Stress Analysis of Orthotropic Plate on Elastic Foundation with Transverse Point Load

An infinite orthotropic plate on an elastic foundation subjected to a transverse point load is studied. A three‐dimensional stress distribution in the vicinity of the applied load is sought without considering the friction between the plate and the foundation. Based on the assumption of a uniform stress distribution for the applied load, a double Fourier transform technique is employed to solve the problem in the transform domain. The Gaussian integration scheme is used to carry out the inverse transformation to obtain the real stress components. Symmetry of the transform response due to the material orthotropy has been used to reduce the effort involved in performing the integration. Distribution of various stress components around the point of load application is presented for a typical orthotropic layer. A comparison of stress distribution for orthotropic and nearly isotropic material is also presented.     

油罐爆炸作用下隧道衬砌动力响应数值模拟研究

为准确分析油气爆炸下隧道及采矿巷道等地下工程的结构稳定性,采用FLACS软件计算LPG爆炸荷载,基于LS-DYNA软件将爆炸冲击荷载施加于结构表面,进而计算爆炸荷载作用下衬砌结构动力响应。研究结果表明：隧道的“角状结构”对冲击波反射具有强化作用,致使相应位置形成应力集中,应力波强度衰减缓慢,随着传播距离的增加,衬砌所受应力逐渐减小且同一截面应力值趋于一致;同一截面不同测点处的速度、位移值受爆心距和隧道几何结构的共同影响,当爆心距大于12 m时,速度和位移值变化趋于稳定;顶部衬砌和底部结构更易发生破坏,边墙位置损伤程度较小。该研究成果为地下工程安全稳定性分析提供了方法依据,也为巷道抗爆设计及支护优化提供了理论参考。     

Nonlinear Response of Deep Immersed Tunnel to Strong Seismic Shaking

Critical for the seismic safety of immersed tunnels is the magnitude of deformations developing in the segment joints, as a result of the combined longitudinal and lateral vibrations. Analysis and design against such vibrations is the main focus of this paper, with reference to a proposed 70?m-deep immersed tunnel in a highly seismic region, in Greece. The multisegment tunnel is modeled as a beam connected to the ground through properly calibrated interaction springs, dashpots, and sliders. Actual records of significant directivity-affected ground motions, downscaled to 0.24 g peak acceleration, form the basis of the basement excitation. Free-field acceleration time histories are computed from these records through one-dimensional wave propagation equivalent-linear and nonlinear analyses of parametrically different soil profiles along the tunnel; they are then applied as excitation at the support of the springs, with a suitable time lag to conservatively approximate wave passage effects. The joints between the tunnel segments are modeled realistically with special nonlinear hyperelastic elements, while their longitudinal prestressing due to the great (7?bar) water pressure is also considered. Nonlinear dynamic transient analysis of the tunnel is performed without ignoring the inertia of the thick-walled tunnel, and the influence of segment length and joint properties is investigated parametrically. It is shown that despite ground excitation with acceleration levels exceeding 0.50 g and velocity of about 80?cm/s at the base of the tunnel, net tension and excessive compression between the segments can be avoided with a suitable design of joint gaskets and a selection of relatively small segment lengths. Although this research was prompted by the needs of a specific project, the dynamic analysis methods, the proposed design concepts, and many of the conclusions of the study are sufficiently general and may apply in other immersed tunneling projects.     

Dynamic and Seismic Analysis of Foundations based on Free Field B-Spline Characteristic Response Histories

A direct time domain formulation for the analysis of unbounded media and foundations is developed that treats dynamic excitations and ground motion in a uniform manner. The method uses the boundary element method with higher order B-Spline fundamental solutions to compute the characteristic responses of the surface of the elastodynamic domain. Subsequently, time histories of the system response to general excitations are computed by a mere superposition scheme that accommodates in a uniform manner arbitrary time histories of external loads and/or ground motion. The characteristic responses are computed in the form of time dependent flexibility matrices of the medium that are sparse due to the finite duration of the B-Spline excitation signal and the characteristics of the wave propagation. The duration of the B-Spline impulse response is limited to only a few time steps. Consequently, significant savings in computing time and storage requirements are achieved. Furthermore, the characteristic responses do not depend on the type or wave form of the actual external excitations and the presence of rigid foundations. This is a significant advantage when the response of a system to excitations of long duration is to be computed. In addition, the proposed approach significantly reduces the size of the problems under consideration and yet fully considers the effects of the free field. The significance of nonrelaxed boundary conditions and correct representation of the free field is established. The method is demonstrated and validated through applications pertaining to the analysis of foundations and inclusions subjected to transient loads and seismic excitations.     

应力波形对岩石爆生裂纹扩展机制影响的数值模拟

运用RFPA3D动力分析软件模拟了冲击动力作用下含预制裂纹岩石的裂纹扩展过程,探究了应力波峰值、能量、上升及下降速率对岩石裂纹扩展过程的影响。研究表明动载下岩石裂纹扩展形态受应力波上升速率影响,应力波上升速率越快,孔周边岩石越破碎;应力波能量影响裂纹扩展长度,能量越大裂纹扩展越长,而相同能量条件下,应力波上升速率越小,裂纹扩展距离越远,但孔边破碎程度越弱;上升速率和应力波上升沿能量共同影响着炮孔粉碎区半径。数值模拟结果很好地揭示了不同应力波峰值、能量与上升/下降速率对岩石的破碎机制,在实际爆破作业中可以通过水炮泥封口或者采用空气柱间隔装药结构来延长应力波作用时间,以达到扩大爆破影响范围的目的,而通过选取合适类型与配比的炸药来提升应力波上升速率从而增强孔边破碎效果。      

Applicability of Kinematic, Noninertia, and Quasi-Steady Dynamic Wave Models to Unsteady Flow Routing

Propagation of flood waves in an open channel can be mathematically approximated by the Saint-Venant equations (dynamic wave) or by their simplifications including the kinematic wave, noninertia wave, gravity wave, and quasi-steady dynamic wave models. All of these wave approximations differ not only in the physical propagation mechanism, but also in the degree of complexity involved in computation. In order to efficiently implement the approximate wave models for flood routing, their criteria of applicability should be developed. The applicability of the kinematic wave, noninertia wave, and quasi-steady dynamic wave approximations to the full dynamic wave equations for unsteady flow routing is examined by comparing the propagation characteristics of a sinusoidal perturbation to the steady gradually varying flow for different simplified wave models. Development of the applicability criteria provides a guideline for selecting an appropriate wave model for unsteady flow modeling, thus enabling an assessment of the capabilities and limitations of different simplified wave models. By using the linear stability analysis, the derived criteria can be expressed in terms of dimensionless physical parameters that represent the unsteadiness of the wave disturbance, characteristics of the downstream boundary condition (backwater effect), and the location along the channel. The developed criteria are for a specific point and time, thereby providing a more refined indication than the integrated criteria based on the testing for a hydrograph found commonly in the literature. In this study, we have justified whether the simplified wave models such as the kinematic, noninertia, or gravity wave models would be appropriate and reliable approximations to the full Saint-Venant equations with a comparable accuracy for a given flow condition. The downstream backwater effect has been taken into consideration in the developed criteria for broader engineering applications. One hypothetical example is presented for illustration.     

BEM Analysis of Two-Dimensional Elastodynamic Problems of Anisotropic Solids

A direct BEM (boundary element method) formulation and its numerical implementation for steady-state elastodynamic analysis of two-dimensional problems involving orthotropic and nonorthotropic solids of arbitrary shape is presented. The present formulation is developed by incorporating isoparametric quadratic boundary elements, a rigorous self-adapting numerical integration scheme, and the Green's functions of Wang and Rajapakse for two-dimensional orthotropic solids. The full-space as well as the half-space Green's functions have been implemented. The formulation is capable of treating multidomain problems by substructuring and satisfying the equilibrium and displacement compatibility at the interfaces. Thus, problems related to the layered media and soil-structure interaction can all be analyzed. The accuracy and reliability of the present BEM analysis are demonstrated through comparison of results obtained for a few example problems with published solutions. Finally, the applicability of this methodology is demonstrated by analyzing three types of problems, a rigid strip footing embedded in an orthotropic half-space, a strip footing resting on an orthotropic stratum overlaying an orthotropic half-space, and a rigid strip footing embedded in a nonorthotropic half-space.     

Analysis of Thick Circular Plates Undergoing Large Deflections

This investigation considers the effect of transverse shear deformation on bending of the axisymmetrically loaded isotropic and orthotropic circular and annular plates undergoing large deflection. The analysis treats the nonlinear terms of lateral displacement as fictitious loads acting on the plate. The solution of a von Kármán‐type plate is, therefore, reduced to a plane problem in elasticity and a linear plate‐bending problem. Results are presented for simply supported and clamped plates and are in good agreement with the available solutions. For plates considered in this study, the influence of shear deformation on lateral displacement becomes more significant as the orthotropic parameter increases. The linear and nonlinear solutions for orthotropic plates deviate at a low value of the maximum deflection‐to‐thickness ratio (w/h). Consequently, the extent of w/h within which the small‐deflection theory is applicable to orthotropic plates is much lower than the value of about 0.4 typically used for isotropic plates, and it depends, in general, on the degree of orthotropy. The technique employed in this study is well suited for the analysis of nonlinear plate problems.     

冲击荷载对具有轴向静应力红砂岩应力波传播速度的影响特性

岩体工程爆破开挖时,距爆源不同距离处的围岩体承受不同大小的冲击荷载和地应力。为研究冲击荷载和地应力对岩石应力波传播速度的影响,利用改进SHPB试验装置对红砂岩进行应力波传播试验,设置7个等级的轴向静应力和冲击速度,分别模拟工程中的地应力和冲击荷载大小。基于试验得到入射波和透射波起跳点的时间差,计算岩石的应力波传播速度,得到静应力和冲击速度对应力波传播速度的影响规律。构建岩石应力波传播速度与冲击速度的关系经验模型,探索拟合参数随轴向静应力的变化规律。通过测量冲击试验后岩石的声波波速,得到受载后岩石声波波速随冲击速度的变化规律,探究动载荷对岩石应力波传播速度的影响机理。研究结果表明,具有轴向静应力岩石的应力波传播速度随冲击速度的增加先增大后减小,二者呈高斯函数的变化关系。轴向静应力显著影响应力波传播速度与冲击速度的变化关系,各个拟合参数随着轴向静应力的增大呈现不同的变化趋势。在不同的轴向静应力工况下,受载后岩石的声波波速随着冲击速度的增大呈现“平缓减小—急剧减小”的变化趋势。研究结果有助于分析深部工程岩体爆破开挖应力波的传播规律以及邻近结构的稳定性分析。      

基于离散元法的金属粉末压制加载速度对压力分布影响

基于离散元原理，采用三维离散元软件PFC3D模拟冲头加载过程，研究以不同冲头速度撞击金属粉末颗粒所产生的透射波以及对侧壁的压力分布。结果表明，对于离散性介质，冲击加载下的应力波传播不单受到颗粒材质波阻抗的影响，还受到颗粒运动和力链形成的很大影响。通过对比不同冲击加载速度下阴模底部的受力，发现随着冲击速度的提高，透射波的峰值成线性增长；通过均分阴模侧壁的方式得到侧壁不同位置所受的侧压力峰值，发现侧壁所受压力呈波谷式分布，从而分析得到颗粒间力链的传播和分布规律。     

不同地应力下爆破振动效应分析

为研究岩石在不同地应力下的爆破振动效应，选择经验证过的岩石本构，利用ANSYS/LS-DYNA隐式—显式序列求解方法，对不同侧压力系数下岩石爆破过程进行数值分析。分别构建了侧压力系数为0.1、0.5、1.0、2.0、4.0条件下的计算模型，数值模拟结果表明：初始地应力对爆破有较强的抑制作用，岩石破碎区受侧压力系数的影响较小，爆破裂纹优先向较大的地应力方向延伸；岩石质点振动速度峰值（PPV）到达时间不受侧压力系数的影响；当侧压力系数小于1.0时，水平方向的质点振动速度峰值大于竖直方向;当侧压力系数大于1.0时，竖直方向的质点振动速度峰值大于水平方向。     

节理粗糙度对应力波传播及试样破坏影响的颗粒流模拟

为了研究节理粗糙度对应力波传播规律的影响以及粗糙节理试样受应力波作用发生破坏的微观机理,利用基于离散元方法的数值分析软件PFC^2D构建了SHPB系统的颗粒流数值模型。在已有SHPB物理试验的基础上对试验中采用的节理试样进行微观参数标定,研究了较低冲击荷载下节理粗糙度对应力波传播的影响规律以及较高冲击荷载下不同形貌节理试样的微观裂纹扩展和破坏机理。研究表明：节理面的存在会降低应力波的透射系数,且节理面粗糙度越大,透射系数越小;冲击载荷下裂纹在节理面处萌生并迅速扩展到试样完整部分尤其是试样端面,大部分裂纹形成于峰后阶段,且张拉裂纹占主导地位;节理面越粗糙,动态强度越低,试样越容易破坏,产生的裂纹数也越多。     

Torsional Surface Waves in Nonhomogeneous Anisotropic Medium under Initial Stress

This paper studies the possibilities of propagation of torsional surface waves in nonhomogeneous anisotropic half-space under compressive initial stress. Two types of variations in nonhomogeneity, mainly hyperbolic and quadratic, have been discussed, and it is observed that in both cases the torsional surface wave will propagate in the media under consideration. The velocities of propagation have been computed and are presented in graphs. The study shows that for hyperbolic variation of nonhomogeneity, the increase of the anisotropic factor, increases the velocity of propagation, always keeping it more than that of shear wave in homogeneous medium. The presence of initial stress increases the velocity of propagation. In the case of quadratic variation it is found that the presence of initial stresses increases the velocity of propagation. The increase of anisotropy decreases the velocity, and the decrease in the nonhomogeneity factor increases the velocity, always keeping the velocity of torsional surface waves less than that of shear wave in the homogeneous medium.     

剧烈瓦斯爆炸隧道洞口致损机理

为探究洛带古镇隧道瓦斯爆炸下洞口衬砌致损机理,对隧道内积聚瓦斯等效、量化研究,采用LS-DYNA建立与洞门几何结构一致的流固耦合数值模型并验证,以RHT模型模拟混凝土并修正参数,对爆炸过程中冲击波的传播特征及强度、洞门致损机理研究分析,并将模拟结果与实际情况对比.研究表明:爆炸冲击波在隧道内无规则的反射效应使其强度剧增、流场复杂,局部位置有聚焦现象,隧道内高压达1.2~2.4 MPa;传播过程中,靠衬砌一侧冲击波运动速度较快,形态也由“球状”变为“喇叭”状;当以平面波形态传至洞门时,拱顶冲击波强度增加56%,达2.8 MPa,并在削竹式洞门周边发生衍射;自隧道传出后,强度逐渐降低,边墙及底板处的冲击波沿纵向径直射出,拱部冲击波向斜上方运动,形成“蘑菇云”.爆炸作用下,衬砌曲边墙脚处完全破坏;爆心距7 m范围内衬砌受损严重;7~15 m范围内拱部几乎未受损;洞门受损严重.缺少围岩的约束作用,洞门拱顶Y向、拱脚X向位移分别达0.26和0.14 m,迎爆面、背爆面拉应力分别介于7.9~31.5 MPa、4.9~15.6 MPa,背爆面出现多个应力峰值,洞门主要为受拉致损.经对比,洞门损伤特征的数值模拟结果与现场实际情况基本一致,可为后续的衬砌灾害处治提供依据.      

深部岩体水耦合爆破裂纹扩展数值模拟研究

为认识深部高地应力岩体水耦合爆破裂纹扩展过程及机理,选择试验验证的RHT本构,采用LS-DYNA对水耦合装药单孔在不同原位应力场下的岩体爆破裂纹扩展进行数值分析。模拟结果表明：水耦合的方法延长了爆炸作用时间,提高了岩体中爆炸应力峰值和PPV（质点振动速度峰值）,增强了爆破致裂岩体的效果;原位应力在深部岩体水耦合爆破中起到增加岩体中应力和PPV的作用。研究表明：在不同的地应力条件下,均存在某一最优水不耦合系数,且最优不耦合系数随原位应力的增加而减小,水耦合时,在原位应力为0,10,20,30,40 MPa的条件下,最优不耦系数分别为5.00、3.30、2.63、1.56和1.25。     

Nondestructive Analysis of a Concrete Tunnel Model Using a Newly Proposed Combined Stress Wave Propagation Method

This paper summarizes the measured properties of a three-layer model concrete tunnel lining using a newly proposed combined stress wave propagation (CSWP) method. The spectral analysis of surface waves (SASW) and impact echo (IE) methods were used in combination to determine the in-place dynamic properties of the tunnel lining and to locate embedded voids. Simultaneously, the free-free resonant column (FFRC) method was independently used to determine the dynamic properties of the materials used to construct the concrete tunnel lining. Finally, a direct P-wave (DPW) measurement was used to compare and verify measurements recorded using the CSWP method. Results indicate that the combination of the SASW and IE methods, along with FFRC measurements, provides a more efficient procedure that leads to the accurate determination of the P-wave and shear wave velocities, depths of layers, and locations of embedded voids without the need to make any assumptions of material properties. Thus, more physical properties can be found using this proposed procedure than by using the techniques independently, and the procedure is more efficient than performing each task separately.     

露天矿中深孔柱状药包爆破应力场分布研究

文章建立了两组柱状药包模型及一组集中爆破药包模型,通过集中药包与柱状药包爆炸应力波传播特性的比较,得出二者在应力场动态分布及强度大小的不同及柱状药包的不同起爆方式下应力波的传播规律和应力分布的差别,进一步充实了柱状药包爆破理论。     

Discontinuous Galerkin Finite-Element Method for Transcritical Two-Dimensional Shallow Water Flows

A total variation diminishing Runge Kutta discontinuous Galerkin finite-element method for two-dimensional depth-averaged shallow water equations has been developed. The scheme is well suited to handle complicated geometries and requires a simple treatment of boundary conditions and source terms to obtain high-order accuracy. The explicit time integration, together with the use of orthogonal shape functions, makes the method for the investigated flows computationally as efficient as comparable finite-volume schemes. For smooth parts of the solution, the scheme is second order for linear elements and third order for quadratic shape functions both in time and space. Shocks are usually captured within only two elements. Several steady transcritical and transient flows are investigated to confirm the accuracy and convergence of the scheme. The results show excellent agreement with analytical solutions. For investigating a flume experiment of supercritical open-channel flow, the method allows very good decoupling of the numerical and mathematical model, resulting in a nearly grid-independent solution. The simulation of an actual dam break shows the applicability of the scheme to nontrivial bathymetry and wave propagation on a dry bed.     

子波穿过黏弹性节理的波形变化规律

将岩体和节理抽象为Kelvin黏弹性介质,建立谐波穿过黏弹性节理的传播模型,分析了谐波在黏弹性节理的透、反射系数和子波穿过节理后的波形变化规律。研究结果表明,黏弹性节理具有低通滤波特性,导致Ricker子波穿过黏弹性节理后,透射波振幅减小,主瓣不突出,波形在时域上变得更平缓;波形相关系数主要反映子波穿过黏弹性节理后发生的相位变化,而波形变化系数能综合反映子波的振幅和相位变化,因而两者描述子波波形变化时具有不同的变化规律;相对于切向刚度和切向黏性系数,节理的法向刚度和法向黏性系数对子波波形变化影响更大。