含梯度渐变残余应力的弹性半无限体的广义Rayleigh波

研究含梯度残余应力的弹性半无限体的平面应变型表面波,即广义Rayleigh波。将该结构等效为含梯度初应力的弹性覆盖层和无初应力的弹性基底构成的半无限体结构。求得覆盖层中位移函数的幂级数解与均质基底位移函数的解析解,并代入边界条件,得到频散方程。针对拉、压残余应力,分别讨论了其随厚度方向均匀分布、线性变化和指数变化情况下广义Rayleigh波的一阶模态频散特性。数值结果表明:随着拉应力增大,广义Rayleigh波波速会增加,反之,压应力的增大会导致波速的降低;残余应力均匀分布时波速的改变量较大,线性变化次之;当残余应力按照指数函数变化时,梯度参数越趋近于零,其结果越趋近于线性变化情况,随着梯度参数的减小,波速改变量也随之减小。当使用广义Rayleigh波频散特性实现残余应力无损检测时,如果采用与实际梯度渐变残余应力不符的均匀残余应力模型将会低估表面残余应力。本文所得结论可为利用广义Rayleigh波实现梯度残余应力无损检测提供理论基础。     

爆破作用下山岭隧道锚固壁动态响应及衬砌的影响研究

基于现场位移收敛计监测数据,利用FLAC3D研究了拱桥铺山岭隧道在底部爆破作用下锚固壁动态响应及衬砌的影响。研究结果表明:通过静载下位移对比及应力波传播规律分析,说明数值分析结果比较可靠;由于衬砌能够很好地限制隧道动态位移,所以使隧道拱底正下方1.42m范围内的垂直压应力峰值明显增大,在与拱脚同一水平方向9.51m范围内的垂直压应力峰值也明显增大,并且离拱脚越近增大越明显;隧道衬砌对锚固壁拱底位移、振动速度、振动加速度的运动规律没有影响,都是先向隧道中心方向运动;而其它监测点由于衬砌的"拱作用"使锚固壁位移、振动速度、振动加速度的运动规律相反,并且衬砌能使隧道锚固壁振动最强烈位置(拱底)的位移峰值、振动速度峰值、振动加速度峰值分别减小76.6%、9.4%和5.0%。     

平面P波在充满流体的任意形状孔洞上的散射

采用复变函数的保角映射方法和波函数展开法,根据孔洞与内部流体在界面上的应力和位移连续的边界条件,得到了充满流体的任意形状的孔洞对入射平面P波的散射问题的理论解,以椭圆形孔洞为例,着重分析了椭圆的长短轴之比、流体的存在与否以及入射频率对散射幅值的影响,结果表明:(1)圆形孔洞的分波波谱的峰值分布均匀,而椭圆形孔洞则不均匀;(2)散射P波的波谱主要集中于前进方向和背向一侧,而散射S波的波谱主要集中于与传播方向垂直的一侧;(3)入射波与孔洞的作用面积越大,散射P波的波谱也越大,而散射S波的波谱也越小;(4)当孔洞为圆形时,流体对散射P波和S波的波谱影响最小,即此时流体与孔壁的动力相互作用最小.     

各向异性对半圆形河谷散射影响的数值分析

半圆形河谷场地可构造为包含河谷的广义子结构和具有规则边界的开挖场地两部分,基于土-结构相互作用SSI原理,建立子结构控制方程。利用比例边界有限元SBFEM求解开挖场地动刚度,解析求解各向异性介质自由场qP波波动,将两者代入控制方程,可求得广义结构的动力响应。与文献中各向同性半空间中半圆形河谷在P波入射下的位移结果对比,验证了方法的精度和有效性。进一步分析了椭圆各向异性和非椭圆各向异性对半圆形河谷在qP波入射下位移分布的影响。数值算例显示,介质的各向异性改变了半圆形河谷散射位移的空间分布,增大了水平向位移的峰值;同时,介质的各向异性加剧了入射角对散射波场位移分布的影响。     

各向异性对半圆形河谷散射影响的数值分析

半圆形河谷场地可构造为包含河谷的广义子结构和具有规则边界的开挖场地两部分，基于土-结构相互作用SSI原理，建立子结构控制方程。利用比例边界有限元SBFEM求解开挖场地动刚度，解析求解各向异性介质自由场qP波波动，将两者代入控制方程，可求得广义结构的动力响应。与文献中各向同性半空间中半圆形河谷在P波入射下的位移结果对比，验证了方法的精度和有效性。进一步分析了椭圆各向异性和非椭圆各向异性对半圆形河谷在qP波入射下位移分布的影响。数值算例显示，介质的各向异性改变了半圆形河谷散射位移的空间分布，增大了水平向位移的峰值；同时，介质的各向异性加剧了入射角对散射波场位移分布的影响。     

含松软覆盖层V型峡谷对Rayleigh波的宽频散射

含松软覆盖层峡谷地形对地震动具有放大效应已被多次地震观测所证实。本文对Rayleigh波入射下V形覆盖层峡谷的地震反应进行宽频模拟,讨论了V形峡谷深度、覆盖层软硬程度、倾角以及波的频率等因素对地表位移幅值的影响。数值结果表明:在中低频段(量纲为一的频率η5.0),含覆盖层峡谷地形对地震波的放大效应显著。在高频波段(η10.0),覆盖层放大效应减弱甚至出现缩幅效应;随覆盖层深度增加,位移放大频段的带宽逐渐减小,第一峰值频率降低,且在低频段频谱曲线振荡剧烈;覆盖层越软,位移越大,峡谷表面位移空间变化越剧烈;峡谷右边界与水平面夹角不同,导致地表位移幅值的空间分布相差较大,在中低频时峡谷右侧的图线差异比较明显,在高频时变化差异不大。由此可见覆盖层软硬程度和形状对地震波聚焦特征也具有重要影响。     

流体饱和弹性半空间裂隙对平面P_I波的衍射

采用间接边界元法,求解了饱和半空间裂隙对平面PI波的二维衍射问题。基于单层位势理论,将边界离散并直接在边界单元上施加虚拟荷载(水平作用力、竖向作用力和流量源的叠加)以构造散射波场,并由边界条件确定虚拟荷载密度,总波场由自由波场和散射波场共同组成。通过参数分析研究了入射波频率、入射倾角、埋深、孔隙率、边界渗透条件等因素对饱和半空间中裂隙对平面PI波衍射的影响规律。结果表明:裂隙随埋深增大,地表位移谱振荡加剧,峰值有所降低;随着入射频率增加,孔隙率影响逐渐增大;垂直入射时,水平位移的放大区域主要分布在裂隙两端,斜入射时,主要集中在裂隙正上方地表附近;透水和不透水两种情况下的地表位移幅值和相位差别较小,但干土情况与饱和情况下的位移幅值相差较大。     

曲面曲率对Rayleigh波传播特性的影响

对任意形状的均匀各向同性线弹性曲面物体,用 WKB～（1）方法求解了沿曲面传播的Rayleigh表面波的运动微分方程,同时考虑了波传播方向及其垂直方向曲面曲率对波的穿透性的影, 所获波动方程的势函数解答表明,在一般情况下垂直波传播方向的曲面曲率对波的穿透深度的影响是不容忽视的.进而以同种介质平面表面情况下的Rayleigh面波的传播特性为基准,给出了曲面曲率引起波数或波速变化的解析表达式.通过理论分析和数值算例,描述了曲面上Rayleigh面波传播行为的一些基本特征.     

高速DSPI研究PLC剪切带成核演化过程

在适当的温度、应变率和预变形下,合金材料的拉伸试验中,将会出现伴随应力锯齿形跌落的雪崩式剪切变形带,即PLC(Portevin-Le Chatelier)效应。本文利用高速(1000 fps)数字散斑干涉法(DSPI),对不同加载应变率下,铝合金(LY10)试件中出现的连续(A-type)、间断(B-type)传播和随机(C-type)出现的三种PLC剪切带的瞬态成核与演化过程进行捕捉,通过对捕捉的试件表面系列散斑干涉图进行顺序相减处理,得到试件表面变形过程中位移的分布和演化系列条纹图。实验结果显示,对应于三种类型的剪切带,有两种主要的成核演化形式:1.A型剪切带的主要成核形式为先形成一个在观察平面上与拉伸轴方向成60°角并且横跨试件宽度的窄带,伴随着应力下落,剪切带开始沿自身宽度方向高速扩展达到最终宽度;2.对应于B、C型剪切带,先在观察平面上试件的一侧形成沿与拉伸轴方向呈60°角、长度约为最终长度一半的窄带。随着应力下落,带的前沿开始向试件的另一侧面沿自身长度方向传播,在传播过程中带逐渐沿自身宽度方向膨胀。带的前沿贯穿试件后,带开始高速膨胀,导致雪崩式剪切变形发生。     

考虑剪切面积修正的土的剪应力-剪切位移及强度分析

在直剪试验过程中,随着剪切位移的增大,试样的剪切面积不断减小,如果以恒定的剪切面积来计算,所得的剪应力是不真实的,为了克服以上缺点,通过理论推导,得到了不同剪切位移下的剪应力表达式。研究表明,本文所得剪应力比恒定剪切面积法所得剪应力大,其差值随剪切位移的增大而增大,随剪切面直径或边长的增大而变小。当试样的直径或剪切边长为6.18～50 cm,剪切位移为2～60 mm时,本文所得的土的粘聚力提高了4.9%～14.6%,内摩擦角提高了3.9%～13.4%。建议尽量使用剪切面积大的试样进行直剪试验。     

STEADY-STATE RESPONSE OF A TIMOSHENKO BEAM ON AN ELASTIC HALF-SPACE UNDER A MOVING LOAD

By introducing the equivalent stiffness of an elastic half-space interacting with a Timoshenko beam, the displacement solution of the beam resting on an elastic half-space subjected to a moving load is presented. Based on the relative relation of wave velocities of the half-space and the beam, four cases with the combination of different parameters of the half-space and the beam, the system of soft beam and hard half-space, the system of sub-soft beam and hard half-space, the system of sub-hard beam and soft half-space, and the system of hard beam and soft half-space are considered. The critical velocities of the moving load are studied using dispersion curves. It is found that critical velocities of the moving load on the Timoshenko beam depend on the relative relation of wave velocities of the half-space and the beam. The Rayleigh wave velocity in the half-space is always a critical velocity and the response of the system will be infinite when the load velocity reaches it. For the system of soft beam and hard half-space, wave velocities of the beam are also critical velocities. Besides the shear wave velocity of the beam, there is an additional minimum critical velocity for the system of sub-soft beam and hard half-space. While for systems of (sub-) hard beams and soft half-space, wave velocities of the beam are no longer critical ones. Comparison with the Euler-Bernoulli beam shows that the critical velocities and response of the two types of beams are much different for the system of (sub-) soft beam and hard half-space but are similar to each other for the system of (sub-) hard beam and soft half space. The largest displacement of the beam is almost at the location of the load and the displacement along the beam is almost symmetrical if the load velocity is smaller than the minimum critical velocity (the shear wave velocity of the beam for the system of soft beam and hard half-space). The largest displacement of the beam shifts behind the load and the asymmetry of the displacement along the beam increases with the increase of the load velocity due to the damping and wave radiation. The displacement of the beam at the front of the load is very small if the load velocity is larger than the largest wave velocity of the beam and the half space. The results of the present study provide attractive theoretical and practical references for the analysis of ground vibration induced by the high-speed train.     

Load motion along a beam on a viscoelastic half-space

An expression is derived for equivalent foundation of a viscoelastic half-space interacting with an Euler–Bernoulli beam. It is shown that this equivalent viscoelastic foundation depends on frequencies and wave numbers of the waves in the beam. The real and imaginary part of it substantially varies for phase velocities in between the Rayleigh and shear waves velocities. Radiation of elastic waves occurs for velocities larger than some velocity in that interval. The steady-state beam displacements due to a uniformly moving constant load are calculated for different velocities. The maximum displacement under the load takes place for a velocity of order of the Rayleigh waves velocity.     

Shock-Induced Borehole Waves and Fracture Effects

We perform wave experiments using a vertical shock tube setup. Shock waves are generated by the rupture of a thin membrane. In the test section the incident pressure waves generate borehole-guided waves along water-saturated samples. The tube is equipped with side wall gages and a mobile pressure probe, so that the attenuation and reflection of the wave can be measured. The computation for a single horizontal fracture intersecting a vertical borehole gives a quantitative prediction of reflection and transmission of borehole-guided waves. Three different fracture apertures are used for the calculation. Fracture aperture significantly affects both reflection and transmission coefficients. Large fractures increase reflectivity and decrease transmissivity. In the experiment, we found that both pressures above and below the fracture are influenced by the fracture aperture indeed, thus indicating the potential for fracture detection by borehole waves.     

Shock-Induced Borehole Waves and Fracture Effects

We perform wave experiments using a vertical shock tube setup. Shock waves are generated by the rupture of a thin membrane. In the test section, the incident pressure waves generate borehole-guided waves along water-saturated samples. The tube is equipped with side wall gages and a mobile pressure probe, so that the attenuation and reflection of the wave can be measured. The computation for a single horizontal fracture intersecting a vertical borehole gives a quantitative prediction of reflection and transmission of borehole-guided waves. Three different fracture apertures are used for the calculation. Fracture aperture significantly affects both reflection and transmission coefficients. Large fractures increase reflectivity and decrease transmissivity. In the experiment, we found that both pressures above and below the fracture are influenced by the fracture aperture indeed, thus indicating the potential for fracture detection by borehole waves.     

Experimental analysis of sand particles＇ lift-off and incident velocities in wind-blown sand flux

The probability distributions of sand particles' lift-off and incident velocities in a wind-blown sand flux play very important roles in the simulation of the wind-blown sand movement. In this paper, the vertical and the horizontal speeds of sand particles located at 1.0 mm above a sand-bed in a wind-blown sand flux are observed with the aid of Phase Doppler Anemometry (PDA) in a wind tunnel. Based on the experimental data, the probability distributions of not only the vertical lift-off speed but also the lift-off velocity as well as its horizontal component and the incident velocity as well as its vertical and horizontal components can be obtained by the equal distance histogram method. It is found, according to the results of the χ ²-test for these probability distributions, that the probability density functions (pdf's) of the sand particles' lift-off and incident velocities as well as their vertical components are described by the Gamma density function with different peak values and shapes and the downwind incident and lift-off horizontal speeds, respectively, can be described by the lognormal and the Gamma density functions. These pdf's depend on not only the sand particle diameter but also the wind speed.     

汶川地震地表破裂影响带调查与建筑场地避让宽度探讨

5.12汶川Ms8.0级地震沿龙门山中央断裂带形成长度约270km的地表破裂带,破裂带垂直和水平位移一般为1.0～5.0m,最大可达9.8m。在地表破裂带附近,建筑物破坏严重。笔者系统调查了龙门山中央断裂带地表破裂的垂直和水平位移以及地震地表破裂影响带宽度,并采用物探测试方法对部分影响带宽度进行了验证。统计结果表明,汶川地震地表破裂影响带宽度主要集中在16～60m,影响带宽度（D）与垂直位移（H）具有较好的线性关系,即D=10.11H+16.0。对于逆冲性质为主的地震地表破裂而言,上盘影响带宽度与下盘的比值一般为3：1～2：1,据此可确定地表破裂带上、下盘的避让带宽度。笔者根据现场调查并借鉴国外经验提出,上盘避让宽度下限一般不应低于15m,下盘避让宽度下限不应低于10m。本项研究对于汶川地震灾后重建场地选址具有重要的实际意义。
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多维地震波作用下地铁车站及场地的地震反应

研究了不同类型多维地震波作用下地铁车站及软土场地的地震反应特征。以上海软土场地条件下的某双层地铁车站为背景,采用有限元方法建立了描述场地土与地铁车站结构相互作用的二维非线性力学模型,其中利用等效线性化方法模拟了土的非线性。以不同类型基岩的多维(含水平向和竖向）地震波作为输入,运用ANSYS软件数值分析了软土场地中地铁车站结构及场地的地震反应,比较了不同类型地震波作用下地铁车站结构和场地地震反应的差异．算例结果表明：在长周期地震波作用下地铁车站结构的内力响应峰值以及场地地表的加速度响应峰值和位移响应峰值均明显大于普通地震波作用下的相应值;考虑竖向地震动时双层地铁车站底层中柱的柱底轴力较单一水平向地震动作用的情形有明显增大;地铁车站的存在使结构上覆土层加速度响应峰值和位移响应峰值有所降低．     

Experimental analysis of sand particles'' lift-off and incident velocities in wind-blown sand flux

The probability distributions of sand particles' lift-off and incident velocities in a wind-blown sand flux play very important roles in the simulation of the wind-blown sand movement. In this paper, the vertical and the horizontal speeds of sand particles located at 1.0 mm above a sand-bed in a wind-blown sand flux are observed with the aid of Phase Doppler Anemometry (PDA) in a wind tunnel. Based on the experimental data, the probability distributions of not only the vertical lift-off speed but also the lift-off velocity as well as its horizontal component and the incident velocity as well as its vertical and horizontal components can be obtained by the equal distance histogram method. It is found, according to the results of the χ²-test for these probability distributions, that the probability density functions (pdf's) of the sand particles' lift-off and incident velocities as well as their vertical components are described by the Gamma density function with different peak values and shapes and the downwind incident and lift-off horizontal speeds, respectively, can be described by the lognormal and the Gamma density functions. These pdf's depend on not only the sand particle diameter but also the wind speed. The project supported by the National Natural Science Foundation of China (10532040) and the Hundred Talents Project, the Knowledge Innovation Project of Chinese Academy of Sciences (KZCX2-304). The English text was polished by Keren Wang.     

On wave and fracture propagation in Rock Media

Experimental-stress-analysis techniques were used to study wave and fracture propagation in rock media. Marble and granite plates were loaded explosively. Wave propagation was observed through isochromatic-fringe patterns on bonded photoelastic coatings and moiré-fringe patterns. These patterns were recorded with a Beckman and Whitley camera operating at rates from 250,000 to 1,000,000 frames per second. Dilatational, shear and Rayleigh wave velocities were determined. The leading part of the pulse is compressive and shows appreciable attenuation. The trailing part goes into tension, causing widespread tensile fracture. The velocity of propagation of this fracture zone in marble was nearly equal to the theoretical terminal velocity. In the case of induced cracks in marble and granite, the velocities of crack propagation were appreciably lower than the theoretical terminal values. Experimental results obtained were discussed and interpreted for their relevance to the rapid-excavation process in rock.     

Gas-dynamic analogy for vortex free-boundary flows

The classical shallow-water equations describing the propagation of long waves in flow without a shear of the horizontal velocity along the vertical coincide with the equations describing the isentropic motion of a polytropic gas for a polytropic exponent γ = 2 (in the theory of fluid wave motion, this fact is called the gas-dynamic analogy). A new mathematical model of long-wave theory is derived that describes shear free-boundary fluid flows. It is shown that in the case of one-dimensional motion, the equations of the new model coincide with the equations describing nonisentropic gas motion with a special choice of the equation of state, and in the multidimensional case, the new system of long-wave equations differs significantly from the gas motion model. In the general case, it is established that the system of equations derived is a hyperbolic system. The velocities of propagation of wave perturbations are found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 8–15, May–June, 2007.