A complex variable solution for a deforming buoyant tunnel in a heavy elastic half‐plane

An analytical solution is presented for a buoyant tunnel in an elastic half‐plane. The tunnel undergoes a prescribed displacement along its boundary, and the surface of the half‐plane is stress‐free. The solution uses the complex variable method and consists of conformally mapping the hole and half‐plane to an annular region. The complex potentials each contain two logarithmic terms due to the resultant buoyancy force acting on the tunnel, and as a result the displacements at infinity are unbounded. An example is presented for the case of a rigid buoyant tunnel in a half‐plane with gravity loading. Even though the tunnel does not deform, the buoyancy effect can be clearly seen in the contours of the displacements and stresses. Copyright © 2002 John Wiley & Sons, Ltd.     

半无限含水层中带衬砌隧洞渗流解析研究

现有关于半无限含水层中隧洞渗流的解析解不能考虑衬砌部分排水的特性。假定土体和衬砌均为饱和均匀连续介质,采用土体与衬砌分算;利用复变函数解决孔口问题基本方法,对土体采用共形映射坐标变换,将土体中的渗流方程转换为与衬砌部分类似的二维Laplace方程圆环域的Dirichlet问题;通过Fourier解法,根据边界条件并利用流量连续条件,求得半无限空间中带衬砌隧洞渗流量和衬砌周边水头解析解答。分析了径深比、土体与衬砌渗透系数相对值、内壁水压力等因素对渗流量和衬砌周边水头的影响,并与数值算例进行了比较。结果表明,对浅埋隧洞该解析解仍具有较好的精度,是简便、实用的计算方法。     

半空间饱和土中圆形衬砌对弹性压缩波的散射

借助于Biot 波动理论和弹性波的传播理论,采用复变函数和多级坐标法,对半空间饱和土中圆形衬砌结构对弹性稳态压缩波的散射问题进行求解和分析。利用一个半径很大的圆弧来逼近半空间直边界,将待解问题转化为稳态弹性压缩波在一个大圆孔和一个弹性衬砌结构的散射问题。通过引入势函数,将饱和土的Biot波动方程和衬砌的弹性波动方程解耦成Helmholtz 方程,借助复变函数级数展开便可以预先写出该组Helmholtz方程的通解。然后,通过引用复变量,把饱和土和衬砌结构中的应力、位移及孔压用设定的势函数表示出来,再利用半空间饱和土和衬砌结构的连续性条件和近似直边界的圆弧边界和衬砌内边界的边界条件求解出该组势函数的特解。最后,利用势函数的特解,得到饱和土中的位移,应力和孔压及衬砌结构的位移和应力;变换不同的参数求解衬砌结构内外边界的动应力和孔压的集中系数,通过对算例结果的分析得出一系列有益的结论。     

爆炸荷载作用下深埋圆形隧洞的饱和黏弹性土-衬砌系统动力响应

假定土骨架服从标准线性固体黏弹性本构关系,研究了深埋圆形隧洞的饱和黏弹性土-弹性衬砌耦合系统在轴对称爆炸作用下的瞬态动力响应。首先,基于饱和土的Biot模型和衬砌的弹性理论,通过引入势函数和Laplace变换,利用弹性衬砌和饱和黏弹性土界面处的连续性条件以及边界条件,得到饱和黏弹性土体和弹性衬砌位移、应力和孔隙水压力等在Laplace变换域中的解析解。其次,利用Laplace数值Crump逆变换得到耦合系统在时间域的动力响应,数值分析了不同土体模型下土体-衬砌耦合系统的径向位移和环向应力以及土体孔隙水压力等。结果表明：对不同土体模型的土体-衬砌耦合系统,其在爆炸载荷作用下的动力响应性态基本一致,但动力响应的振动周期和幅值等具有明显的差异。同时,对于饱和黏弹性土-弹性衬砌系统,土体黏性参数对土体径向位移和孔隙水压力有明显的影响,但对土体环向应力影响较小。     

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.     

太湖软土地基沉降特性分析

根据太湖地区某高速公路路基沉降实测资料,通过现场原位取样结合室内试验,分析了太湖冲湖积相软土的压缩特性,总结出软土路基的沉降变化规律,研究了工程地质条件和填土高度对路基沉降的影响,并采用归一化指标得到不同地基处理方式下的沉降估算公式,同时对两种常用全过程路基沉降预测方法进行了比较。结果表明,太湖冲湖积相软土具有较强的结构性;相似地质条件下的路基沉降差异较大,土体结构性是影响路基沉降的重要因素之一;归一化指标分析可得到不同路基处理方式下的简单沉降估算式;常用的全过程沉降量预测方法对于最终沉降量的预测均存在一定的偏差,可综合分析预测结果得到较为准确的预测值。     

地层沉降协调法防治煤矿立井破坏试验研究

近年来已有许多专家学者对立井附加应力的产生以及相应的消除方法进行了理论和试验研究,在此基础上,本文首次提出地层沉降协调法,分析了其作用机理,进行了立井井壁变形破坏防治的试验研究,对地层沉降协调法消除附加应力的有效性进行了分析。试验中通过设置不同的隔离协调条件,得出了地层排水固结沉降过程中井壁应变变化以及土体表面沉降变形规律。结果表明,开始阶段的井壁纵向应变都有突然增大的现象,其中未加隔离体试验的突增较大。隔离协调体对井壁纵向应变的突变有减小作用。此外,隔离体能够有效减缓其内侧沉降速率以及最终沉降量。地层沉降协调法可以明显降低沉降过程中井壁纵向应变突增值与稳定值以及竖向力与最大主应力,同时可以保持井壁横向变形及受力的稳定,因此,可以发展为防治矿山立井井壁破坏的有效方法。     

路堤沉降计算中邓肯-张模型参数灵敏度分析

灵敏度分析是土木工程中解决多参数辨识问题的一个主要方法。目前,在地下工程的分析和计算中邓肯-张模型是比较理想的模型,通过大量的非线性有限元计算,找到了该模型中影响软基路堤沉降的主要参数,并给出了各参数与路堤沉降之间的定性关系,这为路堤沉降计算中的参数反演分析的简化处理奠定了基础     

复合式衬砌结构中衬砌分担围岩压力比例的研究

复合式衬砌结构中衬砌分担围岩压力的评价方法是隧道工程技术的重要研究课题之一。依托某新建铁路隧道工程,提出了一种基于监测位移反分析评价围岩和支护应力,进而计算初期支护和衬砌背后压力的方法。根据监测位移和衬砌施作时间,确定初期支护的已发生变形和剩余变形。通过有限元反分析求出与已发生变形和剩余变形相对应的围岩和支护应力,得到初期支护和衬砌背后压力。对比初期支护背后压力及衬砌背后压力的现场监测和反分析的计算结果,两者比较一致,说明了该方法的可行性。该新建隧道初期支护闭合95 d后施作衬砌,计算得到衬砌背后压力约0.04～0.06 MPa,衬砌分担围岩压力比例约13%～16%。研究成果对复合式衬砌结构的设计具有一定的参考意义。     

Analytical approach for circular-jointed shield tunnel lining based on the state space method

This paper presents a new analytical solution to the circular segmental tunnel lining subjected to overburden and surrounding earth pressures. The governing equations are derived by adopting the curved Euler beam theory and the principle of minimum potential energy. Based on the state space method, the displacements and the relevant energy-conjugated internal forces are treated as the fundamental unknown state vector and can be obtained by solving the state function. The inter-segment joints on the lining are modeled by a set of linear springs, including shear, compression, and rotation. The presented method allows for the arbitrary distribution of the segmented joints and loads along the circumferential direction. The most striking advantages of the proposed method include the rigid body displacement treatment, lining-displacement-dependent soil reaction, and internal force direction dependency of the joint stiffness. Using this method, the displacements and internal forces of the entire lining can be obtained conveniently and simultaneously under the arbitrary loading and joint distribution conditions. The verification of the analytical solutions is provided by several examples.     

On the mechanical interaction between a fluid-filled fracture and the earth's surface

The mechanical interaction between a fluid-filled fracture (e.g., hydraulic fracture joint, or igneous dike) and the earth's surface is analyzed using a two-dimensional elastic solution for a slit of arbitrary inclination buried beneath a horizontal free surface and subjected to an arbitrary pressure distribution. The solution is obtained by iteratively superimposing two fundamental sets of analytical solutions.For uniform internal pressure the slit behaves essentially as if it were in an infinite region if the depth-to-center is three times greater than the half-length. For shallower slits interaction with the free surface is pronounced: stresses and displacements near the slit differ by more than 10% from values for the deeply buried slit. The following changes are noted as the depth-to-center decreases:

1. (1) the mode I stress intensity factor increases for both ends of the slit, but more rapidly at the upper end;

2. (2) the mode II stress-intensity factor is significantly different from zero (except for vertical slits) suggesting propagation out of the original plane of the slit;

3. (3) displacements of the slit wall are asymmetric such that the slit gaps open more widely near the upper end. Similar changes are noted if fluid density creates a linear pressure gradient that is smaller than the lithostatic gradient. Under such conditions natural fractures should propagate preferentially upward toward the earth's surface requiring less pressure as they grow in length.

If deformation near the surface is of interest, the model should account explicitly for the free surface. Stresses and displacements at the free surface are not approximated very well by values calculated along a line in an infinite region, even when the slit is far from the line. As depth-to-center of a shallow pressurized slit decreases, the following changes are noted:

1. (1) displacements of the free surface increase to the same order of magnitude as the displacements of the slit walls,

2. (2) tensile stresses of magnitude greater than the pressure in the slit are concentrated along the free surface. The relative surface displacements over a shallow vertical slit are downward over the slit and upward to both sides of this area. The tensile stress acting parallel to the free surface over a shallow vertical slit is concentrated in two maxima adjacent to a point of very low stress immediately over the slit.

The solution is used to estimate the length-to-depth ratio at which igneous sills have gained sufficient leverage on overlying strata to bend these strata upward and form a laccolith. The pronounced mode II stress intensity associated with shallow horizontal slits explains the tendency for some sills to climb to higher stratigraphie horizons as they grow in length. The bimodal tensile stress concentration over shallow vertical slits correlates qualitatively with the distribution of cracks and normal faults which flank fissure eruptions on volcanoes. The solution may be used to analyze surface displacements and tilts over massive hydraulic fractures in oil fields and to understand the behavior of hydraulic fractures in granite quarries.     

Variational elastic solution for axially loaded piles in multilayered soil

Most analytical or semi‐analytical solutions of the problem of load‐settlement response of axially loaded piles are based on the assumption of zero radial displacement. These solutions also are only applicable to piles embedded in either a homogeneous or a Gibson soil deposit. In reality, soil deposits consist of multiple soil layers with different properties, and displacements in the radial direction within the soil deposit are not zero when the pile is loaded axially. In this paper, we present a load‐settlement analysis applicable to a pile with circular cross section installed in multilayered elastic soil that accounts for both vertical and radial soil displacements. The analysis follows from the solution of the differential equations governing the displacements of the pile–soil system obtained using variational principles. The input parameters needed for the analysis are the pile geometry and the elastic constants of the soil and pile. We compare the results from the present analysis with those of an analytical solution that considers only vertical soil displacements. The analysis presented in this paper also provides useful insights into the displacement and strain fields around axially loaded piles. Copyright © 2011 John Wiley & Sons, Ltd.     

某基坑位移、沉降和内力实测结果及预警值讨论

以某深基坑支护结构位移、沉降、内力及水位的施工监测数据为依据,探讨了位移、沉降与内力大小及变化规律。实测表明：支护桩及外侧土体各点随着基坑开挖深度和时间的递增,水平位移逐步增大,增大速度由快逐步趋于平稳。另外,位移大小还与周围建筑物位置和支撑条件有关。周围建筑物的沉降随时间增大,且离基坑越近则越大;立柱沉降及土的隆起量与承受的支撑重量及基坑形状有关;支撑轴力的大小及变化与地质条件、支撑刚度和施工开挖顺序及速度等因素有很大关系;桩身偏心较小,底部可按轴心受力计算。最后,对预警值进行了讨论。     

积分方程法研究均质地基中单桩的工程性状

采用积分变换方法求解弹性半空间中圆形荷载的基本解,按照虚拟桩法建立分析模型,基于圆形荷载的基本解推导出单桩分析的第二类Fredholm积分方程,对其进行数值计算求得桩身各点处的轴力、剪力和位移等,与经典的弹性解答相比,本文的理论更为严密.通过对单桩的荷载传递、沉降特性以及临界桩长等问题的参数分析,得出一些具有工程应用价值的结论.     

深厚淤泥爆破挤淤堤坝沉降计算与分析

爆破挤淤技术在海洋围垦和潮汐电站等工程堤坝建设中发挥着重要作用,随着海洋工程的不断推进,堤坝修建需要处理淤泥(软基)厚度在逐渐加深,在超过12 m的深厚淤泥中往往采用“悬浮式”堤坝结构,对该种堤坝结构开展沉降计算与分析有着重要的意义和应用价值。以惠州港兴盛油库护岸工程为工程实例,分别采用传统沉降计算方法、基于多孔介质渗透理论的考虑浮力作用沉降计算方法及数值模拟方法,对其爆破挤淤形成的“悬浮式”堤坝开展沉降计算,并与实际监测结果对比验证,分析几种沉降计算方法的适用性和合理性。研究表明,传统沉降计算方法得到的沉降值比实际监测值明显偏大,不适合于“悬浮式”堤坝沉降计算;考虑浮力作用方法和数值模拟方法的计算结果较为接近实际监测值,可用于“悬浮式”堤坝沉降计算。     

The axisymmetric consolidation of a semi‐infinite transversely isotropic saturated soil

This paper presents an exact analytical solution to fully coupled axisymmetric consolidation of a semi‐infinite, transversely isotropic saturated soil subjected to a uniform circular loading at the ground surface. The analysis is under the framework of Biot's general theory of consolidation. First, the governing equations of consolidation are transformed into a set of equivalent partial differential equations with the introduction of two auxiliary variables. These partial differential equations are then solved using Hankel–Laplace integral transforms. Once solutions in the transformed domain have been obtained, the actual solutions in the physical domain for displacements and stress components of the solid matrix, pore‐water pressure and fluid discharge can be finally obtained by direct numerical inversion. The accuracy of the numerical solutions developed is confirmed by comparison with an existing exact solution for an isotropic and saturated soil that is a special case of the more general problem addressed. Numerical analyses are also presented to investigate the influence of the degree of material anisotropy on the consolidation settlement. Copyright © 2005 John Wiley & Sons, Ltd.     

隧道水平冻结施工期地表融沉的历时预测模型

隧道冻结工程中所形成的人工冻结壁为临时支护结构,隧道衬砌结构施工后,冻结壁要进入解冻期,由于冻结壁解冻过程中的地层融沉现象对隧道周边环境影响较大,因此,应建立合理的方法对地表融沉量进行预测,以便于实际施工中采取相应的融沉控制措施。为此,考虑冻结壁的自然解冻过程,基于随机介质理论,建立了隧道水平冻结施工期地表融沉的历时预测模型。并提出冻结壁自然解冻条件下瞬态温度场由平板解冻理论近似求解,基于平板解冻理论和一维情况下已融土层的稳定融沉量计算公式,确定了预测模型中解冻锋面半径和融缩区域内半径这2个关键参数的取值方法。将所建立的预测模型应用于隧道全断面水平冻结工程中,得到了地表融沉随解冻时间的变化规律。研究结果表明,地表融沉在解冻初期增长速度较快,而在解冻后期增长速度减缓,地表历时融沉量与崔托维奇通过试验得出的天然冻土历时融沉量变化规律相一致。     

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。     

盾构施工引起地表固结沉降问题的研究

将隧道周围土体视为均质连续各向同性的饱和弹性介质,采用保角变换的方法将含有隧道的半无限平面映射为同心圆环计算域。根据Terzaghi-Rendulic二维固结理论,建立隧道在不透水的情况下周围土体超孔隙水压力分布的控制方程。然后,采用分离变量法计算得到土体超孔隙水压力分布的解析解,最后,根据弹性理论计算得出隧道中线上方地表固结沉降的计算公式。结合算例,分析盾构施工扰动程度、土体渗透系数、土体弹性模量及隧道埋深等因素对隧道中心上方地表处固结沉降的影响。研究结果表明,地表固结沉降的增加值与隧道外侧初始超孔隙水压力值C0的变化量成正比例关系,施工扰动程度越大所引起的固结沉降越大;土体的渗透系数越大固结沉降速度越快,但土体的渗透系数与最终的地表固结沉降量无关;土体的弹性模量越大,最终的地表固结沉降量越小;隧道埋深越深,地表固结沉降所需时间越长,最终的地表固结沉降量也越大。     

粘弹-塑性岩体中衬砌与围岩的共同作用问题

在许多类型的岩层中(比如粘土质的沉积岩、岩盐以及其他较软弱的岩质等)地下洞室在开挖完成之后,其围岩的变形特性,强度特性以及整体的稳定性有明显的时间效应.因此,近年来在国内外的研究工作中已有不少人致力于时间因素对围岩稳定性影响的研究.