Scattering of elastic waves by a plane crack of finite width in a transversely isotropic medium

This work presents a numerical algorithm for solving crack scattering in a transversely isotropic medium whose symmetry axis is perpendicular to the crack surface. The crack is modelled as boundary discontinuities in the displacement u and the particle velocity v, of the stresses [κu+ζv], where the brackets denote discontinuities across the interface. The specific stiffness κ introduces frequency-dependence and phase changes in the interface response and the specific viscosity ζ is related to the energy loss. The numerical method is based on a domain decomposition technique that assignes a different mesh to each side of the interface, that includes the crack plane. As stated above, the effects of the crack on wave propagation are modelled through the boundary conditions, that require a special boundary treatment based on characteristic variables. The algorithm solves the particle velocity–stress wave equations and two additional first-order differential equations (two-dimensional case) in the displacement discontinuity. For each mesh, the spatial derivatives normal to the interface are solved by the Chebyshev method, and the spatial derivatives parallel to the interface are computed with the Fourier method. They allow a highly accurate implementation of the boundary conditions and computation of the spatial derivatives, and an optimal discretization of the model space. Moreover, the algorithm allows general material variability. © 1998 John Wiley & Sons, Ltd.     

Unraveling the Schneeberg garnet puzzle: a numerical model of multiple nucleation and coalescence

A quantitative kinetic model for the growth of the different garnet porphyroblast microstructures (type 1 and type 2) of the Western Schneeberg Complex (WSC) is presented. These porphyroblasts formed by a multiple nucleation and coalescence mechanism. Our numerical simulation shows that at constant diffusion rates: (1) low interface reaction rates result in a fully amalgamated porphyroblast (type 2); (2) intermediate reaction rates result in a porphyroblast, where coalescence of grains closer to the margin prevented amalgamation of those in the centre (similar to type 1 porphyroblasts); and (3) high interface reaction rates result in a porphyroblast microstructure with an atoll form. All three microstructures are characterised by distinctive cluster size distributions. A 2-D cluster size distribution analysis of type 1 porphyroblasts of WSC shows that these did not form because of intermediate interface reaction rates, but because the diffusion rate of nutrients was too low to keep pace with the interface reaction rate.Editorial responsibility: T.L. Grove     

Montecarlo DLA-type simulations of wetting effects in fluid displacement in porous media

In this work, we report diffusion-limited aggregation (DLA)-type Montecarlo computations of a stochastic model of displacement of a viscous fluid by another that preferentially wets a porous medium, for the case when both fluids are immiscible in the absence of buoyancy forces. The model has the aim to simulate cooperative invasion processes found in experiments of immiscible wetting displacement. The model considers the nonlocal effects of the Laplacian pressure field and the capillary forces via hydrodynamic equations in the Darcy regime with a boundary condition for the pressure at the interface. The boundary condition contains two different types of disorder: the capillary term, which constitutes an additive random disorder, and a term containing an effective random surface tension, which couples to a curvature (it constitutes a multiplicative random term that carries nonlocal information of the whole pressure). We generate different displacement patterns for different setting of the parameters of the model. We analyze these patterns by studying the scaling properties of the interface that separate the two fluids and calculating the fractal dimension of the interface. The results show the existence of three distinct regimes of scaling. One regime at the smallest-length scales is due to the multiplicative random disorder together with the nonlocal coupling; it reveals itself in a roughness exponent α ≈ 0.80. Additionally, we find a DLA-type scaling regime with a roughness exponent α ≈ 0.60 at the largest scales and intermediate scaling regime with α ≈ 0.70 corresponding to invasion percolation with trapping. Each regime has definite scaling ranges that depend on the capillary number and the relative wetting tendency of the fluids. The behavior of the fractal dimensions of the interfaces of the aggregates constitutes a further confirmation of the existence of three scaling regimes and the multi-self-affinity of the perimeter of the interface boundaries.     

Elastic waves at a corrugated interface between two dissimilar fibre‐reinforced elastic half‐spaces

The reflection and transmission phenomena of elastic waves incident at a corrugated interface between two dissimilar fibre‐reinforced elastic half‐spaces have been analysed. Using Rayleigh method of approximation, the expressions of the reflection and transmission coefficients are obtained in closed form for the plane interface as well as for the first order approximation of the periodic interface ζ = d cos px. All these reflection and transmission coefficients of regular and irregular waves are found to be the functions of angle of incidence and elastic parameters of the media. Moreover, the coefficients of irregularly reflected and transmitted waves are found to be proportional to the amplitude of the corrugated interface and are functions of the frequency of the incident wave. Numerical computations have been performed for a specific model to compute these coefficients and results obtained are shown graphically. The results of Singh and Singh (Sadhana 2004; 29 :249–257) and Ben‐Menahem and Singh (Seismic Waves and Sources. Springer: New York) have been derived from our analysis as particular cases. Copyright © 2006 John Wiley & Sons, Ltd.     

Internal soil moisture response to rainfall-induced slope failures and debris discharge

Predictions of rainfall-induced fast-moving mass flow and/or debris flows require better knowledge of the mechanism controlling the debris discharge of slopes in debris source areas. A series of rainfall tests on 0.32 m-deep, 0.7 m-high, 1.35 m-wide sandy slopes resting on a bi-linear impermeable rigid base was performed. Soil moisture content and solid discharge measurements were performed to gain insights into the rainfall-induced retrogressive slope failure. The solid (or debris) discharge is a result of the wash-out of the fluidized slope toe by the interflow along the soil–bedrock interface. Characteristics of the failure process for the slopes are represented by mass wasting curves or ‘solid discharge (Q_s) vs. time (t)’ curves which are functions of the rainfall intensity and/or the cumulative rainfall. The mass wasting curves have inflection points representing transitions from minor toe failures into remarkable retrogressive failures. The first inflection point of the soil moisture (ω) vs. t curve measured at the soil–bedrock interface signaling the arrival of the descending ‘wet front’, may serve as a precursor for predicting the onset of an abrupt solid discharge induced by shallow slope failures. The time of peak water content measured at the soil–bedrock interface may approximate the time of 5% total solid volume discharge. Up to the time of 5% of total slope volume discharge, a fully saturated state (S_r  100%) was never observed at the 0.2 m-below-surface zone; however, it was observed along the soil–bedrock interface at near-toe zone of the slope, regardless of the intensity of rainfall investigated. Retrogressive failures were essentially associated with nonuniformly distributed water content in the slope. For both the 0.2 m-below-surface zone and the soil–bedrock interface, a more uniform distribution of S_r along the full height of the slope was found for slopes subjected to high rainfall intensities of 47 and 65 mm/h than that for the slope subjected to a low rainfall intensity of 23 mm/h. At the inflection point of the Q_s vs. t curve and 5% of total solid volume discharge, values of S_r at a certain distance from the toe for the soil–bedrock interface were higher than those measured at the same distance from the toe for the 0.2 m-below-surface zone, indicating the effect of infiltration-induced interflow along the soil–bedrock interface and its effects on the fluidization of the slope toe and the retrogressive failure of the slope.     

Coupled HM analysis using zero‐thickness interface elements with double nodes. Part I: Theoretical model

In recent years, the authors have proposed a new double‐node zero‐thickness interface element for diffusion analysis via the finite element method (FEM) (Int. J. Numer. Anal. Meth. Geomech. 2004; 28 (9): 947–962). In the present paper, that formulation is combined with an existing mechanical formulation in order to obtain a fully coupled hydro‐mechanical (or HM) model applicable to fractured/fracturing geomaterials. Each element (continuum or interface) is formulated in terms of the displacements (u) and the fluid pressure (p) at the nodes. After assembly, a particular expression of the traditional ‘u–p’ system of coupled equations is obtained, which is highly non‐linear due to the strong dependence between the permeability and the aperture of discontinuities. The formulation is valid for both pre‐existing and developing discontinuities by using the appropriate constitutive model that relates effective stresses to relative displacements in the interface. The system of coupled equations is solved following two different numerical approaches: staggered and fully coupled. In the latter, the Newton–Raphson method is used, and it is shown that the Jacobian matrix becomes non‐symmetric due to the dependence of the discontinuity permeability on the aperture. In the part II companion paper (Int. J. Numer. Anal. Meth. Geomech. 2008; DOI: 10.1002/nag.730 ), the formulation proposed is verified and illustrated with some application examples. Copyright © 2008 John Wiley & Sons, Ltd.     

A computational method for approximating a Darcy–Stokes system governing a vuggy porous medium

We develop and analyze a mixed finite element method for the solution of an elliptic system modeling a porous medium with large cavities, called vugs. It consists of a second-order elliptic (i.e., Darcy) equation on part of the domain coupled to a Stokes equation on the rest of the domain, and a slip boundary condition (due to Beavers–Joseph–Saffman) on the interface between them. The tangential velocity is not continuous on the interface. We consider a 2-D vuggy porous medium with many small cavities throughout its extent, so the interface is not isolated. We use a certain conforming Stokes element on rectangles, slightly modified near the interface to account for the tangential discontinuity. This gives a mixed finite element method for the entire Darcy–Stokes system with a regular sparsity pattern that is easy to implement, independent of the vug geometry, as long as it aligns with the grid. We prove optimal global first-order L ² convergence of the velocity and pressure, as well as the velocity gradient in the Stokes domain. Numerical results verify these rates of convergence and even suggest somewhat better convergence in certain situations. Finally, we present a lower dimensional space that uses Raviart–Thomas elements in the Darcy domain and uses our new modified elements near the interface in transition to the Stokes elements.     

Finite element modelling of thick plates on two‐parameter elastic foundation

This paper is intended to give some information about how to build a model necessary for bending analysis of rectangular and circular plates resting on a two‐parameter elastic foundation, subjected to combined loading and permitting various types of boundary conditions. The formulation of the problem takes into account the shear deformation of the plate and the surrounding interaction effect outside the plate. The numerical model based on an 18‐node zero‐thickness isoparametric interface element interacting with a thick Reissner–Mindlin plate element with three degrees of freedom at each of the nine nodes, which enforce C⁰ continuity requirements for the displacements and rotations of the midsurface, is proposed. Stiffness matrices of a special interface element are superimposed on the global stiffness matrix to represent the stiffening elastic foundation under and beyond the plate. Some numerical examples are given to illustrate the advantages of the method presented. Copyright © 2001 John Wiley & Sons, Ltd.     

Response of shear wave from a corrugated interface between elastic solid/viscoelastic half‐spaces

The propagation of plane shear wave at a corrugation interface between elastic solid and viscoelastic liquid half‐spaces has been investigated. Adopting Rayleigh's method of approximation, the reflection and refraction coefficients corresponding to reflected and refracted SH‐waves have been derived for the first order of approximation of the corrugated interface. These coefficients are derived in the closed form for a periodic interface. Numerical computation has been performed for a particular model and the results are depicted graphically. The results of Asano (Bull. Earthquake Res. Inst. 1960; 38 (2):177–197) and Kielczynski and Pajewski (J. Acoust. Soc. Am. 1987; 81 (3):599–605) are recovered from this study. Copyright © 2010 John Wiley & Sons, Ltd.     

Method for Quantification of Wear of Sheared Joint Walls Based on Surface Morphology

Roughness and wear evolution of three different joint wall surfaces were characterized using surface roughness and surface wear parameters. Parameters were defined by considering the two components of morphology: waviness (“primary” roughness) and surface roughness (“secondary” roughness). Two surface roughness parameters are proposed: joint interface (or single wall) specific surface roughness coefficient SR _s (0 ≤ SR _s  ≤ 1) for quantifying the amount of “pure” roughness (or specific roughness), and degree of joint interface (or single wall) relative surface roughness DR _r (0 ≤ DR _r  ≤ 0.5). Two further parameters are also proposed in order to quantify the wear of wall surface: joint interface (or single wall) surface wear coefficient Λ_interface, and the degree of joint interface (or single wall) surface wear D _w(interface). The three test specimens were: man-made granite joints with hammered surfaces, man-made mortar joints with corrugated surfaces, and mortar joints prepared from natural rough and undulated schist joint replicas. Shearing under monotonic and cyclic shearing was performed using a computer-controlled bidirectional and biaxial shear apparatus. Joint surface data were measured using a noncontact laser sensor profilometer prior to and after each shear test. Calculation of specific surface roughness coefficient SR _s , and degree of surface wear D _w , indicated that the hammered joint interface with predominant interlocking wears much more (>90%) than the corrugated (27%) and the rough and undulated (23%) joint interfaces having localized interlocking points. The proposed method was also successfully linked to the classical wear theory.     

Development of viscous fingering between mafic and felsic magmas: evidence from the Terra Nova Intrusive Complex (Antarctica)

Summary A wide range of types of contact morphology among mafic and felsic magmas are observed in outcrops on Vegetation Island (Terra Nova Intrusive Complex, Antarctica). Image analysis and fractal geometry techniques were applied for in-depth study of the mafic/felsic interface, with the aim of studying the origin of the varied morphologies. In particular, the length (IP_N) and fractal dimension (D_box) of interfaces were measured. Results indicate that there is a close exponential dependence of IP_N on D_box.The observed morphologies are identical to those observed during viscous fingering processes induced by the displacement of a more viscous fluid by a less viscous one. To test if viscous fingering was responsible in this case too, IP_N and D_box values were measured on viscous fingering structures obtained experimentally using various viscosity ratios (V_R) from the literature. Results indicate that, as in the natural case, there is an exponential dependence of IP_N on D_box, leading to the conclusion that the varied interface morphologies between mafic and felsic magmas are the result of viscous fingering dynamics. In addition, experimental studies clearly show that there is an exponential relationship between the viscosity ratio of fluids and the interface fractal dimension (D_box), and the ratio between the two types of magma was estimated using this relationship. It is shown that viscosity contrasts between mafic and felsic magmas varied considerably, ratios ranging from ca. 6 to 49. These results, together with outcrop evidence, provide indications regarding the evolution of the magmatic system, which generated the actual mafic/felsic associations on Vegetation Island.     

Observations on fabric evolution to a common micromechanical state at the soil-structure interface

The fabric plays an important role in the mechanical behavior of granular material. The aim of this paper is to investigate the evolution of fabric in a soil-structure interface (SSI) to a large shearing in an effort to clarify whether and how this form of fabric evolution can lead to a common microstructure. Using the discrete element method (DEM), two-dimensional (2D) numerical interface shear tests were carried out, and certain macromechanical and micromechanical properties were exploited. All samples exhibited prominently localized strain in a zone covering the structure's surface (named the localized zone), and much lower density and higher soil fabric anisotropy levels were found inside this zone than outside it. Disregarding different initial void ratios, a common critical state microstructure was observed in large shear deformations of soil samples, with essentially the same fabric arrangement in terms of contact orientation and internal force transmission. Due to the systematic forming, buckling, and collapsing of force chains, an angular zone (called an α -zone), in which contact density was sluggish to varying degrees, appeared and extended around the main direction of the distribution of contact orientation inside the localized zone. The gradual deterioration of the force chains' stability, as a result of an increasing void ratio, seemed to drive the α -zone's extension and lead to the rare variation of microstructures in the critical state.     

Mechanical response of a jointed rock beam—numerical study of centrifuge models

In this paper we present a comparison between a set of benchmark centrifuge models of a jointed beam and the predictions of two numerical models: fast Lagrangian analysis of continua (FLAC) and discontinuous deformation analysis (DDA). The primary objective of this paper is a comparison between the measured deformation profiles and thrust evolution to predictions of the numerical methods employed. A secondary objective is an attempt to clarify the issue of compressive arch geometry which is still in controversy among researchers. It is found that both FLAC and DDA result in insufficiently accurate predictions to the measured displacements. The mode of deformation is only partially captured and is dependent on the aspect ratio of the individual blocks which made up the beam. It is shown that the accuracy of the predicted displacements is a function of the assigned interface stiffness. The thrust predicted by both methods is found to be considerably lower than that measured in the model; however, the linear evolution of thrust and equilibrium conditions are correctly captured. The geometry of the compressive arch as predicted by FLAC compares extremely well with the data measured in the physical model. Based on the FLAC analysis it is found that for a beam composed of equidimensional blocks the thickness of the compressive arch varies from 0.8t at the abutment interface to the entire beam thickness (1t) at a distance of a half block width from the abutment face, extending across the interface separating the block and its neighbour, and attains a value of 0.5t at the beam mid span. Copyright © 2006 John Wiley & Sons, Ltd.     

Fatty acids and sterols of particulate matter in a brackish and seasonally anoxic coastal salt pond

Particulate matter and interfacial sediment from a seasonally anoxic coastal salt pond were analyzed for fatty acids and sterols to examine variations in organic sources, and compositional changes across the oxic-anoxic interface in the water column and at the sediment-water interface. Fatty acid distributions in suspended particles varied seasonally and as a function of depth. Fatty acids of algal origin (e.g. 16:3, 16:4, 18:3, 18:4) were abundant in particles in oxic surface waters, but these labile components were depleted in particles from the anoxic zone which instead were enriched in bacterial fatty acids (e.g. 16:1Δ⁹, 18:1Δ¹¹, anteiso-C₁₅). Sterol distributionsvaried less than fatty acid distributions and particles throughout the water column reflected an upper water algal source with little in situ alteration. There was evidence for an in situ conversion of Δ⁵-stenols to 5(α)H-stanols in suspended particles in the anoxic zone. Sinking particles and the interfacial sediment were compositionally similar to each other, but different from suspended particles. These data reflect differences in particle source, transport and transformation processes occuring in the water column.     

15 years of in situ cement–argillite interaction from Tournemire URL: Characterisation of the multi-scale spatial heterogeneities of pore space evolution

The solution selected by some countries to isolate radioactive wastes from the biosphere for up to one million years in deep geological repositories includes a multi-barrier disposal design, with steel canister, bentonite and cement materials. The geochemical contrast between such materials and the host rock formation creates perturbations potentially altering the confinement properties of the formation. In this context, the French Institute for the Radiological protection and Nuclear Safety (IRSN) have developed an in situ experimental programme based on the study of cement/argillaceous formation interfaces in their Underground Research Laboratory at Tournemire (Aveyron, France). An in situ engineered analogue of a cement/clay-rock interface which has undergone 15 years of interaction has been characterised. Such important interaction time for an in situ engineered analogue provides a bridge between laboratory-derived data and the long time scale of safety assessment modelling. As the mineralogical and petrological investigations have already been published, this work presents for the first time a quantitative characterisation of the spatial distribution of the porosity in the cement and the clay-rock in terms of time scale and design. Interfaces have been characterised using an autoradiography technique in addition to petrophysical measurements. This technique enables visualisation and quantification of the spatial distribution of the porosity using 2D mapping of decimetric-scale specimens. Thus autoradiographs allow highlighting the relationship between the field heterogeneities and the pore space evolution in each material in contact. Moreover, the porosity measurements show a clogging of the porosity in the clay-rock while the porosity increases in the cement. The extension of the porosity evolution extends to a centimetre on both sides of the interface but is heterogeneously distributed in space as a function of the fissure network and interface geometries. The connected fissure network visualised using autoradiography in the clogged area could permit solute (e.g. radionuclide) transport and may also be interpreted as an evolution of the mechanical properties of the clay-rock formation upon alkaline perturbation. This set of data, with the spatial quantification of the porosity in both cement and clay materials will be useful to constrain reactive transport modelling and thus to predict long term evolution of an engineered barrier.     

Discrete element modelling of deep penetration in granular soils

This paper presents a numerical study on deep penetration mechanisms in granular materials with the focus on the effect of soil–penetrometer interface friction. A two‐dimensional discrete element method has been used to carry out simulation of deep penetration tests on a granular ground that is under an amplified gravity with a K₀ lateral stress boundary. The numerical results show that the deep penetration makes the soil near the penetrometer move in a complex displacement path, undergo an evident loading and unloading process, and a rotation of principal stresses as large as 180°. In addition, the penetration leads to significant changes in displacement and velocity fields as well as the magnitude and direction of stresses. In general, during the whole penetration process, the granular ground undergoes several kinds of failure mechanisms in sequence, and the soil of large deformation may reach a stress state slightly over the strength envelope obtained from conventional compression tests. Soil–penetrometer interface friction has clear effects on the actual penetration mechanisms. Copyright © 2005 John Wiley & Sons, Ltd.     

贵州省水银洞金矿地质特征及成因浅析

水银洞金矿是滇黔桂“金三角”卡林型金矿的重要代表,金矿体赋存于二叠系龙潭组与茅口组不整合界面间,受背斜轴部断裂构造控制,走向上具波状起伏向东倾伏、空间上具多个矿体上下重叠的特点。该矿床属产于沉积碳酸盐岩和构造蚀变体中的“卡林型”金矿,为构造-热液成矿,同时具有中—低温超高压成矿特点。     

Estimation of static earth pressures for a sloping cohesive backfill using extended Rankine theory with a composite log-spiral failure surface

The Rankine earth pressure theory is extended herein to an inclined c–? backfill. An analytical approach is then proposed to compute the static passive and active lateral earth pressures for a sloping cohesive backfill retained by a vertical wall, with the presence of wall–soil interface adhesion. The proposed method is based on a limit equilibrium analysis coupled with the method of slices wherein the assumed profile of the backfill failure surface is a composite of log-spiral and linear segments. The geometry of the failure surface is determined using the stress states of the soil at the two boundaries of the mobilized soil mass. The resultant lateral earth thrust, the point of application, and the induced moment on the wall are computed considering global and local equilibrium of forces and moments. Results of the proposed approach are compared with those predicted by a number of analytical models currently adopted in the design practice for various combinations of soil’s frictional angles, wall–soil interface frictional angles, inclined angles of backfill and soil cohesions. The predicted results are also verified against those obtained from finite element analyses for several scenarios under the passive condition. It is found that the magnitude of earth thrust increases with the backfill inclination angle under both the passive and active conditions.

     

Dolomite formation in the dynamic deep biosphere: results from the Peru Margin

Early diagenetic dolomite beds were sampled during the Ocean Drilling Programme (ODP) Leg 201 at four reoccupied ODP Leg 112 sites on the Peru continental margin (Sites 1227/684, 1228/680, 1229/681 and 1230/685) and analysed for petrography, mineralogy, δ¹³C, δ¹⁸O and ⁸⁷Sr/⁸⁶Sr values. The results are compared with the chemistry, and δ¹³C and ⁸⁷Sr/⁸⁶Sr values of the associated porewater. Petrographic relationships indicate that dolomite forms as a primary precipitate in porous diatom ooze and siliciclastic sediment and is not replacing the small amounts of precursor carbonate. Dolomite precipitation often pre‐dates the formation of framboidal pyrite. Most dolomite layers show ⁸⁷Sr/⁸⁶Sr‐ratios similar to the composition of Quaternary seawater and do not indicate a contribution from the hypersaline brine, which is present at a greater burial depth. Also, the δ¹³C values of the dolomite are not in equilibrium with the δ¹³C values of the dissolved inorganic carbon in the associated modern porewater. Both petrography and ⁸⁷Sr/⁸⁶Sr ratios suggest a shallow depth of dolomite formation in the uppermost sediment (<30 m below the seafloor). A significant depletion in the dissolved Mg and Ca in the porewater constrains the present site of dolomite precipitation, which co‐occurs with a sharp increase in alkalinity and microbial cell concentration at the sulphate–methane interface. It has been hypothesized that microbial ‘hot‐spots’, such as the sulphate–methane interface, may act as focused sites of dolomite precipitation. Varying δ¹³C values from −15‰ to +15‰ for the dolomite are consistent with precipitation at a dynamic sulphate–methane interface, where δ¹³C of the dissolved inorganic carbon would likewise be variable. A dynamic deep biosphere with upward and downward migration of the sulphate–methane interface can be simulated using a simple numerical diffusion model for sulphate concentration in a sedimentary sequence with variable input of organic matter. Thus, the study of dolomite layers in ancient organic carbon‐rich sedimentary sequences can provide a useful window into the palaeo‐dynamics of the deep biosphere.     

The variation of Nγ with footing roughness using the method of characteristics

By using the method of characteristics, the effect of footing–soil interface friction angle (δ) on the bearing capacity factor N_γ was computed for a strip footing. The analysis was performed by employing a curved trapped wedge under the footing base; this wedge joins the footing base at a distance B_t from the footing edge. For a given footing width (B), the value of B_t increases continuously with a decrease in δ. For δ=0, no trapped wedge exists below the footing base, that is, B_t/B=0.5. On the contrary, with δ=?, the point of emergence of the trapped wedge approaches toward the footing edge with an increase in ?. The magnitude of N_γ increases substantially with an increase in δ/?. The maximum depth of the plastic zone becomes higher for greater values of δ/?. The results from the present analysis were found to compare well with those reported in the literature. Copyright © 2008 John Wiley & Sons, Ltd.