental precast circular tunnel lining. The effects of joint stiffness on the performance of the tunnel lining are discussed. The ‘force method’ is used to determine the internal forces and displacements of jointed tunnel lining. Five shield‐driven tunnel cases are adopted to study the effects of joint stiffness, soil resistance, joint distribution and joint number on the internal forces and displacements of circular tunnels. Laboratory model tests are conducted to verify the proposed analytical solution. Copyright © 2001 John Wiley & Sons, Ltd.     

节理岩体的块体尺寸特征分析及其可靠度评价

通过对块体形成机制的讨论,根据岩体内节理面间距分布的随机性,分析了不同尺寸块体的出现概率。在计算块体的可靠度时,考虑了结构面的产状,粘结系数,磨擦系数等多个随机因素的影响。     

软土一维非线性固结近似解析解

软土非线性固结变形计算目前还主要依赖于数值方法,致使非线性固结理论的工程应用受到极大限制。引入经典的e-lg?' 和e-lgkv非线性关系,在自重应力均匀分布假定下通过变量代换并利用迭代法给出压缩指数Cc与渗透指数Ck比值不等于1时的非线性固结近似解析解。在Cc /Ck趋近1时本文解与其等于1时的差分解及精确解相差无几。但如果Cc /Ck值偏离1,该近似解会存在一定偏差,且偏差值会随Cc /Ck值偏离1的程度和外荷载增加而逐渐增大。在一般工程荷载作用下,如果Cc /Ck值介于0.9～1.1之间,本文解的平均固结度与差分解间最大偏差在2%左右。当Cc /Ck值在0.75～1.25之间时,本文解的平均固结度与差分解最大偏差在5%左右。如果Cc /Ck值在0.5～1.5之间,本文解的平均固结度与差分解间最大偏差在10%左右。当外荷载一定时,土层的非线性固结速率会随着Cc /Ck值的增大而减慢。如果Cc /Ck<1,土层的非线性固结速率会随外荷载的增大而加快;相反,如果Cc/Ck>1,土层的非线性固结速率会随外荷载增大而减慢。     

A novel analytical solution for constant‐head test in a patchy aquifer

A mathematical model describing the hydraulic head distribution for a constant‐head test performed in a well situated at the centre of a patchy aquifer is presented. The analytical solution for the mathematical model is derived by the Laplace transforms and the Bromwich integral method. The solution for the hydraulic head has been shown to satisfy the governing equations, related boundary conditions, and continuity requirements for the hydraulic head and flow rate at the interface of the patch and outer regions. An efficient numerical approach is proposed to evaluate the solution, which has an integral covering an integration range from zero to infinity and an integrand consisting the product and square of the Bessel functions. This solution can be used to produce the curves of dimensionless hydraulic head against dimensionless time for investigating the effect of the contrast of formation properties on the dimensionless hydraulic head distribution. Define the ratio of outer‐region transmissivity to patch‐region transmissivity as α. The dimensionless hydraulic head for α=0.1 case is about 2.72 times to that for α=10 case at dimensionless large time (e.g. τ?10⁶) when the dimensionless distance (ρ) equals 10. The results indicate that the hydraulic head distribution highly depends on the hydraulic properties of two‐zone formations. Copyright © 2006 John Wiley & Sons, Ltd.     

热-水-力共同作用下圆形洞室弹塑性解析解

基于已有的工作和Mohr-Coulomb屈服准则,建立了热-水-力三场共同作用下的圆形洞室弹塑性解析解,并分别在单力场、热-力场、水-力场、热-水-力场以及改变介质强度参数的条件下计算和比较了围岩中的应力分布、变化及塑性区范围。结果显示,温度场使得塑性区半径有所减小,但总的来看温度作用不明显;与仅有力作用时相比,孔隙水压力使得塑性区半径、径向应力和切向应力有较大幅度增长。     

挡墙水平变位诱发地表沉降的简化解析解

推导了平移模式下的地表沉降理论显式解,在此基础上提出了任意挡墙变位诱发墙后地表沉降的简化计算方法。分别与平移、绕墙趾及绕墙顶等3种变位模式下的弹性有限元数值解进行对比分析,对简化解析方法进行了验证。最后将这一简化解析方法应用于工程案例预测,与软土地基现场实测结果进行对比,发现理论预测的地表沉降曲线与实测值相吻合,且较准确地预测了最大沉降发生的位置,表明了该简化解析方法的实用性。     

球模仪测试冻土松弛模量的非线性Kelvin解答及其试验研究

冻土的松弛模量是进行蠕变力学分析的关键参数。但在理论方面, 尚未基于球模仪试验建立较完善的松弛模量表征公式。基于半空间黏弹性理论和分数阶微积分理论, 获得了松弛模量公式的非线性Kelvin模型解答并进行了材料参数影响分析。在给出恒载条件下, 可以用单轴蠕变试验的分析结果评估基于球形压痕试验的冻土松弛模量来预测准确性。随后分别以冻结细砂的球模仪试验曲线、 冻结砂和冻结砂质黏土的单轴蠕变曲线为例, 预测了各条试验曲线和冻土的松弛模量, 并通过其他试验实测数据进行了检验。结果表明： 该松弛模量表征公式的材料参数最少, 随各材料参数变化具有较佳单调性; 基于球形模板试验, 非线性Kelvin解答能对冻结细砂的松弛模量和位移曲线做出合理可靠的预测。非线性Kelvin模型能很好地吻合单轴蠕变试验曲线, 基于单轴蠕变试验的冻结砂松弛模量随时间变化规律和数值范围与球模仪试验分析结果较一致, 冻结砂质黏土的松弛模量随应力和温度的变化规律再现了已有研究结论。     

Simplified analytical solution for point load acting behind a cantilever wall

The analysis of earth pressure resulting from an applied point load behind a retaining wall is to be carried out in three dimensions as the earth pressure distribution varies both in vertical and horizontal directions. In this research, the semi‐empirical expressions developed by Terzaghi [Trans. ASCE 1954; 119 ] for earth pressure due to point load are integrated and a correction factor is introduced to develop equivalent equations for two‐dimensional analyses. A new parameter referred to as the design width, which is the horizontal distance retained by the individual vertical retaining element is introduced. The used procedure and the resulted equations are tested and verified by adopting different design width values covering the practical range. The resulted equations together with the semi‐empirical expressions of earth pressure due to line load developed by Terzaghi [Trans. ASCE 1954; 119 ] can be easily used for two‐dimensional analysis of the effect of point load. Copyright © 2011 John Wiley & Sons, Ltd.     

A simple analytical solution to one‐dimensional consolidation for unsaturated soils

This paper presents a simple analytical solution to Fredlund and Hasan's one‐dimensional (1‐D) consolidation theory for unsaturated soils. The coefficients of permeability and volume change for unsaturated soils are assumed to remain constant throughout the consolidation process. The mathematical expression of the present solution is much simpler compared with the previous available solutions in the literature. Two new variables are introduced to transform the two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved with standard mathematical formulas. It is shown that the present analytical solution can be degenerated into that of Terzaghi consolidation for fully saturated condition. The analytical solutions to 1‐D consolidation of an unsaturated soil subjected to instantaneous loading, ramp loading, and exponential loading, for different drainage conditions and initial pore pressure conditions, are summarized in tables for ease of use by practical engineers. In the case studies, the analytical results show good agreement with the available analytical solution in the literature. The consolidation behaviors of unsaturated soils are investigated. The average degree of consolidation at different loading patterns and drainage conditions is presented. The pore‐water pressure isochrones for two different drainage conditions and three initial pore pressure distributions are presented and discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

Solutions for the deformations and stability of elastoplastic hollow cylinders subjected to boundary pressures

In this paper, a closed-form solution is presented for the stress and displacement distributions throughout a hollow cylinder subjected to uniform pressures acting on its internal and external boundary surfaces under plane strain conditions. The material is assumed to be elastoplastic, obeying a Mohr–Coulomb failure criterion, and exhibiting dilatant plastic deformation according to a non-associated flow rule. The newly developed analytical solution is verified through comparison with the solutions obtained from an infinite boundary problem (for which a closed-form solution exists), and numerical analyses using the program FLAC. The solution is also compared with the results of a borehole collapse test on a thick-walled hollow cylinder of synthetic shale. The analytical solution can be used to calculate the stress and displacement distributions around boreholes and other cylindrical cavities under both infinite and finite boundary conditions under both drained and undrained conditions. Copyright © 1999 John Wiley & Sons, Ltd.     

An analytical solution for deforming twin‐parallel tunnels in an elastic half plane

The interaction between twin‐parallel tunnels affects the tunnelling‐induced ground deformation, which may endanger the nearby structures. In this paper, an analytical solution is presented for problems in determining displacements and stresses around deforming twin‐parallel tunnels in an elastic half plane, on the basis of complex variable theory. As an example, a uniform radial displacement was assumed as the boundary condition for each of the two tunnels. Special attention was paid to the effects of tunnel depth and spacing between the two tunnels on the surface movement to gain deep insight into the effect of the interaction between twin‐parallel tunnels using the proposed analytical approach. It is revealed that the influence of twin tunnel interaction on surface movements diminishes with both the increase of the tunnel depth and the spacing between the two tunnels. The presented analytical solution manifests that, similar to most of the existing numerical results, the principle of superposition can be applied to determine ground deformation of twin‐parallel tunnels with a certain large depth and spacing; otherwise, the interaction effect between the two tunnels should be taken into account for predicting reliable ground movement. Copyright © 2014 John Wiley & Sons, Ltd.     

非均匀土壤中溶质运移的两区模型及其解析解

给出了非均匀土壤中考虑水动力弥散尺度效应的一维溶质运移两区模型。然后在初始浓度为零,半无限一维空间内常数通量边界条件下,推导出了可动区和不动区溶质浓度分布的解析表达式。并用Mathematica软件包作了数值计算。计算结果表明,该模型的模拟结果符合溶质运移的一般规律,因而该模型在土壤溶质运移的研究和应用中有一定的价值。     

节理泊松圆盘模型直径分布推断的解析方法

节理圆盘直径分布是节理网络模拟中的重要参数之一。在节理为Poisson圆盘的假设下,根据三维齐次Poisson点过程的数学特征,给出迹长分布概率密度函数的多项式形式和相应的约束条件;对Warburton提出的迹长分布概率密度函数和节理直径分布概率密度函数关系公式进行Santalo变换,推导了多项式形式的迹长分布所对应的直径分布概率密度函数的解析解,并采用Priest给出的解析解验证其正确性;根据概率密度函数的性质,给出了直径分布概率密度函数定义域的推断方法。编制节理网络模拟程序,采用Monte Carlo方法验证节理Poisson圆盘直径分布概率密度函数解析解的正确性和直径分布概率密度函数定义域推断方法的适用性。     

采空区块体稳定性的模糊随机可靠性研究

在介绍块体稳定可靠性分析各种方法的基础上,分析了采空区块体稳定状态的随机性和模糊性的特点,根据块体理论与模糊分析学中的模糊测度理论,提出了块体稳定性的模糊随机可靠性分析方法,建立了块体稳定性模糊概率测度计算公式,并将该方法应用于浙江遂昌金矿采空区顶板围岩块体稳定性分析的工程实践中,计算结果表明,块体稳定性较差,采空区残留矿柱回采前,需采取相应的安全措施。