Mechanical and transport constitutive models for fractures subject to dissolution and precipitation

Transient changes in the permeability of fractures in systems driven far‐from‐equilibrium are described in terms of proxy roles of stress, temperature and chemistry. The combined effects of stress and temperature are accommodated in the response of asperity bridges where mineral mass is mobilized from the bridge to the surrounding fluid. Mass balance within the fluid accommodates mineral mass either removed from the flow system by precipitation or advection, or augmented by either dissolution or advection. Where the system is hydraulically closed and initially at equilibrium, reduction in aperture driven by the effects of applied stresses and temperatures will be augmented by precipitation on the fracture walls. Where the system is open, the initial drop in aperture may continue, and accelerate, where the influent fluid is oversaturated with respect to the equilibrium mineral concentration within the fluid, or may reverse, if undersaturated. This simple zero‐dimensional model is capable of representing the intricate behavior observed in experiments where the feasibility of fracture sealing concurrent with net dissolution is observed. This zero‐order model is developed as a constitutive model capable of representing key aspects of changes in the transport parameters of the continuum response of fractured media to changes in stress, temperature and chemistry. Copyright © 2009 John Wiley & Sons, Ltd.     

Micromechanical modeling for rate‐dependent behavior of salt rock under cyclic loading

The dependence of rock behavior on the deformation rate is still not well understood. In salt rock, the fundamental mechanisms that drive the accumulation of irreversible deformation, the reduction of stiffness, and the development of hysteresis during cyclic loading are usually attributed to intracrystalline plasticity and diffusion. We hypothesize that at low pressure and low temperature, the rate‐dependent behavior of salt rock is governed by water‐assisted diffusion along grain boundaries. Accordingly, a chemo‐mechanical homogenization framework is proposed in which the representative elementary volume (REV) is viewed as a homogeneous polycrystalline matrix that contains sliding grain‐boundary cracks. The slip is related to the mass of salt ions that diffuse along the crack surface. The relationship between fluid inclusion‐scale and REV‐scale stresses and strains is established by using the Mori–Tanaka homogenization scheme. It is noted from the model that a lower strain rate and a larger number of sliding cracks enhance stiffness reduction and hysteresis. Thinner sliding cracks (i.e., thinner brine films) promote stiffness reduction and accelerate stress redistributions. The larger the volume fraction of the crack inclusions, the larger the REV deformation and the larger the hysteresis. Results presented in this study shed light on the mechanical behavior of salt rock that is pertinent to the design of geological storage facilities that undergo cyclic unloading, which could help optimize the energy production cycle with low carbon emissions.     

Analytical solutions for Euler‐Bernoulli Beam on Pasternak foundation subjected to arbitrary dynamic loads

In this paper, the dynamic response of an infinite beam resting on a Pasternak foundation and subjected to arbitrary dynamic loads is developed in the form of analytical solution. The beam responses investigated are deflection, velocity, acceleration, bending moment, and shear force. The mechanical resistance of the Pasternak foundation is modeled using two parameters, that is, one accounts for soil resistance due to compressive strains in the soil and the other accounts for the resistance due to shear strains. Because the Winkler model only represents the compressive resistance of soil, comparatively, the Pasternak model is more realistic to consider shear interactions between the soil springs. The governing equation of the beam is simplified into an algebraic equation by employing integration transforms, so that the analytical solution for the dynamic response of the beam can be obtained conveniently in the frequency domain. Both inverse Laplace and inverse Fourier transforms combined with convolution theorem are applied to convert the solution into the time domain. The solutions for several special cases, such as harmonic line loads, moving line loads, and travelling loads are also discussed and numerical examples are conducted to investigate the influence of the shear modulus of foundation on the beam responses. The proposed solutions can be an effective tool for practitioners. Copyright © 2017 John Wiley & Sons, Ltd.     

An analytical model for vapor‐phase volatile organic compound diffusion through landfill composite covers

One‐dimensional mathematical models for vapor‐phase volatile organic compound (VOC) diffusion through composite cover barriers are presented. An analytical solution to the model was obtained by the method of separation of variables. The results obtained by the proposed solution agree well with those obtained by a numerical analysis. Based on the proposed analytical model, the VOC breakthrough curves of five different composite covers are compared. The effects of degree of saturation of geosynthetic clay liner (GCL) or compacted clay liner (CCL) on VOC migration in the composite covers are then presented. Results show that the composite cover barriers provide much better diffusion barriers for VOC than the single CCL. The top surface steady‐state flux for a composite barrier, consisting of a 1.5 mm geomembrane (GM) and a 20 cm CCL, can be 8.3 times lower than that for a 30 cm CCL. The surface steady‐state flux for the case with (1.5 mm GM + 6 mm GCL) was found to be 2.3 times lower than that for the case with (1.5 mm GM + 20 cm CCL). The degree of saturation S_r of the CCL has a great influence on VOC migration in composite covers when S_r is larger than 0.5. The steady‐state flux at the surface of GM for the case with S_r = 0.7 can be 1.8 times lower than that for the case with S_r = 0.2. The proposed analytical model is relatively simple and can be used for verification of complicated numerical models, analysis of experimental data and performance assessment of composite cover barriers. Copyright © 2016 John Wiley & Sons, Ltd.     

A general solution for groundwater flow in an estuarine's leaky aquifer system after considering aquifer anisotropy

This paper presents an analytical model for describing the tidal effects in a two‐dimensional leaky confined aquifer system in an estuarine delta where ocean and river meet. This system has an unconfined aquifer on top and a confined aquifer on the bottom with an aquitard in between the two. The unconfined and confined aquifers interact with each other through leakage. It was assumed that the aquitard storage was negligible and that the leakage was linearly proportional to the head difference between the unconfined and confined aquifers. This model's solution was based on the separation of variables method. Two existing solutions that deal with the head fluctuation in one‐dimensional or two‐dimensional leaky confined aquifers are shown as special cases in the present solution. Based on this new solution, the dynamic effect of the water table's fluctuations can be clearly explored, as well as the influence of leakage on the behaviour of fluctuations in groundwater levels in the leaky aquifer system. Copyright © 2015 John Wiley & Sons, Ltd.     

Timoshenko beam solution for the response of existing tunnels because of tunneling underneath

An analytical solution for the deflection and internal forces of an existing tunnel because of tunneling underneath is presented. The existing tunnel is modeled as a Timoshenko beam resting on a Winkler foundation, which takes into account the contribution of shear deformation to the total deflection of the existing tunnel. The validity of the analytical solution is verified by a centrifuge test, and the merit of this analytical method is confirmed by comparison with the conventional Euler–Bernoulli beam model. Influential factors on the behavior of the existing tunnel are investigated by consideration of the variations of subgrade modulus, ground loss induced by the new tunnel construction, vertical clearance between the new tunnel and the existing tunnel, and relative existing tunnel–soil stiffness. Results show that the proposed analytical method is a valid and effective method to evaluate shearing‐induced deformation in existing tunnels with large diameters. Results also show that the pattern and the amplitude of the response of the existing tunnel are affected largely by ground loss induced by the new tunnel construction, vertical clearance between the new tunnel and the existing tunnel, and relative existing tunnel–soil stiffness. Copyright © 2015 John Wiley & Sons, Ltd.     

多GNSS系统组合PPP定位精度评估

采用MGEX网提供的GPS、GLONASS、BDS、GALILEO四系统双频观测数据,以CODE、GBM、WUM、GRG精密产品进行了静/准动态模式下多系统组合无电离层延迟PPP浮点解与整数钟法固定解实验。结果表明多系统的组合提升了定位精度,尤其是GLONASS的加入效果最明显,CODE与GBM产品的解算精度优于WUM、GRG产品。部分模糊度固定相比全模糊度固定的效果显著,模糊度固定明显缩短了PPP收敛时间,在静态模式下相对浮点解精度提升10%以内,动态模式下E方向与U方向精度提升效果最好。     

广义Khasminskii条件下非线性混杂随机时滞微分方程的解的存在唯一性

利用广义伊藤公式证明了混杂随机时滞微分方程(SDDE)在局部Lipschitz和广义Khasminskii条件下存在唯一解,从而涵盖了一大类非线性混杂SDDE.最后给出实例说明了理论的可行性.     

非均匀地基与均匀地基一维固结解答之间的转换关系

基于一维固结理论,研究了土层物理力学性质沿深度非均匀连续变化的固结问题。首先,利用分离变量法,获得了渗透系数和压缩系数随深度按指数函数变化的非均匀地基一维固结方程的解析表达式; 然后与Terzaghi固结理论的经典解答进行了比较,获得了两种解答之间的相似转换关系。这样,非均匀地基固结问题就可以用相同荷载以及边界条件下的均匀地基固结的经典解线性表示。因此,非均匀地基固结问题的求解转化为对相似转换系数的计算。该系数集中反映土层非均匀性对地基固结的影响,从而为解决非均匀地基一维固结问题提供了便捷途径。     

河北省涞源县木吉村铜(钼)多金属矿田成矿物质来源探讨

木吉村铜(钼)矿田位于太行山脉中、北段阜平幔枝构造的北东倾伏端,涞源哑铃状杂岩体连接处西侧上盘拆离带的次级断陷盆地中,主要由斑岩型铜(钼)矿、矽卡岩型铁铜矿和外围热液脉型铅锌矿构成,是河北省目前探明的唯一大型铜(钼)多金属矿田,找矿远景巨大。鉴于矿床成矿物质来源在研究矿床成因和指导找矿中的重要作用,对木吉村矿田主要矿床矿石中黄铁矿、黄铜矿、方铅矿、辉钼矿、磁铁矿、石英和石膏等单矿物进行了硫、铅、碳、氢、氧、硅、铼等同位素测定、对比和分析。结果表明:矿田中硫同位素主值域δ34S=-3.5‰~3.2‰,主平均值为0.3‰;铅同位素206 Pb/204 Pb=15.566 0~17.072 0,平均为16.547 0,207Pb/204Pb=15.031 0~15.523 0,平均为15.258 0,208 Pb/204 Pb=36.292 0~37.375 0,平均为36.721 0;碳同位素δ13 C为-2.94‰~-2.18‰,平均为-2.62‰;硅同位素δ30 SiNBS-28值域为-0.3‰~0.2‰,平均0.0‰;辉钼矿w(Re)为(23.65~266.50)×10-6,平均值为142.33×10-6;δ18 OH2O值为-10.64‰~7.70‰,极差为18.34‰,平均值为-1.47‰,较标准岩浆水值稍低,δD值为-148.4‰~-89.0‰,极差为59.4‰,平均值为-113.7‰,略低于岩浆岩δD值域。从而认为,木吉村矿田成矿物质主要来源于地球深部,成矿溶液以岩浆水为主,部分来自大气降水。