初期支护对软岩隧道围岩稳定性和位移影响分析

软弱岩体隧道开挖后,围岩变形具有异常显著的流变性。基于Poyting-Thomoson模型,对隧道围岩位移进行了粘弹性解析分析,根据所得出的解析解,结合渝（重庆）沙（长沙）高速公路石龙隧道位移监控量测实践,对初期支护后隧道围岩变形特征量进行了分析对比,结果表明,理论曲线能较好地反映围岩实际位移变化特征。最后通过将支护前后围岩受力状态与单轴和三轴应力状态岩石蠕变进行类比,得知初期支护在一定程度上减小了围岩的最终变形量,可以有效地抑制隧道围岩的变形速率。其结果为确定合理的二次支护时机提供了理论依据,对同类隧道的施工支护具有很好的指导意义和较高的参考价值。     

Research for time-temperature equivalence effect of rock (I):Theory research

In order to know about the rheological properties of rock in a long range of the time scale,method of increasing temperature was brought forward to accelerate the rheological process of rock,which could extend the time scale of experimental test data.Firstly,based on the generalized linear viscoelastic constitutive equation with temperature variable,the creep behavior of rock was divided into three types according to the different strain dependences of the time,that is,Hookean deformation,Newtonian flow,and retarded elasticity.Then the general equivalence relationship between time parameter and temperature parameter was derived for each type of strain.Finally,the relation between time parameter and temperature parameter in the whole creep was considered and the general theory of time-temperature equivalence effect(TTEE) of rock was established.This research reveals: ①The temperature effect on the instantaneous strain could be modified through vertical shift.②The key point of the TTEE of Newtonian flow depends on whether in the study of linear viscoelastic behavior of rock change of temperature is completely equivalent to a shift of the logarithmic time scale or not.③By plotting the results of a creep experiment performed at different temperatures and comparing the curves obtained,one can decide whether the rock considered have TTEE.④The TTEE of the whole creep should satisfy that the horizontal shift function of Newtonian flow and retarded elasticity is consentaneous.     

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。     

Semi-Analytic Modelling of Subsidence

This paper presents a forward model for subsidence prediction caused by extraction of hydrocarbons. The model uses combinations of analytic solutions to the visco-elastic equations, which approximate the boundary conditions. There are only a few unknown parameters to be estimated, and, consequently, calculations are very fast. The semi-analytic model is applicable to a uniform and layer-cake stratigraphy, with visco-elastic parameters changing per layer, and an arbitrary depletion pattern. By its capabilities to handle a multi-layered visco-elastic subsurface, the semi-analytic model fills the gap between the analytic single-layered elastic models available to date and the more elaborate numerical, e.g. finite element, models.     

基于谱元法的各向异性黏弹性介质地震波场模拟和分析

基于谱元法计算理论,通过坐标旋转算法实现任意各向异性黏弹性介质中的地震波场计算,研究复合介质中地震波场特征。根据计算结果,qSV波表现为剪切滞弹性形变,qP波表现为膨胀滞弹性形变;品质因子不仅影响地震波振幅,还影响其传播频率;黏弹性介质吸收高频快,在一定频率范围内,黏弹性介质没有频散现象。     

SH Wave Propagation in Viscoelastic Media

When comparing solutions for the propagation of SH waves in plane parallel layered elastic and viscoelastic (anelastic) media, one of the first things that becomes apparent is that in the elastic case the location of the saddle points required to obtain a high frequency approximation are located on the real p axis. This is true of the branch points also. In a viscoelastic medium this is not typical. The saddle point corresponding to an arrival lies in the first quadrant of the complex p-plane as do the branch points. Additionally, in the elastic case the saddle point and branch points lie on a straight line drawn through the origin (the positive real axis in the complex p-plane), while in the viscoelastic case this is generally not the case and the saddle point and branch points lie in such a manner as to indicate the degree of their complex values.In this paper simple SH reflected and transmitted particle displacement arrivals due to a point torque source at the surface in a viscoelastic medium composed of a layer over a half space will be considered. The path of steepest descent defining the saddle point in the first quadrant will be parameterized in terms of a real variable and the high frequency solutions and intermediate analytic results obtained will be used to formulate more specific constraints and observations regarding saddle point location relative to branch point locations in the complex p-plane.As saddle point determination for an arrival is, in general, the solution of a non-linear equation in two unknowns (the real and imaginary parts of the complex saddle point p ₀), which must be solved numerically, the use of analytical methods for investigating this problem type is somewhat limited.Numerical experimentation using well documented solution methods, such as Newton's method, was undertaken and some observations were made. Although fairly basic, they did provide for the design of algorithms for the computation of synthetic traces that displayed more efficient convergence and accuracy than those previously employed. This was the primary motivation for this work and the results from the SH problem may be used with minimal modifications to address the more complicated subject of coupled P-SV wave propagation in viscoelastic media.Another reason for revisiting a problem that has received some attention in the literature was to approach it in a fairly comprehensive manner so that a number of specific observations may be made regarding the location of the saddle point in the complex p-plane and to incorporate these into computer software. These have been found to result in more efficient algorithms for the SH wave propagation and a significant enhancement of the comparable software in the P-SV problem.     

方位各向异性粘弹性介质波场数值模拟

当地震信号通过复杂地球介质时,地层除了表现为各向异性,还表现为内在的粘弹性特征.因此,为准确描述地震波在地球介质中的传播特征,理想的地球介质模型应该能够模拟岩石的各向异性特征和衰减特征.本文给出了各向异性粘弹性介质模型的波动方程及其差分格式,并利用有限差分法实现了地震波波场数值模拟.结果表明了该介质模型中地震波场特征与各向异性主轴方位和介质的粘滞性参数之间的关系.     

适用于更广渗透率范围含泥质砂岩的广义粘弹性BISQ模型

To simultaneously take into account the Biot-flow mechanism, the squirt-flow mechanism, and the frame-viscoelasticity mechanism, a generalized viscoelastic BISQ （Biot/squirt） model is developed for wave propagation in clay-bearing sandstones based on Dvorkin＇s elastic BISQ model. The present model is extended to a wide range of permeabilities （k 〉 0.05 mD） by introducing a dimensionless correction factor for viscoelastic parameters, defined as a function of the permeability and the clay content. We describe the frame＇s stress-strain relationship of the clay-bearing sandstones by the differential constitutive equations of generalized viscoelasticity and then derive the viscoelastic-wave dynamic equations. With the assumption of a plane-wave solution, we finally yield the phase velocities and the attenuation coefficients by solving the dynamic wave equations in the frequency and wave number domain. The comparison of numerical results and experimental data shows that the generalized viscoelastic BISQ model is applicable for modeling the wave propagation in most of the sandstones mainly bearing kaolinite clay.     

黏弹性介质中瑞利波频散曲线和衰减系数曲线的反演

瑞利波具有能量大、信噪比高等特点,可以用来反演介质内部的力学信息,近年来在浅层地球物理勘探、深层地震学研究以及超声波无损检测等多个领域都有较广泛的应用。目前大多数瑞利波的应用中都假设介质是弹性的,然而实际中岩石、土壤和金属等介质都在一定程度上体现出了黏弹性。当介质的黏弹性较强时仍然采用弹性假设研究其中瑞利波的反演将增大误差,因此有必要考虑黏弹性介质中的瑞利波反演,但是目前这方面的研究仍不够深入。本文研究黏弹性介质中瑞利波频散曲线和衰减系数曲线的反演问题,给出其在半空间中联合反演的方法,并对该方法的误差进行分析。     

Influence of the quality factor on simulated seismic waves: A case study of the 1994 Northridge earthquake

In numerical simulations of ground motion, the constant quality factor Q of a viscoelastic medium can be determined using the time-domain constitutive approximation method of the generalized standard linear solid (GSLS) model. This study introduces a numerical seismic wavefield simulation method which combines the spectral element method with the constant-Q model. The method is used to simulate the seismic wavefield of the 1994 Northridge earthquake. The optimal attenuation coefficient for the simulated seismic waves in this study area is determined empirically based on a quantitative analysis of the deviation curve. Further, the effect of the quality factor on the simulated wavefield are analyzed according to the site characteristics of each seismic station. The quality factor shows a variable effect on the different frequency components of the simulated wavefield. The effect of the quality factor also varies with the characteristic parameters of each seismic station site, such as site velocity structure, fault distance, and azimuth angle.