基于Copula理论的粗粒土渗透破坏临界水力比降估值

破坏水力比降是土体渗透稳定性分析和渗流控制的基础。以渗透变形试验为基础,分析了粗粒土临界水力比降与孔隙比、级配不均匀系数和曲率系数间的相关性。利用Copula理论适合建立多个非独立变量间联合分布函数的优点,构造了拟合粗粒土临界水力比降 、孔隙比e、级配不均匀系数 和曲率系数 间相关关系的最优Copula函数,并将其应用于粗粒土临界水力比降估值。结果表明：具有单参数的四维对称Archimedean Copula函数的Nelsen No 6为最优Copula函数。利用构造的最优Copula函数求条件概率,便可得到粗粒土临界水力比降估值的保证率,或者计算在一定保证率条件下临界水力比降估值。通过比较临界水力比降试验值与Copula理论方法、Terzaghi公式及刘杰公式估值,阐述了Copula理论的可靠性,为建立粗粒土临界水力比降与孔隙比及级配特征的多变量统计概率关系及临界水力比降估值提供了一种新途径。     

A Thermodynamics-Based Model on the Internal Erosion of Earth Structures

The present paper describes a model of internal erosion of earth structures, based on rigorous thermodynamic principles and the theory of porous media. A particular focus of this paper is concerned with the initial stage of internal erosion, when the pore volume forms a continuous network, without the formation of macroscopic cavities or channels. The continuum approach is applicable in this case. The soil skeleton saturated by a pore fluid is treated as the superposition of three continua in interaction, with independent velocity fields. The pore fluid itself consists of a mixture of water and eroded particles. The erosion kinetics is based on the shear stress developed at the solid–fluid interface. The applicability of the model is illustrated by numerical simulations based on the finite element method. These simulations show how the phenomenon of piping can progressively arise, and preferentially in regions where hydraulic gradients are critical. Effects of mechanical degradations due to internal erosion are at the same time demonstrated.     

Parameters affecting the occurrence of quicksand and the drying up of large diameter wells that gain water from the bottom: a case study from Iran

Large diameter fully cased wells that gain water from the bottom are often dug in sandy and collapsible aquifers. They have cylindrical vertical walls lined with brick or concrete. The well bottom is partially filled with aquifer material through which the flow is vertically upward. When the vertical hydraulic gradient reaches a critical value, quicksand occurs and the well structure can be destroyed. Another difficulty encountered is drawdown in the wellbore and the drying up of the well. To overcome these problems, the flow around and beneath these wells is numerically simulated. The simulation results are used to investigate the effect of well and aquifer parameters on quicksand and drawdown. For practical purposes, the dimensionless drawdown-time and dimensionless vertical gradient-time curves are developed. It was found that the ratio of filling material thickness to well radius affects the shape of these type curves. The type curves may be used to predict the time after pumping commences when quicksand occurs and the well dries up. They are also useful to design the safe pumping rate and duration as well as the optimum well radius. These are demonstrated by analyzing the pumping test data from a case study in the arid Chah Kutah region, southern Iran.     

Understanding multiple thresholds of coupled social–ecological systems exposed to natural hazards as external shocks

External suffusion, as selective erosion of fine particles through the contact with a coarser layer and moving away, is an important phenomenon in dams which may lead to their failure. To study the initiation of external suffusion, caused by water level increase upstream the dam, a series of experimental investigations were conducted on laboratory-scale model, in the hydrodynamic laboratory of école polytechnique de Montreal. On the built model, clay/moraine formed the core, sand was used as a filter and gravel performed the role of the pervious layer. Several different models (in geometry and constituent materials) were built and subjected to the water level increase upstream, which resulted in changes in the hydraulic gradient. The results showed no evidence of considerable suffusion on the clay/moraine and sand interface, while the visual and quantitative data show the presence of suffusion on the sand and gravel interface. The results of the experiments show that, when focusing on the critical hydraulic gradient that initiates the movement of the clay/moraine particles, it can be concluded that despite the differences in test conditions, the critical hydraulic gradient has approximately the same value in all cases. It was also shown that increasing the length of the filter layer or applying stair-like slopes does not have great impacts on the initiation of suffusion, whereas the gravel-size distribution has a great impact on the erosion rate.     

Analysis of Steady-State Flow To Multiscreened Wells Under Natural Vertical Flow Conditions

Water levels measured at multiscreened wells in unconfined aquifers may not coincide, in general, with the elevation of the water table. The presence of vertical gradients (as often is the case in recharge areas) or the existence of confining layers may cause the water levels to differ from local hydraulic heads in the aquifer. In these cases, a misinterpretation of water levels may lead to the erroneous conclusion that observed drawdowns are provoked by overpumping. In this paper, we analyze the effect that a natural vertical gradient has on water levels in wells screened over their entire saturated thickness. As one would expect, it is observed that, even without pumping, the water level in the wells lies below the water table. Type curves relating the steady-state drawdown to the vertical gradient and to the hydraulic conductivity anisotropy are presented. These curves were obtained using a groundwater flow numerical model (FREESURF: Neuman and Witherspoon, 1970). The theoretical results are checked with field data from deep wells in the detrital Madrid aquifer. In this particular aquifer, it is observed that the effect of vertical gradients is important both in terms of drawdowns and flow rates.

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A coupled 3‐dimensional bonded discrete element and lattice Boltzmann method for fluid‐solid coupling in cohesive geomaterials

This paper presents a 3D bonded discrete element and lattice Boltzmann method for resolving the fluid‐solid interaction involving complicated fluid‐particle coupling in geomaterials. In the coupled technique, the solid material is treated as an assembly of bonded and/or granular particles. A bond model accounting for strain softening in normal contact is incorporated into the discrete element method to simulate the mechanical behaviour of geomaterials, whilst the fluid flow is solved by the lattice Boltzmann method based on kinetic theory and statistical mechanics. To provide a bridge between theory and application, a 3D algorithm of immersed moving boundary scheme was proposed for resolving fluid‐particle interaction. To demonstrate the applicability and accuracy of this coupled method, a benchmark called quicksand, in which particles become fluidised under the driving of upward fluid flow, is first carried out. The critical hydraulic gradient obtained from the numerical results matches the theoretical value. Then, numerical investigation of the performance of granular filters generated according to the well‐acknowledged design criteria is given. It is found that the proposed 3D technique is promising, and the instantaneous migration of the protected soils can be readily observed. Numerical results prove that the filters which comply with the design criteria can effectively alleviate or eliminate the appearance of particle erosion in dams.     

Prevention of water and quicksand inrush during extracting contiguous coal seams under the lowermost aquifer in the unconsolidated Cenozoic alluvium—a case study

Extracting the contiguous coal seams under the lowermost aquifer in the unconsolidated Cenozoic alluvium is apt to water and quicksand inrush. By using a series of investigation methods including empirical formulas, numerical simulation, theoretical analysis, etc., the study focused on the fracture and the excess pore water pressure in the overlying strata in the process of extracting no. 8 coal seam firstly and no. 9 coal seam (under no. 8 coal seam) subsequently in no. 8102 working face of Luling coal mine in the north of Anhui Province of China. When no. 8 coal seam was extracted, the water-conducting fractured zone penetrated into the lowermost aquifer and rapid dissipation of excess pore water pressure above the gob occurred, accompanied by relatively high seepage hydraulic gradient over the headgate and the tailgate. When no. 9 coal seam was extracted, failure did not obviously extend upwards and the excess pore water pressure decreased slowly and a relatively high seepage hydraulic gradient transferred downwards from the headgate to the tailgate in the inclined profile. The safe water head (H _s) in the lowermost aquifer was confirmed to 15.6 m. Therefore, water and quicksand inrush was avoided effectively in the process of extracting the contiguous coal seams by dewatering, controlling mining height, and laying double resistance nets in the working face.     

A multidimensional fuzzy least-squares regression approach for estimating hydraulic gradients in unconfined aquifer formations and its application to the Gulf Coast aquifer in Goliad County,Texas

Epistemic uncertainties arise during the estimation of hydraulic gradients in unconfined aquifers due to planar approximation of the water table as well as data gaps arising from factors such as instrument failures and site inaccessibility. A multidimensional fuzzy least-squares regression approach is proposed here to estimate hydraulic gradients in situations where epistemic uncertainty is present in the observed water table measurements. The hydraulic head at a well is treated as a normal (Gaussian) fuzzy variable characterized by a most likely value and a spread. This treatment results in hydraulic gradients being characterized as normal fuzzy numbers as well. The multidimensional fuzzy least-squares regression has an exact analytical form and as such can be implemented easily using matrix algebra methods. However, the method was noted to be sensitive to round-off and truncation errors when the epistemic uncertainties are small. A closeness index based on the cardinality of a fuzzy number is used to evaluate how well the regression model fits the fuzzy hydraulic head observations. A fuzzy Euclidian distance measure is used to compare two fuzzy numbers and to evaluate how fuzziness in the observed hydraulic heads affects the fuzziness in the estimated hydraulic gradients. The Euclidian distance measure is also used to ascertain the influence of each well on the fuzzy hydraulic gradient estimation. The fuzzy regression framework is illustrated by applying it to evaluate hydraulic gradients in the unconfined portion of the Gulf Coast aquifer in Goliad County, TX. The results from the case-study indicate that there is greater uncertainty associated with the estimation of the hydraulic gradients in the vertical (Z-axis) direction. The epistemic uncertainties in the hydraulic head data at the wells have a significant impact on the gradient estimates when they are of the same order of magnitude as the most likely values of the observed heads. The influence analysis indicated that 5 of the 13 wells in the network had a critical influence on at least one of the hydraulic gradients. Three wells along the northeastern section of the study area and bordering the Victoria County were noted to have the least influence on the regression estimates. The fuzzy regression framework along with the associated goodness-of-fit and influence measures provides a useful set of tools to characterize the uncertainties in the hydraulic heads and gradients arising from data gaps and planar water table approximation.     

Effect of sand lenses on groundwater flow and contaminant migration

The effect of homogeneous sand lenses on the groundwater flow in an otherwise homogeneous clayey deposit is examined by performing Monte Carlo simulations using a finite element flow model. In the simulations, the locations of the sand lenses are assumed to be mutually independent. The paper examines the effect on the flow field in a clayey deposit of (a) different percentages of sand lenses, (b) different hydraulic conductivities of the sand lenses, (c) different average sand lens sizes, (d) non-uniformity of the sizes of the sand lenses, and (e) localization of the sand lenses. The effect of these non-uniform flow fields on contaminant migration is then examined using a finite element contaminant transport model. For the range of cases considered it is shown that: the volume of sand lenses present has a greater influence than the shape, size, location and hydraulic conductivity of the sand lenses; simplified calculations performed using the geometric and harmonic means of hydraulic conductivity bracket the behaviour evident from more complex analyses; and the maximum impact on an aquifer separated from a waste disposal facility by a deposit containing sand lenses can be modelled to sufficient accuracy, using quite simple flow and contaminant transport models.     

Stability of sandy slopes under seepage conditions

Stability against shallow mass sliding in saturated sandy slopes under seepage depends on the flow direction and hydraulic gradient, particularly near the ground surface. Two modes of instability i.e., Coulomb sliding and liquefaction have been studied and the critical flow directions discussed. The utility of the numerical approach in solving complex flow problems with irregular boundaries and surface topography is demonstrated by means of two slope examples with different internal drainage conditions. The numerical results for the seepage gradients at different points are compared with those predicted by the simple expression derived in this study, and the corresponding effects on the stability are evaluated.     

The role of pore pressure during hydraulic fracturing and implications for groundwater outbursts in mining and tunnelling

Water outbursts from the floor during underground mining, and those from the surrounding rock mass of tunnels, involve the basic principle of hydraulic fracturing. Based on the hydraulic-fracturing mechanism, considered to be dependent on the coupling between seepage and damage, it is deemed that the variation of the pore-fluid pressure coefficient must be taken into account during this coupled process, in order to correctly establish the crack propagation mechanism during hydraulic fracturing. The coupled seepage-damage model is validated using numerical simulations of hydraulic fracturing around one hole and three holes; the model may also enable scientific and reasonable explanation of the dominance of hydraulic gradient on the crack propagation path in permeable rock. Finally, the water outburst from the floor at a coal mining site in Hebei Province, China, is numerically simulated, and the coupled seepage and damage mechanism during the mining-induced rock failure is clarified. The numerical simulation implies that the seepage-damage is the main mechanism for controlling the water outburst. Therefore this mechanism should be considered in the numerical simulation to understand the essence of water outburst induced in mines.     

等效水力隙宽和水力梯度对岩体裂隙网络非线性渗流特性的影响

等效水力隙宽和水力梯度是影响岩体裂隙网络渗流特性的重要因素。制作裂隙网络试验模型,建立高精度渗流试验系统;求解纳维-斯托克斯方程,模拟流体在裂隙网络内的流动状态,研究等效水力隙宽和水力梯度对非线性渗流特性的影响。结果表明,当水力梯度较小时,等效渗透系数保持恒定的常数,流体流动属于达西流动区域,流量与压力具有线性关系,可采用立方定律计算流体流动;当水力梯度较大时,等效渗透系数随着水力梯度的增加而急剧减少,流体流动进入强惯性效应流动区域,流量与压力具有强烈的非线性关系,可采用Forchheimer方程计算流体流动。随着等效水力隙宽的增加,区别线性和非线性流动区域的临界水力梯度呈幂函数关系递减。当水力梯度小于临界水力梯度时,控制方程可选立方定律;当水力梯度大于临界水力梯度时,控制方程可选Forchheimer方程,其参数A和B可根据经验公式计算得到。其研究结果可为临界水力梯度的确定及流体流动控制方程的选取提供借鉴意义。     

砂性土细颗粒起动临界水力坡降计算方法

地下水渗流作用下内部不稳定砂性土将发生潜蚀现象,潜蚀作用引起的土体渗透破坏会对土工建筑物或地基造成不良影响。考虑土体有效应力和细颗粒应力折减,建立渗流场中细颗粒受力模型,根据极限受力平衡状态得到潜蚀过程中砂性土细颗粒起动临界水力坡降计算公式,并通过DEM-CFD耦合方法以及现有试验数据进行验证。结果表明：砂性土中细颗粒以滚动方式起动,起动临界水力坡降受渗流水流、土体特性以及颗粒自身特性共同影响;砂性土表层细颗粒起动临界水力坡降受埋深影响较大,埋深1 cm的细颗粒最高、最低起动临界水力坡降相差10.169%,埋深10 cm时差异减少至1.061%。该计算方法与数值模拟和渗流试验结果的最大标准误差分别为6.038%、11.211%,可以较为准确地预测砂性土细颗粒起动临界水力坡降。     

云南压实黏土层对油类污染物的防渗性能实验研究

目前在压实黏土层(CCL)应用于油类污染物的防渗工程设计中,以水在CCL中的渗透系数低于10-7 cm/s为依据,该依据可能存在偏颇。文中以0#柴油和93#汽油作为典型油类污染物,在云南CCL中进行油相水相交替渗流实验。结果表明：(1)不同渗透压力下,水在云南CCL中的渗透系数为(0.41~2.52)×10-8 cm/s,云南黏土压实后可作为天然防渗衬层。(2)0#柴油和93#汽油穿透饱水的云南CCL时,存在临界水力梯度,分别为0.05和0.02 MPa;一旦突破临界水力梯度,CCL的渗透性急剧增大,0#柴油和93#汽油在CCL中的渗透系数较水在CCL中的高出1~3个数量级。(3)水相驱替0#柴油和93#汽油的过程中,CCL的渗透系数为10-7～10-6 cm/s;被油浸透过的CCL不能继续作为防渗衬层使用。(4)针对油类污染物的CCL防渗工程设计,以水在CCL中的渗透系数低于1.0×10-7 cm/s为标准是不适用的,需要提高CCL防渗的设计等级。     

Geohydrological models and earthquake effects at Yucca Mountain, Nevada

 Yucca Mountain, the proposed site for the high-level nuclear waste repository, is located just south of where the present water table begins a sharp rise in elevation. This large hydraulic gradient is a regional feature that extends for over 100 km. Yucca Mountain and its vicinity are underlain by faulted and fractured tuffs with hydraulic conductivities controlled by flow through the fractures. Close to and parallel with the region of large hydraulic gradient, and surrounding the core of the Timber Mountain Caldera, there is a 10- to 20-km-wide zone containing few faults and thus, most likely, few open fractures. Consequently, this zone should have a relatively low hydraulic conductivity, and this inference is supported by the available conductivity measurements in wells near the large hydraulic gradient. Also, slug injection tests indicate significantly higher pressures for fracture opening in wells located near the large hydraulic gradient compared to the opening pressures in wells further to the south, hence implying that lower extensional stresses prevail to the north with consequently fewer open fractures there. Analytical and numerical modeling shows that such a boundary between media of high and low conductivity can produce the observed, large hydraulic gradient, with the high conductivity medium having a lower elevation than the water table. Further, as fractures can close due to tectonic activity, the conductivity of the Yucca Mountain tuffs can be reduced to a value near that for the hydraulic barrier due to strain release by a moderate earthquake. Under these conditions, simulations show that the elevation of the steady-state water table could rise between 150 and 250 m at the repository site. This elevation rise is due to the projected shift in the location of the large hydraulic gradient to the south in response to a moderate earthquake, near magnitude 6, along one of the major normal faults adjacent to Yucca Mountain. As the proposed repository would only be 200–400 m above the present water table, this predicted rise in the water table indicates a potential hazard involving water intrusion. Received: 7 June 1996 / Accepted: 19 November 1996     

Physics of Atoll Groundwater Flow

Large-scale steady-state groundwater flow in atoll carbonate platforms results from temperature and salinity-induced density gradients. Atolls are built on top of a basaltic substrate that provides geothermal heating from beneath. Moreover, they are immersed in the tropical ocean where temperature decreases rapidly with depth. Groundwater circulation in these platforms has long been associated with the geothermal heat flux because it is capable of generating inward and upward flow of oceanic origin water by buoyancy effects. This study shows that hydraulic circulation occurs even in the absence of a geothermal flux because the combination of the cold subsurface ocean waters with the warm surface conditions is sufficient to maintain a convection cell within the carbonate platform. Using a one-dimensional analytical model, validated by more sophisticated two-dimensional simulations, we can investigate the interaction between these two driving forces. The flow rate inside the platform is, in fact, a function of the ratio of the geothermal flux to the temperature gradient in the ocean. It increases with the geothermal flux but decreases with the oceanic temperature gradient. This one-dimensional model also shows that taking salinity effects on density into account increases the flow rates transiting through the platform by a third.     

非开挖穿河工程对堤防稳定性影响评价

非开挖穿河工程对堤防稳定性的影响,主要是管道施工在地层中形成的扰动带对地下水渗流场的影响;依据工程实例,在考虑高洪水位以及洪水对河道冲刷等不利因素的条件下,建立地下水流数值模拟模型计算地下水流场中最大水力坡度,利用临界水力坡度法,结合有关规范推荐的安全系数,对工程诱发渗透破坏的可能性,进行定量分析。     

滑坡碎屑流冲击拦挡结构的离散元模拟

拦挡结构可以有效减小滑坡致灾范围、减弱致灾强度。文章以滑坡碎屑流为研究对象,通过对比模型试验和数值模拟结果,校正三维离散元模拟参数,进而研究不同坡脚角度和挡板高度对冲击力、最大水平运动距离的影响。研究结果表明:三个坡脚角度碎屑流冲击力的变化过程存在明显区别,坡脚角度为35°和45°时,冲击力时程曲线经历了两个显著的变化阶段:线性增大、线性减小。而坡脚角度为55°时,碎屑流冲击力时程曲线出现三个变化阶段:线性增加、恒力阶段、线性减小。挡板高度越高,恒力阶段的持续时间越短,冲击力线性减小阶段时间越长。小颗粒（2.5~10 mm）对挡板的冲击效应显著;中等颗粒（10~25 mm）随着挡板高度的增加,对挡板的冲击效应逐渐增大;而大颗粒（25~60 mm）作用在挡板上的冲击效应出现突变,与其他两种颗粒对比,整个运动过程冲击效应不显著。碎屑流的运程随着挡板高度的增加逐渐减小。对比三个坡脚角度下挡板的拦挡效果,坡脚角度α≤45°时,拦挡效果显著。     

循环往复水流对反滤系统的作用机理研究

通过自行研制的循环往复水流试验装置,研究了不同频率的正弦循环水流对反滤系统的作用机制,建立了与试验模型相一致的定解条件,并求得孔压微分方程的解析解。理论分析表明,土的固结系数与循环往复水流的频率的比值越小,靠近边界处土体的水力梯度就越大,土体内部的水力梯度就越小。试验中,当周期为0.5 min时,边界处水力梯度振幅接近系统平均水力梯度振幅的2倍;当周期为62.5 min时,则基本没有边界水力梯度集中现象。实测结果与理论分析结果较为一致。这种水力梯度边界集中现象,容易加剧渗透边界层的冲刷,降低反滤系统的渗透稳定性,应当在试验研究和工程实践中引起注意。     

上覆流沙层隧道开挖面稳定性分析与数值试验研究

为解决上覆流沙层隧道开挖面极易发生坍塌破坏的技术难题,以典型该地质条件下的青岛地铁M2号线啤苗区间（啤酒城站至苗岭路站）为研究对象,基于开挖面的实际破坏特征建立了开挖面失稳破坏力学模型,从功能转化平衡角度,进行了隧道开挖面稳定性上限分析,并利用强度折减与重力加载两种方式,提出了隧道开挖面安全系数,得到了不同开挖面土体黏聚力、摩擦角、重度、隔水层厚度及隧道开挖高度下的临界土体破裂范围及破裂模式。理论研究表明：随着开挖面土体黏聚力、摩擦角、隔水层厚度等参数的增加,开挖面安全系数不断增大,稳定性不断提高;随着土体重度、隧道开挖高度增加,开挖面安全系数不断减小,稳定性不断降低。通过建立不同工况的数值模型验证了理论研究的正确性,得到了上覆流沙层地质条件下开挖面的典型破坏模式和临界参数,并提出了相应工程建议。研究成果为青岛地铁M2号线的顺利贯通及该类地质条件下的隧道施工提供了理论指导和科学对策。