饱和分数导数型粘弹性土-深埋圆形隧洞衬砌系统的动力特性

在频率域研究了分数导数型粘弹性饱和土体和深埋圆形隧洞弹性衬砌相互作用的耦合简谐振动。将土骨架视为具有分数阶导数型本构的粘弹性体,基于饱和多孔介质理论和平面弹性理论,分别给出了饱和粘弹性土、弹性衬砌简谐振动的解析解。通过弹性衬砌和饱和土接触面处的连续性条件和衬砌内边界条件,得到了饱和粘弹性土-衬砌系统的稳态动力响应,给出了衬砌和饱和粘弹性土位移、应力和孔隙压力的解析表达式。在此基础上,进行了参数研究,讨论了物理和几何参数对系统响应的影响。研究表明:饱和分数导数型粘弹性土-衬砌系统的动力响应与经典饱和弹性/粘弹性土-衬砌系统的动力响应差异很大。     

粘弹性饱和土中深埋圆形隧道衬砌-土相互作用

基于Biot理论,采用渗流-力学耦合模型研究分析了粘弹性饱和土体中深埋圆形隧道衬砌-土相互作用问题,并考虑了衬砌材料的徐变特性。假定衬砌和土体完全接触,运用积分变换理论在Laplace变换域中得到了衬砌和土体接触面上的应力、变形及衬砌的薄膜力和弯矩。利用Laplace数值逆变换得到时域中的解,并由此分析讨论了衬砌和土体的相对刚度、阻尼比、以及衬砌的相对厚度对隧道衬砌与土体相互作用的影响。数值结果同时也反映了应力、变形、薄膜力和弯矩的随时间变化过程。     

饱和黏弹性土中圆柱形隧洞的振动特性

基于流体不可压缩饱和多孔介质理论,将衬砌视为具有分数导数本构关系的多孔黏弹性体,在频率域内研究了在内水压力作用下饱和黏弹性土和衬砌系统的振动特性。通过引入与孔隙流体体积分数有关的应力系数,合理地确定了隧洞边界衬砌和孔隙水共同承担的内水压力值。利用衬砌内边界上的边界条件以及衬砌和土体界面处应力和位移的连续性条件,给出了隧洞边界部分透水条件下饱和黏弹性土和分数导数型黏弹性衬砌系统简谐耦合振动时系统动力响应的解析解。结果表明:饱和黏弹土和衬砌结构的动力响应与衬砌材料的黏性有关;应力系数合理地确定了衬砌和孔隙水共同承担的内水压力值。     

准饱和粘弹性土-隧道衬砌系统的动力特性

将衬砌和土骨架分别视为多孔弹性材料和具有分数阶导数本构关系的粘弹性体,在频率域内研究了饱和度对分数导数型准饱和粘弹性土-半封闭圆形隧洞弹性衬砌系统动力特性的影响。将水-气混合物视为一种均匀流体,基于Biot两相动力固结理论和弹性理论,分别得到了简谐轴对称荷载和流体压力作用下分数导数型准饱和粘弹性土的位移、应力和孔压以及衬砌的位移和应力解析表达式。利用衬砌内边界上的边界条件及土体和衬砌界面处的连续性条件,得到了待定系数的具体表达式。通过算例分析,发现:衬砌和土体相对渗透系数对孔压幅值的影响与饱和度有关;流体压力作用下,随着饱和度的减小,位移幅值逐渐增大。另外,分数导数模型参数对系统动力响应有较大影响。     

饱和横观各向同性分数导数黏弹性土中半封闭衬砌振动响应

在频率域内研究了饱和横观各向同性分数导数黏弹性土体中深埋圆形隧道半封闭衬砌振动响应问题。根据土体在长期沉积过程中存在各向异性的特点,将土骨架视为具有分数导数本构关系的横观各向同性黏弹性体,采用饱和多孔介质理论和弹性理论,利用衬砌内边界应力协调以及土体和衬砌界面处应力和位移连续,得到了简谐荷载作用下饱和横观各向同性黏弹性土和弹性衬砌的位移、应力和孔隙水压力解析表达式。考察了饱和经典弹性土、饱和分数导数性黏弹性土和饱和经典黏弹性土三种条件下饱和黏弹性土和衬砌各参数的影响,表明：横观各向同性面的弹性模量和衬砌厚度对系统动力响应的影响与分数导数阶数和土骨架的黏性有关;渗透系数较小时,系统存在明显的共振现象。另外,在三种条件下半封闭衬砌振动响应存在较大差异。     

埋置移动荷载作用下成层饱和地基的动力响应

利用Fourier变换和传递反射矩阵法（TRM法）研究了成层饱和地基在埋置移动荷载作用下的动力响应。土体被假设为完全饱和的多孔弹性介质并且服从Biot多孔弹性波动方程,用修正粘滞阻尼模型来描述土体的粘弹性行为,采用TRM法来考虑饱和地基的成层性,利用Fourier变换和Fourier逆变换得到了埋置移动荷载作用下饱和地基动力响应积分形式解答。当饱和成层地基退化单层饱和地基时,该文解与已有解能很好的吻合。最后,通过数值计算分析了埋置荷载深度﹑荷载速度、荷载频率及软硬夹层对动力响应的影响。     

饱和地基上弹性圆板的固结位移

 采用Laplace变换及Hankel变换研究弹性圆板在饱和地基上的固结位移．在Laplace变换域上建立了求解弹性圆板固结位移的第二类Fredholm积分方程，由数值反变换获得时域解，给出了对工程实践有参考价值的计算结果．计算结果表明，弹性板的固结位移随饱和土的排水泊松比的减少而增加，而弹性板的初始位移随饱和土的不排水泊松比的减少而增加．     

深埋圆形隧洞非饱和土-衬砌结构系统的动力特性

采用解析方法在频率域内研究了深埋圆形隧洞非饱和土-衬砌结构系统的动力特性。基于Bishop非饱和土有效应力原理和单相流固结理论,建立了单相流条件下非饱和土的运动方程。通过位移势函数解耦,得到了非饱和土在简谐荷载作用下的动力响应解答。将衬砌结构视为均匀弹性介质,基于弹性理论,得到了简谐荷载作用下圆柱形衬砌结构的稳态形式解答。利用土体与衬砌界面的连续性条件和衬砌结构内边界上的边界条件,确定了表达式的待定系数。在此基础上,考察了饱和度、吸力折减系数、衬砌厚度等参数对非饱和土响应幅值的影响。结果表明:随着衬砌厚度的增加,系统响应幅值逐渐减小;饱和度和吸力折减系数对孔隙水压力幅值的影响较大,而对径向位移和环向应力幅值的影响较小。     

水位变化对于移动荷载作用下土体动力响应的影响研究

采用上覆弹性层饱和地基土模型描述水位于地表以下的地基动力响应问题,利用改变弹性层厚度模拟土体中水位的变化。基于Biot饱和多孔介质动力方程和层间连续性条件,求解出上覆弹性层饱和半空间频域波数内位移场表达式,通过Fourier逆变换得到3维空间域的结果,研究了水位变化对于土体动力响应的影响。数值计算结果表明,水位的变化会对地基中波的传播产生一定影响。当水位离地面较深时,地面竖向位移值与弹性半空间情况类似;随着水位上升,弹性层和饱和半空间界面上的反射波会对地面竖向位移产生影响,导致地表位移值较弹性半空间下的结果有所增大,当水位接近地表时,位移值变化类似于饱和地基土。     

黏弹性土中衬砌隧道振动响应的解析解

该文采用解析方法在频率域内对黏弹土层和衬砌结构简谐振动特性进行了研究。首先, 将土骨架视为具有分数阶导数本构关系的黏弹性体, 根据黏弹性理论, 推导得到了简谐荷载作用下分数导数型黏弹性土层的位移和应力等解析表达式。其次, 建立了两种类型的衬砌运动方程:第一, 将衬砌结构视为均匀弹性介质, 研究了分数导数黏弹性土中弹性衬砌结构的动力特性;第二, 将衬砌等效为薄壁壳体结构, 利用Flügge薄壳理论, 得到了衬砌结构的运动方程, 并对分数导数黏弹性土和壳体衬砌的动力相互作用进行了分析。根据连续性边界条件, 得到了相关待定系数的表达式。再次, 与以往的解析解进行了对比。最后, 通过算例分析了土体和衬砌各参数对系统动力特性的影响, 结果表明:薄壁壳体衬砌结构条件下系统的动力响应大于均匀弹性衬砌结构条件下系统的动力响应;随着土体和衬砌模量比的增加, 响应幅值逐渐减小。分数导数本构参数对系统的动力特性有较大影响。     

粘弹性土体中深埋圆形隧道的应力和位移分析

基于Biot固结理论,采用渗流-力学耦合模型,研究分析了粘弹性饱和土体中因开挖深埋圆形隧道而引起的周围土体的应力和位移场。假设衬砌和土体均为多孔介质,隧道处于半封闭状态,边界半透水。在拉普拉斯变换域中得到的应力、位移场和孔隙水压力解答,运用拉普拉斯数值逆变换得到数值计算结果,分析了隧道周围土体中应力、位移场及孔隙水压力的消散规律,讨论了隧道边界的渗透特性和土体的流变性质对应力、位移场以及孔隙水压力消散的影响。     

Internal blast loading in a buried lined tunnel

The paper presents a comprehensive approach to simulate an explosion occurring inside a buried axisymmetric lined cavity. The approach considers all the stages of the process: detonation of the internal charge; the shock wave propagation in the internal gas and its following interaction with the cavity's shell lining including multiple reflections; soil–structure dynamic interaction, including multiple gap opening/closure and wave propagation in the surrounding medium. The cavity's lining is modeled as a Timoshenko elastic plastic shell. The soil is modeled by the Grigoryan model that takes into account both bulk and shear elastic plastic behavior, including the effect of soil pressure on the yield strength for the stress tensor deviator. The gas-dynamics problem is solved by the modified Godunov method, based on a fixed Eulerian mesh with the so-called mixed cell. The variational difference method is applied to solve the problem in the soil and in the shell domains. The contact pressures acting on the lining due to both the detonation products on the internal side and the soil on its outer side are computed by solving the coupled system of finite differences equations of gas, shell and soil dynamics using a simple iteration method. The problems of a blast-hole charge and of a periodical system of spherical blast charges that are placed at equal distances from each other were solved. The explosion occurs within a cylindrical steel pipeline, surrounded by an elastic plastic loess soil. The effect of the soil elastic plastic pressure-density behavior and its shear properties on the soil–structure interaction (including the gap opening/closure process) was studied.     

Blast response of a lined cavity in a porous saturated soil

The paper proposes a comprehensive approach to simulate the blast response of a lined cavity in a porous soil. To calculate the soil–structure contact pressure, the coupled Godunov-variational-difference approach was developed. The lining is modeled by a Timoshenko elastic–plastic shell with kinematic linear hardening. To solve the problem in the lining domain, the variational-difference method is applied. The soil is modeled by the Lyakhov three-phase model that takes into account both bulk and shear elastic–plastic behavior, including the effect of soil pressure on the yield strength for the stress tensor deviator. The problem of blast wave propagation within the soil medium is solved by the Godunov method. The coupled approach to calculate the soil–lining contact pressure is based on the relationships on the shock and rarefaction waves with finite-difference equations of the shell motion using a simple iteration method. It allows the reduction of the contact problem to the self-similar symmetric Riemann problem. Solution of the problem of an explosion in a porous medium, and analysis of the soil–obstacle interaction under the blast action using the proposed method show good correspondence with available experimental results. Also, the plane problem of blast response of the circular cavity lined by a thin steel lining was solved. The effect of the gas volumetric content in the soil on the incident shock wave pressure as well as on the contact pressure and lining meridian strain was studied.     

反平面冲击荷载作用下圆柱形洞室的动力响应

对无限弹性土体内圆柱形洞室在反平面冲击荷载的作用下的瞬态响应进行了探讨。用残余变量的方法结合拉普拉斯变换及其逆变换,在频域内的得到土体位移和应力一般表达式,并采用拉普拉斯逆变换的数值方法,给出了问题的数值解。在时域内分析了无限弹性土体内圆柱形孔洞在沿轴向方向的冲击荷载作用下的土体动力响应的变化规律,并将计算结果与静力情况下的作了比较：反平面荷载作用后,波向外发散传播,并沿半径方向衰减,衰减速度较静力情况下的衰减要慢,且距离波源越远二者差别越大;波到达后,该点土体的应力和位移均发生与外荷载相同的三角形变化：先增大,随后减小最后保持为零不变。     

Analytical solutions describing the consolidation of a multi-layered soil under circular loading

Analytical solutions describing the consolidation of a multi-layered soil under circular loading are presented. From the governing equations of saturated poroelastic soil in a cylindrical coordinate system, the eighth-order state-space equation of consolidation is obtained by eliminating the variation of time t using the Laplace transform together with the technique of Fourier expansions with respect to the coordinate θ and the Hankel transform with respect to coordinate r. The solution of the eighth-order state-space equation is derived directly by using the Laplace transform and its inversion of the z-domain. Based on the continuity between layers and the boundary conditions, the transfer-matrix method is utilized to derive the solutions for the consolidation of a multi-layered soil under circular loading in the transformed domain. By the inversion of the Laplace transform and the Hankel transform, the analytical solutions in the physical domain are obtained. A numerical analysis based on the solutions is carried out by a corresponding program.     

瓦斯爆炸在封闭管道内冲击振荡特征的数值模拟

摘要：为了研究爆炸波在封闭型系统的冲击和振荡特征及其特征参数变化规律,采用数值模拟的方法研究了封闭型管道内瓦斯爆炸的传播特征。研究结果表明：闭口型系统内的瓦斯爆炸呈明显的振荡特征,对于爆燃波,反射波有2道,即前驱冲击波的振荡和压缩波的振荡。由于冲击波的振荡叠加,使其最大爆炸超压和瞬态流速峰值与开口型系统相比较高,而且在反射波及稀疏波的影响下,爆炸波超压分为三个区。爆炸温度和动压同样呈明显的振荡特征,使得爆炸高温环境维持较长时间,爆炸动压在爆炸传播方向的动压与其他方向相比明显较大。研究结果解释了受限空间内爆炸破坏比开放型系统强烈的原因,为今后受限空间内爆炸的预防与控制提供了基础理论参考。