深隧道围岩分区破裂的数学模拟

该研究为先前深隧道围岩分区破裂现象内变量梯度塑性模型的进一步发展。利用应变梯度模型研究了深隧道围岩的分区破裂现象。作为额外的状态变量,在此引入应变梯度这一新变量。利用虚功原理得到了深隧道围岩的平衡方程、边界条件和流动准则,利用Clausius-Duhem不等式获得了岩体的本构方程。对于圆形深隧道,由上述模型的一般方程得到了弹性变形情况下、具有下降段的弹塑性变形情况下和不考虑弹性变形的塑性变形情况下圆形深隧道围岩的支配方程,得到了解析解,并讨论了解析解的性质。这一模型不仅扩展了隧道围岩的经典弹塑性模型,也为下一步数值研究深隧道围岩的分区破裂现象奠定了理论基础。     

Numerical modelling of rise and fall of a dense layer in salt diapirs

Numerical models are used to study the entrainment of a dense anhydrite layer by a diapir. The anhydrite layer is initially horizontally embedded within a viscous salt layer. The diapir is down-built by aggradation of non-Newtonian sediments ( n = 4, constant temperature) placed on the top of the salt layer. Several parameters (sedimentation rate, salt viscosity, perturbation width and stratigraphic position of the anhydrite layer) are studied systematically to understand their role in governing the entrainment of the anhydrite layer. High sedimentation rates during the early stages of the diapir evolution bury the initial perturbation and, thus, no diapir forms. The anhydrite layer sinks within the buried salt layer. For the same sedimentation rate, increasing viscosity of the salt layer decreases the rise rate of the diapir and reduces the amount (volume) of the anhydrite layer transported into the diapir. Model results show that viscous salt is capable of carrying separate blocks of the anhydrite layer to relatively higher stratigraphic levels. Varying the width of the initial perturbation (in our calculations 400–800 m), from which a diapir triggers, shows that wider diapirs can more easily entrain an embedded anhydrite layer than the narrower diapirs. The anhydrite layer is entrained as long as rise rate of the diapir exceeds the descent rate of the denser anhydrite layer. We conclude that the four parameters mentioned above govern the ability of a salt diapir to entrain an embedded dense layer. However, the model results show that the entrained blocks inevitably sink back if the rise rate of the diapir is less than the rate of descent of the anhydrite layer or the diapir is permanently covered by a stiff overburden in case of high sedimentation rates.     

Thin elastic shells with variable thickness for lithospheric flexure of one-plate planets

Planetary topography can either be modelled as a load supported by the lithosphere, or as a dynamic effect due to lithospheric flexure caused by mantle convection. In both cases the response of the lithosphere to external forces can be calculated with the theory of thin elastic plates or shells. On one-plate planets the spherical geometry of the lithospheric shell plays an important role in the flexure mechanism. So far the equations governing the deformations and stresses of a spherical shell have only been derived under the assumption of a shell of constant thickness. However, local studies of gravity and topography data suggest large variations in the thickness of the lithosphere. In this paper, we obtain the scalar flexure equations governing the deformations of a thin spherical shell with variable thickness or variable Young's modulus. The resulting equations can be solved in succession, except for a system of two simultaneous equations, the solutions of which are the transverse deflection and an associated stress function. In order to include bottom loading generated by mantle convection, we extend the method of stress functions to include loads with a toroidal tangential component. We further show that toroidal tangential displacement always occurs if the shell thickness varies, even in the absence of toroidal loads. We finally prove that the degree-one harmonic components of the transverse deflection and of the toroidal tangential displacement are independent of the elastic properties of the shell and are associated with translational and rotational freedom. While being constrained by the static assumption, degree-one loads can deform the shell and generate stresses. The flexure equations for a shell of variable thickness are useful not only for the prediction of the gravity signal in local admittance studies, but also for the construction of stress maps in tectonic analysis.     

Numerical inversion of deformation caused by pressure sources: application to Mount Etna (Italy)

The interpretation of geodetic data in volcanic areas is usually based on analytical deformation models. Although numerical finite element (FE) modelling allows realistic features such as topography and crustal heterogeneities to be included, the technique is not computationally convenient for solving inverse problems using classical methods. In this paper, we develop a general tool to perform inversions of geodetic data by means of 3-D FE models. The forward model is a library of numerical displacement solutions, where each entry of the library is the surface displacement due to a single stress component applied to an element of the grid. The final solution is a weighted combination of the six stress components applied to a single element-source. The pre-computed forward models are implemented in a global search algorithm, followed by an appraisal of the sampled solutions. After providing extended testing, we apply the method to model the 1993–1997 inflation phase at Mt Etna, documented by GPS and EDM measurements. We consider four different forward libraries, computed in models characterized by homogeneous/heterogeneous medium and flat/topographic free surface. Our results suggest that the elastic heterogeneities of the medium can significantly alter the position of the inferred source, while the topography has minor effect.     

Quasi-static analysis of strike fault growth in layered media

We study the effects of structural inhomogeneity on the quasi-static growth of strike-slip faults. A layered medium is considered, made up of an upper layer bounded by a free surface and welded to a lower half-space with different elastic property. Mode III crack is employed as a mathematical model of strike-slip fault, which is nucleated in the lower half-space and then propagates towards the interface. We adopt FEM-β, newly proposed analysis method for failure, to simulate the quasi-statistic crack growth governed by the stress distribution in layered media. Our results show that along planar traces across interfaces a compliant upper layer has significant effects on promoting/suppressing crack growth before/after its extension into the layer and vice versa for a rigid one. This proposes a possibility that surface breaks due to strike-slip faulting could be arrested by deposit layers at the topmost part of the Earth's crust.     

Seismic radiation from dynamic coalescence, and the reconstruction of dynamic source parameters on a planar fault

The dynamic coalescence of two mode II cracks on a planar fault is simulated here using the elastodynamic boundary integral equation method. We focus on the complexity of the resultant slip rate and seismic radiation in the crack coalescence model (CCM) and on the reconstruction of a single crack model (SCM) that can reproduce the CCM waveforms from heterogeneous source parameters rather than coalescence. Simulation results reveal that localized higher slip rates are generated by coalescence as a result of stress interaction between the approaching crack tips. The synthesized seismic radiation exhibits a distinct coalescence phase that has striking similarities to stopping phases in the radiation and propagation properties. The corresponding SCM yields a singular increase in the stress drop distribution, which is accompanied by a sudden decrease in it across the point of coalescence in the CCM. This implies that the generation of high-frequency radiation is more efficient from coalescence than from stopping, although both phenomena exhibit the same strong  ω⁻²  -type displacement spectra.     

基于GPS的华北地区地壳水平形变特征研究

利用中国大陆构造环境监测网络2009、2011年2期的GPS数据资料,计算得到华北地区相对于稳定的欧亚板块的区域水平速度场。根据水平速度场,基于连续变形假说,采用三角形方法计算了区域应变场特征值,并用GMT绘制了其分布图像。结合地震地质资料对该区的地壳水平形变特征进行分析研究,得出了有意义的结论:(1)水平相对运动与应变率场分布显示,板块交界处的断裂带及其附近区域地壳运动差异显著,应变率量值较为突出;(2)山西断陷带的活动方式与地质结果具有差异性;(3)区内最大剪应变、面膨胀的高值区主要位于环渤海的京津唐地区、山西断陷带中南部及郯庐断裂带中南段。     

沂沭断裂带构造区光弹实验与地震危险区判定研究

在对沂沭断裂带的地质构造环境、断裂带分布特征进行详细分析的基础上,采用聚碳酸酯材料制成沂沭断裂带构造区域的地质模型,分别运用集中、2点和均布等加载方式,使用光弹实验方法模拟特定构造框架下应力、应变场的变化特征。通过对光弹实验数据的分析,在对比不同加载方式下应力积累区域和地震危险区的基础上判定沂沭断裂带构造区中的地震危险区域。