Application of numerical modelling in the design of a full‐scale heated Tunnel Sealing Experiment

The Tunnel Sealing Experiment (TSX) was a full‐scale in situ demonstration of technology for constructing nearly water tight‐seals in excavations through crystalline rock deep below the surface of the earth. The experiment has been carried out at Atomic Energy of Canada Limited's (AECL's) Underground Research Laboratory near Lac du Bonnet, Canada, in support of international programs for geologic disposal of radioactive waste. The TSX, with partners from Canada, Japan, France and the United States, was carried under conditions of high pressure (up to 4 MPa) and elevated temperature (up to 85°C). Comparing numerical model predictions with eight years of data collected from approximately 900 sensors was an important component of this experiment. Model of Transport In Fractured/porous Media (MOTIF), a finite element computer program developed by AECL for simulating fully coupled or uncoupled fluid flow, solute transport and heat transport, was used to model both the ambient temperature and heated phases of the TSX. The plan to heat the water in the TSX to 85°C was developed using model predictions and a comparison of simulated results with measurements during heating of the water in the TSX to about 50°C. The three‐dimensional MOTIF simulations were conducted in parallel with axisymmetric modelling using Fast Lagrangian Analysis of Continua (FLAC), which computed the heat loss from pipes that carried the heated water through the rock to and from the experiment. The numerical model was initially used to develop a plan for operation of the experiment heaters, and then subsequently used to predict temperatures and hydraulic heads in the TSX bulkhead seals and surrounding rock. Copyright © 2005 John Wiley & Sons, Ltd.     

Mathematical modelling of groundwater flow at Sellafield, UK

Sellafield in West Cumbria was a potential site for the location of the UK's first underground repository for radioactive, intermediate level waste (ILW). The repository was to lie around 650 m beneath the ground surface within rocks of the Borrowdale volcanic group (BVG), a thick suite of SW dipping, fractured, folded and metamorphosed Ordovician meta-andesites and ignimbrites. These are overlain by an onlapping sequence of Carboniferous and Permo-Triassic sediments. In situ borehole measurements showed that upward trending fluid pressure gradients exist in the area of the potential repository site, and that there are three distinct fluid types in the subsurface; fresh, saline and brine (at depth, to the west of the site). Simulations of fluid flow in the Sellafield region were undertaken with a 2D, steady-state, coupled fluid and heat flow simulation code (OILGEN). In both simplified and geologically complex models, topographically driven flow dominated the regional hydrogeology. Fluids trended persistently upwards through the potential repository site. The dense brine to the west of the site promoted upward deflection of topographically driven groundwaters. The inclusion in hydrogeological models of faults and variably saline sub-surface fluids was essential to the accurate reproduction of regional hydraulic head variations. Sensitivity analyses of geological variables showed that the rate of groundwater flow through the potential repository site was dependent upon the hydraulic conductivity of the BVG, and was unaffected by the hydraulic conductivity of other hydrostratigraphic units. Calibration of the model was achieved by matching simulated subsurface pressures to those measured in situ. Simulations performed with BVG hydraulic conductivity 100 times the base case median value provided the “best-fit” comparison between the calculated equivalent freshwater head and that measured in situ, regardless of the hydraulic conductivity of other hydrostratigraphic units. Transient mass transport simulations utilising the hydraulic conductivities of this “best fit” simulation showed that fluids passing through the potential repository site could reach the surface in 15 000 years. Simple safety case implications drawn from the results of the study showed that the measured BVG hydraulic conductivity must be less than 0.03 m year⁻¹ to be simply declared safe. Recent BVG hydraulic conductivity measurements showed that the maximum BVG hydraulic conductivity is around 1000 times this safety limit.     

A study on how to couple thermo-hydro-mechanical behaviour of unsaturated soils: Physical equations,numerical implementation and examples

This paper describes a thermo-hydro-mechanical framework suitable for modelling the behaviour of unsaturated soils. In particular, this paper focuses on bentonite clay subjected to a thermo-hydro-mechanical load, as in the case of nuclear waste engineering barriers. The paper gives a theoretical derivation of the full set of coupled balance equations governing the material behaviour as well as an extended physical interpretation. Finally, a finite element discretisation of the equations and number of simulations verifying their implementation into a custom finite element code is provided. Some aspects of the formulation are also validated against experimental data.     

Numerical modeling of the flow and transport of radionuclides in heterogeneous porous media

This paper is concerned with numerical methods for the modeling of flow and transport of contaminant in porous media. The numerical methods feature the mixed finite element method over triangles as a solver to the Darcy flow equation and a conservative finite volume scheme for the concentration equation. The convective term is approximated with a Godunov scheme over the dual finite volume mesh, whereas the diffusion–dispersion term is discretized by piecewise linear conforming triangular finite elements. It is shown that the scheme satisfies a discrete maximum principle. Numerical examples demonstrate the effectiveness of the methodology for a coupled system that includes an elliptic equation and a diffusion–convection–reaction equation arising when modeling flow and transport in heterogeneous porous media. The proposed scheme is robust, conservative, efficient, and stable, as confirmed by numerical simulations.      

Two-dimensional simulations of surface deformation caused by slab detachment

Detachment of the deeper part of subducted lithosphere causes changes in a subduction zone system which may be observed on the Earth's surface. Constraints on the expected magnitudes of these surface effects can aid in the interpretation of geological observations near convergent plate margins where detachment is expected. In this study, we quantify surface deformation caused by detachment of subducted lithosphere. We determine the range of displacement magnitudes which can be associated with slab detachment using numerical models. The lithospheric plates in our models have an effective elastic thickness, which provides an upper bound for rapid processes, like slab detachment, to the surface deformation of lithosphere with a more realistic rheology. The surface topography which develops during subduction is compared with the topography shortly after detachment is imposed. Subduction with a non-migrating trench system followed by detachment leads to a maximum surface uplift of 2–6 km, while this may be higher for the case of roll-back preceding detachment. In the latter situation, the back-arc basin may experience a phase of compression after detachment. Within the context of our elastic model, the surface uplift resulting from slab detachment is sensitive to the depth of detachment, a change in friction on the subduction fault during detachment and viscous stresses generated by sinking of the detached part of the slab. Overall, surface uplift of these magnitudes is not diagnostic of slab detachment since variations during ongoing subduction may result in similar vertical surface displacements.     

Empirical assessment of the critical time increment in explicit particulate discrete element method simulations

This contribution considers the critical time increment (Δt_crit) to achieve stable simulations using particulate discrete element method (DEM) codes that adopt a Verlet-type time integration scheme. The Δt_crit is determined by considering the maximum vibration frequency of the system. Based on a series of parametric studies, Δt_crit is shown to depend on the particle mass (m), the maximum contact stiffness (K_max), and the maximum particle coordination number (C_N,max). Empirical expressions relating Δt_crit to m, K_max, and C_N,max are presented; while strictly only valid within the range of simulation scenarios considered here, these can inform DEM analysts selecting appropriate Δt_crit values.     

Analysis of the hydration of a bentonite seal in a deep radioactive waste repository

A deep geological repository for nuclear waste requires the backfilling and sealing of shafts and galleries to block any preferential path for radioactive contaminants. The paper presents the coupled hydromechanical analyses of an in situ test carried out in the HADES underground laboratory in Mol, Belgium. The test examines the effectiveness of an expansive clay seal in a horizontal borehole specifically drilled for this purpose. The analysis covers the phase of seal hydration up to saturation and subsequent pore pressure equilibration. Hydraulic and mechanical constitutive laws suited to expansive clay materials have been chosen for the analyses with all the parameters determined independently of the in situ test. A quite good agreement has been found between test observations and computed results suggesting that the numerical formulation employed is able to reproduce the main features of a real sealing system.     

Multi-scale modelling of the permeability evolution of fine sands during cement suspension grouting with filtration

Fluid flow during permeation grouting of fine sands with a microcement-based grout is studied by assuming that the heterogeneous medium composed of the initial granular skeleton, filtered cement and the interstitial fluid phase can be replaced by a continuous equivalent medium at the macroscopic level. Consequently, the method of Homogenization of Periodic Structures (HPS) is used to identify the effective permeability tensor evolution under the effect of cement filtration. The expression of the macroscopic permeability tensor derived through the HPS procedure is shown to depend on the permeating fluid viscosity and the geometrical arrangement of the sand grains and cement deposit within the microstructure. Numerical computations are made using various two-dimensional and three-dimensional microstructures, and the model results are confronted with grouting experiments performed on small scale columns in the laboratory.     

Effects of tunnelling on existing support systems of perpendicularly crossing tunnels

The interactions between perpendicularly crossing tunnels in the Sydney region are investigated using a full three-dimensional (3D) finite element analysis coupled with elasto-plastic material models. Special attention is paid to the effect of subsequent tunnelling on the support system, i.e. the shotcrete lining and rock bolts, of the existing tunnel. The results of the analysis show that in a region such as Sydney, with relatively high horizontal stresses, installation of the new tunnel causes the shotcrete lining of the existing tunnel to be in tension in the side facing towards the tunnel opening and in compression at the crown and invert. The pre-stressed rock bolts are usually tensioned more in the sections closest to the tunnel opening. For this particular study, if a new tunnel is driven perpendicularly beneath an existing tunnel, significant increases are induced in the bending moments in the shotcrete lining at the lateral sides of the existing tunnel and in the axial forces at its crown and invert. The increase in side bending moments causes further tensile cracking but the crown and invert stresses remain within the thresholds for both compressive failure and tensile cracking for shotcrete lining of typical concrete quality. Moreover, the driving of the new tunnel causes the tensile forces in the existing side rock bolts to increase and those in the existing crown rock bolts to decrease. In contrast, if the new tunnel is driven perpendicularly above the existing tunnel, compressive failure of the existing shotcrete lining is induced at the crown of the deeper tunnel for concrete of typical capacity and a significant tensile force increase of the existing rock bolts around the crown. It is concluded that in order to ensure the stability of the existing tunnel, local thickening is needed at the sides of the existing shotcrete lining if the shallow tunnel is installed first and local thickening is needed at the crown if the deep tunnel is installed first.     

FDEM-flow3D: A 3D hydro-mechanical coupled model considering the pore seepage of rock matrix for simulating three-dimensional hydraulic fracturing

A hydro-mechanical coupled model that can simultaneously consider the pore seepage of a rock matrix and the fracture seepage is proposed to simulate three-dimensional hydraulic fracturing. This model appropriately takes into account the fluid leak-off into the surrounding rock matrix from the fracture. Several examples are given to validate the seepage algorithms and the coupled model. The results suggest that this model can solve problems involving pore seepage and fracture seepage through simple pure fracture seepage. Moreover, it can reproduce the fluid pressure distribution and the crack initiation and propagation and consider the fluid loss during hydraulic fracturing.     

Comparative study of the compression and uplift of shallow foundations

This paper compares the compression and uplift capacity of a strip foundation from numerical coupled analyses using the Modified Cam Clay (MCC) soil model. The focus is on the failure mechanism and pore pressure development in the soil. Triaxial compression and tension tests were first modelled to develop a rigorous understanding of the pore pressure responses; then, the compression and uplift of a strip foundation were modelled. The results show that the balance of excess pore pressures due to the changes in mean total stress and deviatoric stress during the compression and uplift of a strip foundation are different, although the ultimate undrained capacities are identical. Furthermore, the resistance and excess pore pressure responses during uplift differ from those in compression under the K₀-consolidated condition because of the elastic unloading. Although the failure mechanisms have identical shape and size between undrained compression and uplift, the pore pressure distribution in the soil is different and affects the load–displacement behaviours under partially drained compression and uplift.     

Crack modelling of concrete, rock and soil with inner softening bands

To model the cracking behaviour of brittle materials, different existing methods for treating the fracture zone can be used. The inner softening band (ISB) approach belongs to those methods which introduce a displacement discontinuity in which a constitutive relationship between opening displacements and tractions is assumed. This group of methods avoids difficulties in the localization zone caused by ambiguous definitions of strain measures and fracture zone widths. Whichever method is used, it is important that the proper amount of energy is dissipated. This is achieved automatically in ISB without the introduction of any extra material parameters other than the elastic constants and those describing the softening curve. Variations in mesh sizes and arrangements have shown no great influence on the total response, and the crack pattern is a part of the solution in contrast to most other methods in which it must be presumed. The concept is simple and inner softening bands have been successfully implemented within triangular three-node elements and preliminary within six-node triangular elements. The results obtained so far from various kinds of tests have shown very good performance and further development is planned.     

Permeable piles: An alternative to improve the performance of driven piles

This paper investigates the soil displacements and excess pore pressures induced by driven piles using a combined 3D finite and infinite element approach. The analyses are compared with analytical evaluations and field measurements. Consolidation analysis is conducted to illustrate the variation in pore pressure with time. A technique of drilling drainage holes on the pipe pile is proposed in this paper to accelerate the dissipation of pore pressure to improve the performance of displacement piles. It has been noticed that optimal performance of piles can be obtained by assigning openings in piles within the bottom 50% of the pile length.     

矿物法--环境污染治理的第四类方法

总结介绍了近10年开展环境矿物材料研究所取得的较为系统的研究成果。新提出环境矿物材料基本性能,包括矿物表面效应、孔道效应、结构效应、离子交换效应、结晶效应、溶解效应、水合效应、氧化还原效应、半导体效应、纳米效应及矿物生物交互效应等。展示环境矿物材料开发应用方面的崭新成就,包括利用天然铁的硫化物矿物强还原性,发明一步法还原Cr(Ⅵ)与沉淀Cr(Ⅲ)废水处理新工艺;利用天然锰的氧化物矿物强氧化性,发明处理高浓度与强污染的印染和酚类废水新方法;利用天然钛的氧化物矿物日光催化性,发明光催化降解卤代有机污染物新方法;利用天然蛭石高温脱水膨胀热效应,发明能大幅度提高型煤固硫率与除尘新方法;利用天然钙基蒙脱石低成本制备出同时防止水体与无机和有机污染物渗漏的自愈性强的填埋场衬层建造用新型防渗材料,发明生活垃圾尤其是危险废物填埋场衬层建造新工艺;发现凝灰岩与花岗岩中长石类矿物发育有良好的孔道结构,核素进入可发生固定化作用,成为有效阻滞核素迁移的天然屏障;利用天然纳米管状纤蛇纹石成功制备二氧化硅纳米管,接枝有机物可由亲水性变为疏水性;利用黄钾铁矾的胶体特征作为多金属矿山废石堆隔离防渗层,防止金属硫化物矿物氧化分解与矿山酸性废水污染等。着重指出今后环境矿物?     

Experiment and validation of numerical simulation of coupled thermal,hydraulic and mechanical behaviour in the engineered buffer materials

Evaluation of the coupled heat transfer, water flow and stress changes in the engineered clay barrier is an important issue in the performance assessment of the high‐level radioactive waste disposal. To demonstrate the function of the engineered barrier system, the large‐scale experiment is conducted, which is called Big Bentonite facility (BIG‐BEN). The facility consists of an electric heater surrounded by glass beads, carbon steel overpack, buffer material and man‐made rock. The buffer is a mixture of bentonite and sand. The heater is operated at 0·8 kW. Water is injected from the interface between the buffer and the man‐made rocks at the pressure of 0·05 MPa. The duration of the experiment is 20 months. The change in temperature and swelling pressure are continuously monitored and gravimetric water content is measured by sampling. The coupled thermal, hydraulic and mechanical processes are simulated with a finite element code THAMES, which can simulate the fully coupled phenomena in the saturated and unsaturated clay under anisothermal condition. To examine the validity of the code, all the parameters used in the model are evaluated from the other laboratory tests. The simulated results are compared with the measured ones without calibration of the parameter values using the results from the BIG‐BEN experiment. It can be concluded that the changes in temperature and gravimetric water content within the buffer can be simulated reasonably well and that the mechanical effect such as swelling pressure is difficult to realize. Copyright © 2000 John Wiley & Sons, Ltd.     

冲击器缸体强度的有限元分析

冲击器缸体是冲击器的重要组成部分，由于其工作和受力情况非常复杂，用常规的方法无法对其进行准确的受力分析。有限元法是一种有效的数值计算方法，通过应用ANSYS有限元软件，对YSC-178型射流冲击器的缸体进行建模，并在不同的工作情况下进行了应力应变分析，最后得出缸体变形主要是径向变形的结论。这一结论与实际情况相符合，说明应用有限元法可以对钻探机具的各部件进行准确的受力分析，进而可以指导和优化设计。     

Influence of initial density of cohesionless soil on evolution of passive earth pressure

This paper focuses on the influence of the initial void ratio on the evolution of the passive earth pressure and the formation of shear zones in a dry sand body behind a retaining wall. For the numerical simulation a rigid and very rough retaining wall undergoing a horizontal translation against the backfill is considered. The essential mechanical properties of cohesionless granular soil are described with a micro-polar hypoplastic model which takes into account stresses and couple stresses, pressure dependent limit void ratios and the mean grain size as a characteristic length. Numerical investigations are carried out with an initially medium dense and initially loose sand using a homogeneous and random distribution of the initial void ratio. The geometry of calculated shear zones is discussed and compared with a corresponding laboratory model test.     

Towards realistic simulations of lava dome growth using the level set method

The level set method has been implemented in a computational volcanology context. New techniques are presented to solve the advection equation and the reinitialisation equation. These techniques are based upon an algorithm developed in the finite difference context, but are modified to take advantage of the robustness of the finite element method. The resulting algorithm is tested on a well documented Rayleigh–Taylor instability benchmark [19], and on an axisymmetric problem where the analytical solution is known. Finally, the algorithm is applied to a basic study of lava dome growth.