准饱和土中圆柱形衬砌的瞬态动力响应分析

内源瞬态荷载作用下圆柱形孔洞的动力响应解答是土动力学的经典问题之一。已有研究大都假设孔洞周围土体为理想弹性介质或完全饱和多孔介质。然而,实际工程中不存在完全弹性和完全饱和土体。分别视衬砌结构和周围土体为弹性材料和准饱和多孔介质（饱和度 95%）,根据牛顿第二定律、达西定律和Biot波动理论推导出准饱和土体的控制方程。根据边界条件导出衬砌和土体的位移、应力和孔隙压力的Laplace变换空间的解答。利用反Laplace变换数值计算方法,将解答转换为时域解。分析了饱和度对衬砌位移、应力和孔压的影响,结果表明,当95% 99%时,饱和度对径向位移和切向应力的影响较小;99% 100%时,饱和度对径向位移和切向应力的影响较大;但饱和度对孔隙压力的影响远大于对径向位移和切向应力的影响。得出位移、应力和孔压沿径向的衰减规律,当95% 99%时,饱和度对径向位移和切向应力沿径向衰减影响较小,99% 100%时,饱和度对径向位移和切向应力沿径向衰减影响较大,但饱和度对孔压沿径向的衰减影响远大于对径向位移和切向应力沿径向的衰减。     

竖向圆形荷载作用下弹性地基半空间问题的解析解

竖向圆形荷载作用下弹性半空间问题的位移和应力解是桩基分析的基础。利用Hankel积分变换,首先导出了弹性地基半空间位移与应力的积分形式的通解。通过适当地引入边界条件和界面位移和应力的连续条件,求得了内部作用竖向圆形荷载时弹性地基半空间位移与应力的积分形式解。在此基础上,给出了不同深度处荷载作用投影范围内竖向位移和竖向正应力的平均值。数值结果验证了解析解的正确性。     

台山核电站边坡爆破振动监测及数值模拟研究

台山核电站场平一期边坡的稳定性直接关系到电站的顺利建设及核电站运营期间的安全。通过现场爆破振动监测,分析了爆破开挖时边坡的振动速度衰减规律, 发现爆区上方马道内侧质点振动速度随高程增加存在放大效应,并且这种放大效应在水平径向比垂直向更为显著;另外,在爆区上方第1级马道内侧,质点垂直向振动速度一般比水平径向振动速度大,平均为其1.5倍左右,而后随着应力波向坡体传播,垂直向速度迅速衰减,而水平径向速度衰减相对较慢,到第3级马道内侧,质点水平径向速度已和垂直向持平或略大。同时,结合三维离散元数值软件(3DEC)进行数值模拟,对边坡在爆破荷载作用下质点振动速度、位移以及塑性区状态进行分析,并与现场监测结果进行比较。结果表明,数值计算值与实测值误差在15%以内;在爆破荷载作用下边坡各级马道外侧顶点产生永久位移,但均较小,且趋于稳定;塑性区仅限于爆区周围,边坡整体是稳定的     

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.     

直角域中凸起和孔洞对SH波的散射与地震动

按照波函数展开法和镜像方法,对直角域中半圆形凸起和圆形孔洞对SH波的散射进行了分析,得到其稳态解。对含孔洞和凸起的直角域做分区,等效为一个含孔洞与凹陷的直角域和一个圆域的契合,其在分界面上满足位移和应力的连续性条件,即契合条件,分别构造两个区域内的位移波函数,按照孔洞边界柱面上的应力自由和契合条件定解波函数展开式的系数。按Fourier级数展开法,得到定解条件的线性代数方程组,截断求解,进而得到问题的解析解。数值算例给出圆形孔洞边沿动应力和地表位移幅值的分布情况,得到直角域自由边界、凸起、孔洞对散射和地震动的影响。     

层状地基中瑞利波随深度的衰减特性

层状地基中瑞利波（Rayleigh wave）的传播规律以及随深度的衰减规律是工程环境微振动分析与控制研究的关键问题之一。采用解析法（矩阵传递法）分析了层状地基中瑞利波弥散曲线,并在此基础上研究了各种频率下不同类型土层（上软下硬、软夹层、硬夹层）中瑞利波位移随深度衰减规律,通过与弹性半空间解的对比发现,瑞利波位移随深度的衰减规律与频率、土层分布密切相关：频率越高,传播深度越浅;特殊土层（软夹层、硬夹层）的存在会局部显著地改变其衰减规律,并且位移峰值的分布受到频率和土层分布的共同影响。最后,将该方法用于分析上海光源工程地基条件下瑞利波随深度的衰减规律,并与现场深孔微振动测试数据进行了比较。结果证明,与弹性半空间解相比,层状地基中瑞利波随深度的衰减规律可以更为准确地反映真实条件下瑞利波随深度的衰减规律。     

不耦合装药爆破对硬岩应力场影响的数值分析

爆破地震勘探石油是一种重要的方法,但爆破地震效应与爆破参数、地质条件等密切相关。采用动力有限元软件ANSYS/LS-DYNA,对柱状炸药与药孔壁之间为空气或其他介质以及空隙间距变化时碳酸盐岩岩石中爆炸应力波的传播规律和爆炸地震波能量的衰减特性进行了数值模拟研究,得到了不耦合装药爆炸时岩石应力、振动速度的衰减规律以及与不耦合系数、间隙介质的关系,分析了不耦合效应对爆炸地震波能量的影响。研究表明,不耦合或耦合不好时会使岩体中爆炸应力波的强度大大降低;耦合状态对岩体应力及速度的衰减系数和衰减指数影响较大;在空隙中注水或灌满泥浆会改善它们的耦合关系,增大下传的爆破能量。所得成果可为我国西南地区优选适合碳酸盐地层地震勘探的激发因素提供技术途径和方法。     

强夯法处理层状软基的动态响应分析

引入双屈服面弹塑性本构模型,将土骨架的变位和孔隙水作为变量进行流、固耦合分析,通过瞬态波动有限元程序模拟冲击荷载作用下层状地基土体的动态响应特征。计算结果表明,土体的应力峰值、孔压峰值和位移峰值随土层深度和距锤底中心的径向距离的增大而逐渐滞后,通过不同位置土体的动态响应分析,表明应力波是以竖向的椭球面形状在土体中传播的,而且衰减很快。数值计算结果与现场测试结果两者之间较为吻合,为实现有限元模拟分析现场实际提供了可靠的依据。     

动荷载作用下岩石非线性弹性响应研究

岩石是一种典型的颗粒孔隙介质。在冲击荷载下,即便是在作用荷载比较低的阶段,由于岩石内部自然缺陷的存在,应力波随着传播距离延伸,其幅值有较大的衰减。文中对饱油和饱水的砂岩、大理岩进行SHPB冲击试验,研究结果表明:对于同种岩石试样,饱油岩样的衰减系数比饱水样品的小;对于不同的岩样,孔隙率大的岩样相应的衰减系数大。应力波在饱和介质中的衰减与介质中液体的粘滞系数有关。同时,材料中的孔隙和液体的存在对应力波的弥散特征也有一定的影响。然后基于Preisach-Mayergoyz(P-M)空间模型对冲击荷载比较低的阶段,岩石内部应力波的衰减和弥散问题进行了较详细的分析,得到了一些初步结论。本研究对于石油开采、物探以及岩土工程有一定的意义。     

黏弹性节理岩体的位移不连续模型研究

选用三参数标准线性固体作为岩石本构,提出了一种考虑岩体黏弹性的位移不连续模型;根据一维黏弹性波的特征线法,推导了节理处质点速度、应力和应变递推公式。首先,基于分离式霍普金森压杆（SHPB）对砂层进行试验,得到其应力-应变关系,并换算出砂层节理的法向刚度;接着,通过一维强间断黏弹性波的波速公式、高频波衰减系数以及任一频率下的衰减系数,确定出数值算法中的三参数。最后,基于自制的摆锤装置,探讨了一维应力波在节理岩体中的传播规律,试验中以两根长1 000 mm、直径为68.50 m的岩杆作为入射和透射杆,以3 mm砂层模拟节理。试验和数值结果吻合度良好,进一步验证了该方法的可靠性。     

准各向同性裂隙岩体中有效动弹性参数与弹性波速关系的研究

从弹性波在介质中传播的特点和弹性波法在岩体工程中的实际应用情况方面,分析了弹性波在含裂隙岩体介质中的传播特征。将岩体中裂隙呈随机分布的裂隙岩体似为准各向同性裂隙岩体,根据能量平衡原理、岩石断裂力学理论和卡氏最小功能定理(Castiglano’s theorem),确定了准各向同性裂隙岩体的有效动弹性参数( 、 、 )与裂隙密度参数(Xv)的数学关系。在此基础上,根据各向同性介质中传播的弹性波理论,建立了准各向同性裂隙岩体中弹性波速( 、 )和 / 与裂隙密度参数(Xv)之间的关系。理论研究表明,在此裂隙岩体中,有效动弹性参数和弹性波速与裂纹密度参数之间相互的关系均近似成倒数函数的非线性关系;裂隙密度参数增加,有效动弹性模量( )也减少,弹性波速( , )也减小;在裂隙密度参数较小时,此裂隙岩体的有效弹性模量和弹性波速随裂隙密度参数的变化较大,说明裂隙体的有效弹性参数和弹性波速对裂隙体非常敏感。     

An analytical solution for wave propagation in a square pile due to transient point load

This paper presents an analytical solution for wave propagation in a square pile due to transient point load. The differential equation of dynamic equilibrium is established considering propagation of waves in both vertical and transverse directions. The soil resistance is simulated by Voigt model. The three-dimensional analytical solution is deduced by using Fourier transform and the separation of variable method. The arithmetical results of the proposed solution show that the velocity responses along the radial direction at the pile top are highly non-uniform. In addition, Young’s modulus and the pile side length exert undisputable influences on the velocity responses.     

Analysis of one-dimesional wave propagation in a fluid-saturated finite soil column

Biot's dynamic equations of motion for one-dimensional wave propagation in a fluid-saturated linear elastic isotropic soil are solved using Laplace transformation followed by numerical inversion and the results compared with a direct finite element formulation. A soil column of finite dimension subjected to velocity boundary conditions is analysed, allowing for reflection of waves from boundaries. Comparison of time histories at given points along the column shows that the finite element solution gives good agreement with the Laplace transform solution for low as well as high drag.     

Numerical and analytical investigation of compressional wave propagation in saturated soils

In geotechnical earthquake engineering, wave propagation plays a fundamental role in engineering applications related to the dynamic response of geotechnical structures and to site response analysis. However, current engineering practice is primarily concentrated on the investigation of shear wave propagation and the corresponding site response only to the horizontal components of the ground motion. Due to the repeated recent observations of strong vertical ground motions and compressional damage of engineering structures, there is an increasing need to carry out a comprehensive investigation of vertical site response and the associated compressional wave propagation, particularly when performing the seismic design for critical structures (e.g. nuclear power plants and high dams). Therefore, in this paper, the compressional wave propagation mechanism in saturated soils is investigated by employing hydro-mechanically (HM) coupled analytical and numerical methods. A HM analytical solution for compressional wave propagation is first studied based on Biot’s theory, which shows the existence of two types of compressional waves (fast and slow waves) and indicates that their characteristics (i.e. wave dispersion and attenuation) are highly dependent on some key geotechnical and seismic parameters (i.e. the permeability, soil stiffness and loading frequency). The subsequent HM Finite Element (FE) study reproduces the duality of compressional waves and identifies the dominant permeability ranges for the existence of the two waves. In particular the existence of the slow compression wave is observed for a range of permeability and loading frequency that is relevant for geotechnical earthquake engineering applications. In order to account for the effects of soil permeability on compressional dynamic soil behaviour and soil properties (i.e. P-wave velocities and damping ratios), the coupled consolidation analysis is therefore recommended as the only tool capable of accurately simulating the dynamic response of geotechnical structures to vertical ground motion at intermediate transient states between undrained and drained conditions.     

Analysis of Blast Wave Interaction with a Rock Joint

The interaction between rock joints and blast waves is crucial in rock engineering when rock mass is suffered from artificial or accidental explosions, bursts or weapon attacks. Based on the conservation of momentum at the wave fronts and the displacement discontinuity method, quantitative analysis for the interaction between obliquely incident P- or S-blast wave and a linear elastic rock joint is carried out in the present study, so as to deduce a wave propagation equation. For some special cases, such as normal or tangential incidence, rigid or weak joint, the analytical solution of the stress wave interaction with a rock joint is obtained by simplifying the wave propagation equation. By verification, it is found that the transmission and reflection coefficients from the wave propagation equation agree very well with the existing results. Parametric studies are then conducted to evaluate the effects of the joint stiffness and incident waves on wave transmission and reflection. The wave propagation equation derived in the present study can be straightforwardly extended for different incident waveforms and nonlinear rock joints to calculate the transmitted and reflected waves without mathematical methods such as the Fourier and inverse Fourier transforms.     

DEM–SPH simulation of rock blasting

A numerical model is proposed for the simulation of rock blasting. A bonded particle system is utilized to mimic the behavior of rock. The particles interact at the contact points through normal and shear springs to simulate rock elasticity. To withstand the deviatoric stresses, the particles are glued to each other. If the applied force exceeds the contact strength, local failure occurs and microcracks are developed in the synthetic rock. For simulation of gas flow, the smooth particle hydrodynamic method is implemented. The interaction of gas particles with the rock grains is assumed to follow a perfect plastic collision model in which the initial momentum of the colliding particles is preserved. A detailed examination of the interaction of gas with blast hole is investigated. It is shown that the proposed hybrid model is capable of simulating the induced shock waves in the gas together with wave propagation in the rock material. The model successfully mimics crack propagation in rock. In particular, the crushed zone around the borehole, radial cracks, and surface spalling are all captured successfully. The results of numerical analysis suggest that gas–rock interaction can, in fact, generate a few successive compressive waves in the rock specimen, causing further extension of radial cracks with time as the weaker secondary and tertiary waves interact with the crack tips.     

Propagation Characteristics of Blasting Stress Waves in Layered and Jointed Rock Caverns

The existence of joint fissures makes explosive actions between rock masses more complex. Therefore, it is of great significance to carry out experiments studying blasting stress waves propagating in jointed rock masses. Based on the Froude Similarity principle, the geological mechanical models of intact rock masses and jointed rocks have been proposed. A blasting vibration experiment was carried out and demonstrated that the propagation of the blasting stress waves and changing structures have an important relationship. A numerical simulation of the blasting stress wave propagation law in a layered jointed rock mass was carried out. This study found that with an increase in the joint angle, the peak velocity of blasting stress wave, transmission coefficient and reflection coefficient all gradually increased, while the attenuation coefficient gradually decreased. With an increase in joint spacing, the attenuation rate of the blasting stress waves increased.     

粘弹性准饱和土中球空腔的动力响应

从工程实际出发,采用粘弹性两相介质模型,考虑土骨架的粘性以及流体与固体之间的耦合作用,利用Laplace变换求解了粘弹性准饱和土中球空腔的动力响应问题,得到了变换域内的解析解。借助数值Laplace反变换,数值分析了粘弹性准饱和土中球空腔动力响应的位移、应力及孔压的变化规律。为分析地下结构动力响应提供了一种有效的方法,模型符合工程实际,有一定的工程应用价值。     

基于径向不变假定的现浇大直径管桩纵向振动响应频域解

假定各物理量沿径向不变化,建立了低应变瞬态集中荷载作用下现浇大直径管桩振动响应的计算模型和波动方程。采用Laplace变换法,求得了波动方程的频域解析解,采用Fourier逆变换求得了时域响应。将文中解计算结果与三维频域解析解进行了对比分析,文中解的入射峰-反射峰时间差与三维频域解差别很小,说明对于PCC桩这种大直径薄壁管桩,采用径向不变假定对计算结果几乎没有影响。因此,在PCC桩低应变检测波形分析时,采用基于径向不变假定的二维解是完全合理的。将文中二维频域解的计算结果与二维时域解的结果进行了对比分析,结果表明,2种解在入射波、第一个桩底反射波、第二个桩底反射波峰值大小和到达时间非常吻合,这说明考虑环向位移与否对计算结果没有太大的影响,研究PCC桩低应变动力响应的问题时忽略水平方向的位移是完全可以的。     

2.5维各向异性介质中地震波场数值模拟

这里实现了在2.5维各向异性介质中地震波传播的数值模拟。首先从2.5维一阶速度-应力弹性各向异性波动方程出发,得出了该方程的拟谱法数值解法;然后通过对Marmousi速度模型进行数值模拟,表明了拟谱法的有效性;最后计算并分析了均匀和混合各向异性介质中波的传播快照和理论模拟的地震记录,进一步认识了波在各向异性介质中的传播规律。