斜边非轴对称位移边界下球孔扩张挤土分析

针对斜边非轴对称位移边界条件下的沉桩球孔扩张,将桩体贯入模拟为球孔扩张过程,在线弹性土体模型的基础上,通过对地表边界以及倾斜边界上应力修正的镜像法,改进现有直边非轴对称球孔扩张理论,得到了斜边非轴对称位移边界下的球孔扩张挤土位移解答,并分析边界倾角及球孔边界距离等因素的挤土位移规律。研究结果表明,边界倾角越小,倾斜边界对球孔挤土位移的影响也越小;球孔边界距离越大,其对挤土位移的影响反而越小。文中解答可为类似斜边工程挤土位移的控制及参数设置提供参考。     

预钻孔对邻近斜坡沉桩挤土影响分析

在沉桩位置处设置预钻孔是工程中减小扩孔挤土效应的常用有效措施。针对邻近斜坡的沉桩挤土问题,假定土体为线弹性模型,采用镜像方法,将桩体的贯入模拟为一系列球形孔连续扩张过程,在已有文献的基础上进一步推导出邻近斜坡设有预钻孔时的沉桩挤土位移表达式。结果表明,受斜边非轴对称位移边界的影响,远离斜边自由边界一侧的挤土位移不如靠近斜边自由边界一侧明显;斜边自由倾斜边界越陡（即参数 越小）,斜坡挤土位移越大;随着边界角度 的增大,斜边倾斜边界对沉桩挤土位移的影响逐渐减弱;预钻孔的孔深和孔径对减小邻近斜坡沉桩挤土位移有较大的影响,二者的结合能更有效地减少挤土位移的范围和深度。     

考虑边界效应的非饱和土圆柱孔扩张问题解析

圆柱孔扩张理论是分析沉桩挤土及旁压试验等岩土工程问题的有效方法,然而已有研究中多假定土体为无限连续介质,当圆柱孔周围存在约束边界时并不适用。采用临界状态模型描述非饱和土的应力-应变关系,在此基础上引入反映土体比体积-吸力关系的液相本构方程,推导了非饱和土中存在固定边界时,圆柱孔扩张问题在不同排水条件下的半解析解。通过计算不同工况,对比分析边界效应、非饱和吸力效应和排水条件对圆柱孔扩张响应的影响。结果表明,受边界效应影响,扩孔压力随着孔径增大而持续增大,这与无边界时扩孔压力趋于某一稳定值的情况有所不同;当圆柱孔扩张相同孔径时,周围固定边界范围越小,所需扩孔压力越大。土体初始吸力越大,扩孔压力也越大,相同应力增量引起的体积压缩量减小,说明土体出现吸力硬化效应。在孔周相同位置处,不排水比排水条件下的土体饱和度高、吸力小,对应的有效应力分量也小;距孔壁越近,该差异越明显。     

软基路堤拓宽静压PHC管桩挤土效应现场试验

PHC（prestressed high-strength concrete）管桩近年来被广泛应用。PHC管桩为挤土沉桩模式,沉桩过程引起的挤土效应对周围环境产生不利影响并对其可打性和承载特性有重要影响。结合广－清（广州至清远）高速公路扩建工程,通过现场监测超静孔隙水压力和土体水平位移,进行PHC管桩挤土效应研究。水平位移利用固定式测斜仪测量,孔隙水压力使用振弦式孔压计测量,并使用自动系统进行数据采集。研究发现,沉桩过程中引起的超静孔隙水压力变化随深度增加近似呈线性增长,水平方向随距离的增加而减小;挤土效应产生的土体水平位移随距离的增大而减小,随深度增加而减小;挤土效应滞后现象明显,可导致成桩后的桩体倾斜;拓宽地基场地上管桩施工对老路地基影响小,场地条件对沉桩挤土效应影响大,老路路堤对垂直于路基方向的水平位移有约束作用。     

黏性土填料下考虑土拱效应的非极限主动土压力计算方法

不论挡土墙填料采用砂性土,还是黏性土,其墙背主动土压力与墙体倾角和位移关系存在较大的联系,因而研究黏性土填料下的非极限主动土压力计算理论具有重要意义。通过应力状态分析给出了非极限状态下考虑土拱效应的侧向主动土压力系数,然后采用水平微分层析法给出了倾斜墙下非极限主动土压力解析解。通过与室内模拟试验及已有理论进行对比,验证了该方法的合理性。最后研究了相关参数包括位移比?,墙土摩擦角与内摩擦角之比? /?,墙体倾角?,黏聚力c等对主动土压力分布及其作用点高度的影响。结果表明：土体由静止状态向极限主动土压力状态发展时,土拱效应的影响会越来越大。随着? /?的不断增大,土压力分布曲线非线性强度会不断增强,土压力合力作用点高度呈上升趋势,并且? /?对土压力的影响会随着位移比? 的增大而增大。随着挡土墙墙背倾斜角度? 的不断增大,土拱效应对非极限主动土压力的影响减小。随着土体填料黏聚力的不断增大,上部张拉裂缝高度也会随之增加,且土压力合力作用点越低。给出的考虑土拱效应的非极限主动土压力计算方法对于丰富挡土墙土压力计算理论具有重要意义。     

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。     

简谐荷载作用下饱和土体中圆形衬砌隧道三维动力响应分析

研究了全空间饱和土体中圆形衬砌隧道在径向简谐点荷载作用下的三维动力响应,将衬砌用无限长圆柱壳来模拟,土体用Biot饱和多孔介质模型来模拟,引入两类势函数来表示土骨架的位移和孔隙水压力,并利用修正Bessel方程来求解各势函数,结合边界条件,得到频率-波数域内衬砌和土骨架位移、孔隙水压力的解答,最后进行Fourier逆变换得到时间-空间域内的响应。通过算例分析了荷载振动频率和土体渗透性对土体和衬砌位移响应及土体孔压的影响。结果表明,饱和土体和弹性土体的位移响应具有明显区别。随着荷载频率的增大,土体和隧道位移幅值减小,土体孔压幅值增大;随着土体渗透性增大,土体位移及孔压幅值减小。     

平动模式下挡土墙非极限主动土压力

针对平动模式下墙背倾斜的挡土墙,假定墙后所形成的土拱为圆弧形,建立位移同内摩擦角、外摩擦角的非线性函数,并考虑土层间剪应力作用,通过水平层分析法,得出了挡土墙平动模式下非极限主动土压力分布、合力、作用点高度的解答,其解析解与试验值较其他方法吻合得更好,验证了该方法的合理性。结果表明：是否考虑土层间剪应力,土压力的大小均随墙体位移的增大而减小,不会影响土压力合力大小,仅影响土压力的分布,且考虑剪应力作用的土压力在墙体上部较不考虑剪应力要小,下部反之。剪应力对土体起阻碍作用,随内摩擦角的增大,剪应力出现先显著增大后略微减小的状态;随外摩擦角、位移的增大,剪应力增大;随着墙背倾角的增大,剪应力先减小,再反向增大,土压力随之增大。同时考虑土拱效应与剪应力所得出的合力作用点高度介于仅考虑土拱效应与库仑解之间。     

半无限平面问题的相对位移

通过Flamant和Melan的解析解答、Mindlin解答的积分蜕化公式以及有限元数值分析计算结果,展示了在半无限平面问题中线荷载作用方向位移解答的不确定性。线荷载作用方向没有绝对位移,只有相对位移,但相对位移会随着与位移约束参考点距离的增大而增大,或随着线荷载在垂直于半平面方向分布长度的增大而增大,不具收敛性。这意味着,在解析和数值分析中,纯粹的半平面问题的位移解答具有多值性,因此,将岩土工程问题作为半空间问题进行分析是必要的。     

土层在周期荷载作用下的一维变形与位移解析解

在线弹性材料假定的前提条件下，通过位移控制方程和相关的4种不同的边界条件导出了可变形隔水层（粘土层）在一维变形位移场中的理论解，这4种不同边界条件为边界上4种（正弦、梯形、三角及方波）周期应变与一线性应变的组合，由此得到的位移解由3部份组成，他们分别与边界上周期应变，线性应变以及控制方程中的常数项B有关，可以发现周期位移分量解与孔压周期变化条件下求得的以超静孔压为变量的解析解相比具有类似的特点，即位移解的分量由周期变化和指数衰减两部分组成，对于与线性变化边界应变条件和与控制方程中常数项B有关的位移分量则分别随时间指数衰减和线性变化，故而对土层的长期累积变形起重要影响，同时基于某些假定，还导出4种边界条件下的变形土层的最大累积位移的表达式，并给出实例以估价ASR技术，应用在美国拉斯维加斯市某地引起的地面沉降。     

基于能量耗散的球孔扩张理论解答

以空间准滑动面（SMP）准则为基础,推导了扩底桩扩孔压力的理论解。从能量耗散的角度分析球孔扩张的全过程,利用应力不变量推导了符合球孔扩张的屈服准则;化简微分方程得到了弹塑性区应力表达式,进而求出位移、应变表达式;分别利用体积守恒和能量守恒性推导出扩孔压力的表达式。该法考虑了塑性区弹性变形,并得到了扩孔压力p、塑性区半径R与扩孔半径a的关系。算例分析表明,该方法计算的扩孔压力与现场试验得出的结果较好地吻合,塑性区半径和扩孔压力均随扩孔半径的增加而增大,但增幅逐渐减小而趋于稳定值,剪胀角对塑性区半径和扩孔压力影响显著,随着剪胀角的增加,塑性区半径和扩孔压力明显增加。     

Displacement analytical prediction of shallow tunnel based on unified displacement function under slope boundary

For slope condition of ground surface, the asymmetrical deformation about the vertical center line and the horizontal center line of the tunnel cross section can be formed. A unified displacement function expressed by the Fourier series is presented to express the asymmetrical deformation of the tunnel cross section. Five basic deformation modes corresponding to the expansion order 2 are a complete deformation mode to reflect deformation behaviors of the tunnel cross section under slope boundary. Such this complete displacement mode is implemented into the complex variable solution for analytically predicting tunneling-induced ground deformation under slope boundary. All of these analytical solutions are verified by good agreements of the comparison between the analytical solutions and finite element method results. A parameter study is carried out to investigate the influence of deformation modes of the tunnel cross section, geometrical conditions of the tunnel and the slope angle, and “Buoyancy effect” on the displacement field. Finally, the proposed method is consistent with measured data of the Hejie tunnel in China qualitatively. The presented solution can provide a simplified indication for evaluating the ground deformation under slope condition of ground surface.     

Drained cavity expansions in soils of finite radial extent subjected to two boundary conditions

The problem of drained cavity expansion in soils of finite radial extent is investigated. Cylindrical and spherical cavities expanded from zero radius subjected to either constant stress or zero displacement at the finite boundary are considered. The generalised analytical solution procedure presented enables more advanced constitutive models to be implemented than have been possible in previous studies. Results generated for Sydney quartz sand highlight substantial differences between cavity limit pressures for the two boundary conditions and for boundaries of finite and infinite radial extent. This is of significance in accounting for boundary effects when interpreting cone penetration tests conducted in calibration chambers. Copyright © 2011 John Wiley & Sons, Ltd.     

A general semi-analytical solution for consolidation around an expanded cylindrical and spherical cavity in modified Cam Clay

This paper presents a general semi-analytical solution for undrained cylindrical and spherical cavity expansion in Modified Cam Clay (MCC) and subsequent consolidation. The undrained cylindrical and spherical cavity expansion response in MCC model is obtained through the similarity solution technique. Then, the subsequent consolidation process around the cavity is governed by the classical partial differential equation for consolidation. Finite Difference Method (FDM) is selected for solving the consolidation equation numerically. The proposed semi-analytical solution is validated by comparing the prediction of the dissipations of the pore pressure with Randolph’s closed-form solution for elastic-perfectly plastic soil. Parametric study shows that G₀/p₀′, R and M have significant influence on the cavity wall excess pore pressure dissipation curve, while it is not sensitive to the value of ν′. It is also found that the negative pore pressure generates around the expanded cylindrical and spherical cavity wall during the consolidation process when R > 5 for typical Boston blue clay. The developed solution has potential applications in geotechnical problems, such as the pile foundation, in-situ test, tunnel construction, compaction grouting, and so forth.     

Analysis of dynamic spherical cavity expansion in undrained modified Cam Clay soil

In order to capture the influence of the cavity expansion velocity, this paper presents a semianalytical solution for dynamic spherical cavity expansion in modified Cam Clay (MCC) soil. The key problem is solving the six coupled partial differential equations (PDEs) of cavity expansion, in which the dynamic term is considered in the stress equilibrium equation. The similarity transformation technique is used to transform the PDEs into ordinary differential equations (ODEs). Subsequently, the numerical method using the function “ODE45” in MATLAB is selected to solve the ODEs, which allows the stress and excess pore pressure around the expanding spherical cavity wall to be obtained. The proposed semianalytical solution for dynamic spherical cavity expansion was validated by comparting the degenerate solution with the published quasistatic solution for the MCC model. Parametric study was then conducted to capture the influence of the cavity wall velocity on the cavity expansion response. The proposed solution has potential application to geotechnical problems such as dynamic pile driving, the dynamic cone penetration test, and so forth.     

Exact solution for drained spherical cavity expansion in saturated soils of finite radial extent

This study presents an exact solution for drained spherical cavity expansion subjected to constant stress and zero displacement boundary conditions in finite medium. The solution is exact as no simplification is involved in the solution procedure in the plastic region and can be solved as an initial value problem. The effect of finite radial extent on the results of cavity expanding to a certain radius is accounted for through the initial values at the elastic-plastic boundary. A critical state constitutive model with a nonassociated flow rule is adopted. The model parameters from literature are then used in generating the results for cavity expansion in infinite and finite radial extent to highlight the difference. Also, the results are presented in a way that can be used to account for the boundary effect for the interpretation of cone penetration tests conducted in calibration chambers.     

基于修正剑桥模型的挤密桩挤土效应分析

将挤密桩挤土过程视作沿桩长不变的一系列点位形成的球形孔扩张过程,把扩张过程中的桩周土体分为3个区域：流动破坏区、塑性变形区、弹性变形区。应用圆孔扩张理论,结合修正剑桥模型推导出了球孔扩张引起的土体应力、位移分布解析解。结果表明,挤密桩塑性区半径为桩半径的2.92倍,与试验结果基本吻合,验证了该分析方法的可行性。其结果可为挤密桩挤土效应的研究提供一种新的思路。     

A novel analytical approach for predicting the noncylindrical pile penetration‐induced soil displacement in undrained soil by combining use of cavity expansion and strain path methods

Since development of cavity expansion theory and strain path method, almost all the conventional analyses of pile penetration problem have been based on circular cross section penetrometer. However, noncylindrical pile (with noncircular cross section) is also required in geotechnical engineering such as rectangular cross‐sectional pile, X‐sectional cast‐in‐place concrete pile, H‐shaped steel pile, prefabricated vertical drains, and flat dilatometer. This paper presents a novel and general analytical approach for capturing the soil deformation mechanism around the pile with arbitrary cross section. The penetration problem is simulated by a new 2‐dimensional (radial and circumferential) cavity expansion model. Based on the theoretical framework of strain path method, the kinematics (velocity field) of the noncylindrical cavity expansion is reduced to solve the Laplace equation with arbitrary velocity boundary conditions by using the conformal mapping technique. Then, solutions for the strain and displacement, which could consider the large deformation effect, are obtained by the integration of the strain rate and velocity along the streamline. The analytical solution is validated by comparing the degenerate solution of this study with conventional circular (cylindrical) cavity expansion theory. Subsequently, typical numerical examples for the deformation mechanism of elliptical and rectangular cavity expansion are presented to prove the advantage of the proposed new solution particularly in capturing the noncylindrical symmetric displacement field. A brief application of the proposed new analytical solution to the interpretation of the smear effect of prefabricated vertical drain installation confirms its useful in geotechnical engineering.