Numerical determination of the effective permeability coefficient of soil–rock mixtures using the numerical manifold method

The present study extends the numerical manifold method to investigate the effective permeability coefficient (k_eff) of soil–rock mixtures. The influence of rock content, rock size, rock shape, and rock blocks' major axis direction on k_eff is studied. The results show the following: (1) k_eff decreases as the rock content increases; (2) the influence of rock size on k_eff can be neglected if other parameters are fixed; (3) the values of k_eff are nearly the same if rock blocks are in circular or regular hexagon shapes; and (4) the major axis direction of rock blocks has some influence on k_eff.     

Numerical modeling of three-dimensional contaminant migration from dissolution of multicomponent NAPL pools in saturated porous media

A three-dimensional model for contaminant transport resulting from the dissolution of multicomponent nonaqueous phase liquid (NAPL) pools in three-dimensional saturated subsurface formations is developed. The solution is obtained numerically by a finite-difference scheme, and it is suitable for homogeneous porous media with unidirectional interstitial velocity. Each dissolved component may undergo first-order decay and may sorb under local equilibrium conditions. It is also assumed that the dissolution process is mass transfer limited. The nonaqueous phase activity coefficients of the NAPL pool components are evaluated at each time step. The model behavior is illustrated through a synthetic example with a NAPL pool consisting of a mixture of TCA (1,1,2-trichloroethane) and TCE (trichloroethylene). The numerical solution presented in this work is in good agreement with a recently developed analytical solution for the special case of a single component NAPL pool. The results indicate the importance of accounting for the necessary changes in the organic phase activity which significantly affects the equilibrium aqueous solubility.Notation C liquid phase solute concentration (solute mass/liquid volume) (M L^–3) - C _s single component aqueous saturation concentration (solubility) (M L^–3) - C ^w equilibrium aqueous solubility (M L^–3) - D molecular diffusion coefficient (L² t ^–1) - D _e effective molecular diffusion coefficient (L² t ^–1) - D _x longitudinal hydrodynamic dispersion coefficient (L² t ^–1) - D _y lateral hydrodynamic dispersion coefficient (L² t ^–1) - D _z hydrodynamic dispersion coefficient in the vertical direction (L² t ^–1) - I() integer mode arithmetic operator - k local mass transfer coefficient (Lt ^–1) - k ^* average mass transfer coefficient (Lt ^–1) - L length - l _x ,l _y pool dimensions inx andy directions (L) - ll _x ,l _y x andy Cartesian coordinates of the pool origin (L) - M number of moles remaining in a pool (moles) - M initial number of moles (moles) - n finite-difference scheme time level - R retardation factor (dimensionless) - t time (t) - U _x average interstitial velocity (Lt ^–1) - x, y, z spatial Cartesian coordinates (L) - X dimensionless mole fraction - dimensionless activity coefficient - _w viscosity of water (=0.8904 cp at 25°C) - decay coefficient (t ^–1) - ^* tortuosity ( 1) - i,j, k finite-difference scheme grid indicators - p component number indicator - P total number of components - s pure single component - o nonaqueous phase - w aqueous phase     

Effect of salt of various concentrations on liquid limit,and hydraulic conductivity of different soil-bentonite mixtures

Effect of the various concentrations of NaCl and CaCl₂ on the four different soil-bentonite mixtures has been evaluated. The results show that the liquid limit of the mixtures decreases with an increase in the salt concentration. Liquid limit decreased significantly with an increase in CaCl₂ concentration from 0 to 0.1 N. However, a further increase in the concentration did not produce any significant decrease in liquid limit. A quite opposite trend was observed for the NaCl solution. An increase in NaCl concentration from 0 to 0.1 N did not produce any major decrease in the liquid limit, but a further increase in concentration from 0.1 to 1 N decreased the liquid limit significantly. Consolidation tests were carried out on the mixtures to evaluate the effect of mineralogical composition of the bentonite on the hydraulic conductivity (k) of the mixture in the presence of various salts concentrations. The k for any mixtures was found to be decreasing with decrease in the salt concentration. At relatively low concentration, Ca²⁺ had more effect on the k in comparison to the same concentration of Na⁺. However, at 1 N of NaCl and CaCl₂ almost an equal value of k was observed. A comparison of the performance of four bentonites showed that the mixture with bentonite having highest exchangeable sodium percentage (ESP) exhibited the lowest k when permeated with de-ionized (DI) water, however, k increased with an increase in the salt concentration. Similarly, mixture with a bentonite of lower ESP exhibited a higher k with DI water but with the increase in the salt concentration alteration in the k, compared to all other mixtures, was relatively less.     

External seismic stability of vertical geosynthetic-reinforced soil walls using pseudo-static method

Analysis of external stability of vertical geosynthetic-reinforced soil (GRS) walls is very important in the seismic prone zone. The scope of this paper is to obtain required minimum reinforcement length, L _min, for external seismic stability of vertical GRS walls by pseudo-static limit equilibrium method. Then, L _min can be calculated to resist sliding, eccentricity, and bearing capacity failure modes. The parameters considered include both horizontal and vertical seismic coefficients (k _h and k _v ), surcharge load (q), wall height (H) and the properties of retained backfill, GRS, and foundation soil. Results show that L _min against sliding failure mode, L _min,S , increases more quickly than that against the other two failure modes with the increase in k _h , q, or unit weight of retained backfill, γ _b , while L _min,S decreases more quickly than that against the other two failure modes with increase in friction angle of retained backfill, ? _b , or unit weight of GRS, γ _r . For the different failure modes, the effect of k _v on L _min is not identical with the change of k _h , and in addition, L _min/H will tend to remain unchanged with the increase in H. In general, L _min against bearing capacity failure mode, L _min,BC, is larger than L _min against the other two failure modes. However, L _min,BC will be less than L _min against eccentricity failure mode, L _min,E , for k _h exceeding 0.35, or friction angle of foundation soil, ? _f , exceeding 37°, and L _min,BC will also be less than L _min,S for friction angle of GRS, ? _r , being no more than 26°.     

Non‐linear consolidation analysis of soil with variable compressibility and permeability under cyclic loadings

In this paper, a simple semi‐analytical method has been developed to solve the one‐dimensional non‐linear consolidation problems by considering the changes of compressibility and permeability of the soil layer, subjected to complicated time‐dependent cyclic loadings at the ground surface. The solution presented here takes into account e ～ lg k_v and e ～ lg σ′ linear responses. With c_k the slope of the e ～ lg k_v line and c_c as the slope of the e ～ lg σ′ line, the identified parameter c_c/c_k is found to control the rate of consolidation. Using the solutions obtained, some diagrams are prepared and the relevant behaviours of one‐dimensional non‐linear consolidation of saturated soft soil under cyclic loadings are discussed. The method in this paper does not require any special data; conventional oedometer data can be used. Therefore, the method is particularly efficient and convenient for engineering practice. Copyright © 2006 John Wiley & Sons, Ltd.     

Topological relations in multisystems of more than n+ 3 phases 1

Multisystems of n+k (k > 3) phases are very complicated and knowledge of them has suffered as a result. The successful solution of the topological relationships in n+ 3 phase multisystems by Zen (1966, 1967) and Zen & Roseboom (1972) has aroused much interest regarding what will happen in a multisystem of more than n+ 3 phases. Since 1979, some important research results on this topic have been published. These results have expounded the substantial rules governing the appearance of phase relations in phase diagrams of n - k (k > 3) phase multisystems. The most significant conclusions include: (1) It is impossible to incorporate all the possible phase relations in an n+k (k > 3) phase multisystem in a single closed net. Therefore, it is no longer enough to use only a single closed net to depict the topological relations involved in these types of multisystems. Instead, one or more groups of closed nets, namely the complete system(s) of closed nets are necessary for this purpose. (2) A principle called the Combination Principle has been proposed and proved. It states: Any closed net of one n+k (k > 3) phase multisystem must be a combination of two or more distinct n+ 3 order submultisystem closed nets belonging to the given n+k phase multisystem, if it is not one of the n+ 3 order submultisystem closed nets itself. The combination principle provides both a theoretical basis and a practical method for the construction of closed nets and, hence, for the derivation of the real phase diagrams for any n+k (k > 3) phase multisystem. (3) A theorem on divariant-assemblage-characteristic-stability-polygons is also important to our understanding of the n+k (k± 3) phase multisystem closed nets. This theorem can be stated as follows: A divariant assemblage of an n+k (k± 3) phase multisystem will be stable in an l-polygon lacking diagonals in an appropriate set of closed-net-diagrams, and this l-polygon may be at least a triangle, and at most a k-polygon. In addition, the closed-net-diagrams of unary and binary n+ 4 phase multisystems derived respectively by Guo (1980b, 1980c, 1981a) and by Roseboom & Zen (1982) have also been summarized. The combination principle is applied to a practical petrological problem in this paper, dealing with 7 phases in the system FeO-Fe₂O₃-SiO₂.     

Fractal trees and Horton''s laws

Fractal trees as a model for drainage systems are described in its generalized non-homogeneous form from the viewpoint of fractal geometry. Box covering techniques are used to show the numerical equivalence between the Hausdorff-Besicovitch dimension and the similarity dimension of the fractally-dominant dust formed by the sources. In this way, the similarity relationD=log (N)/log (1/r) is reinterpreted in terms of bifurcation and length ratio (r _B andr _L ) asD=log (r _B )/log (r _L ). We test this relation for non-homogeneous exact fractal trees and two natural drainage systems. The fact thatr _B andr _L are common parameters in quantitative geomorphology allows a trivial stimation of the fractal dimension of well-known drainage basins.     

The limitations of three-dimensional kinematic vorticity analysis

The kinematic vorticity number (W_k) can be calculated for three-dimensional as well as two-dimensional geologic deformations. For steady-state deformations, W_k can be correlated to and analyzed in terms of finite strains. The analysis shows that assumptions commonly made for two-dimensional deformations are not applicable to three-dimensional deformations. A single W_k describes an infinite number of three-dimensional deformations. Further, even knowledge of flow apophyses orientation, instantaneous stretching axes orientation, and/or W_k are not sufficient to describe deformation. Three-dimensional deformations also require knowledge of the deformation ‘type’ or boundary conditions of deformation (e.g. transpression). Hence, in addition to being difficult to estimate, the value of knowing W_k for three-dimensional deformations is greatly reduced compared with plane strain. The most useful methods of determining W_k from naturally deformed rocks are presented.     

Rhythmic Zoning and Self—organization in Silicate Solid—solution Minerals

Rhythmic zoning is ubiquitous in igneous rocks. Based on polymerization and regular solution models, a non-ideal, disequilibrium and non-linear interface equation has been established to describe the process of crystal growth:f = 1/[1 + (β/x ^s )(1 -x ^s )exp(-W / RT)(1 - 2f)] wheref and x^s represent respectively the mole fraction of a component in the crystal and melt at the interface;W the total exchange energy;R the gas constant; andT the temperature; β=k _B /k _A , withk _A andk _B representing respectively the rate constants of components A and B. Results of numerical simulation of the equation demonstrate that a domain of triple valuedness exists ifW / RT < -2. This model, together with the mass balance equation, explains reasonably the rhythmic phenomena in silicate solid solutions, indicating that self-organization is responsible for this process during mineral growth.     

Laboratory Investigation on High Values of Restitution Coefficients

Restitution coefficients are used to quantify the energy dissipation upon impact when predicting rock fall events. These coefficients can be determined in situ or in the laboratory. In any case, the usual values for the normal restitution coefficient k _n are below unity. Values greater than one are quite rare, seen as unusual and barely explained. Previous experimental research conducted in Australia has shown consistent and systematic values of the normal restitution coefficient greater than one. This was tentatively explained by a combination of parameters such as low impacting angle, rotational energy and block angularity. The study presented in this paper aims at (1) identifying the critical parameters conducting to high k _n values and (2) at explaining the associated motion mechanisms. The objective was reached with values of k _n up to almost 2. In addition, the study has confirmed the significance of low impacting angle, rotational energy and block shape in this context.     

Evolution of pore structure and hydraulic conductivity of randomly distributed soluble particle mixture

The plane strain behavior of particulate mixtures containing soluble particles was investigated by conducting both laboratory tests and numerical analysis. To perform the laboratory experiments, soluble mixtures were prepared using photoelastic disks and ice disks with diameters in the ratios (D_{ice disk}/D_{photoelastic disk}) of 0.5 and 0.7, and the evolution of the force chain and pore structure was monitored during the dissolution of the ice disks. Subsequently, numerical analysis was conducted by using the 2‐dimensional discrete element method for the soluble mixtures, and it was compared with the experimental results. Additionally, parametric studies were implemented by varying the particle size ratios between the soluble and non‐soluble particles and the volumetric fraction of the soluble particles. The results of the laboratory experiments and numerical analysis demonstrate that (1) after the dissolution of the soluble particles, the pore fabric of the specimens changed, resulting in a force chain changes, local void increases, and coordination number decreases; (2) the effects of soluble particles on the macro‐behaviors of the mixtures could be divided into 3 zones based on the particle size ratios between the soluble and non‐soluble particles and volumetric fraction of soluble particles. These zones were as follows: (Zone 1)—with a small total soluble volume, slight decrease in the in situ lateral pressure (K₀), and minor increase in the hydraulic conductivity (k); (Zone 2)—with a moderate soluble particle; the dissolution generated a honey‐comb particle structure; (Zone 3)—the total soluble volume was very large, and the high volumetric fraction of the dissolving particle collapsed the pore structure, decreasing in the in situ lateral pressure (K₀) but increasing the hydraulic conductivity (k). The horizontal stress returned to almost the original level, and the internal arching formation increased significantly with the hydraulic conductivity (k).     

Earthquakes in Switzerland and surrounding regions during 2008

This report of the Swiss Seismological Service summarizes the seismic activity in Switzerland and surrounding regions during 2008. During this period, 451 earthquakes and 75 quarry blasts were detected and located in the region under consideration. The three strongest events occurred in the Valais, near Lac des Toules (M_L 3.6), and in Graubünden, near Ilanz (M_L 3.7) and Paspels (M_L 4.0). Although felt by the population, they were not reported to have caused any damage. However, with a total of only 15 events with M_L ≥ 2.5, the seismic activity in the year 2008 was far below the average over the previous 33 years.     

Dimensional Reduction of Pattern-Based Simulation Using Wavelet Analysis

A pattern-based simulation technique using wavelet analysis is proposed for the simulation (wavesim) of categorical and continuous variables. Patterns are extracted by scanning a training image with a template and then storing them in a pattern database. The dimension reduction of patterns in the pattern database is performed by wavelet decomposition at certain scale and the approximate sub-band is used for pattern database classification. The pattern database classification is performed by the k-means clustering algorithm and classes are represented by a class prototype. For the simulation of categorical variables, the conditional cumulative density function (ccdf) for each class is generated based on the frequency of the individual categories at the central node of the template. During the simulation process, the similarity of the conditioning data event with the class prototypes is measured using the L ₂-norm. When simulating categorical variables, the ccdf of the best matched class is used to draw a pattern from a class. When continuous variables are simulated, a random pattern is drawn from the best matched class. Several examples of conditional and unconditional simulation with two- and three- dimensional data sets show that the spatial continuity of geometric features and shapes is well reproduced. A comparative study with the filtersim algorithm shows that the wavesim performs better than filtersim in all examples. A full-field case study at the Olympic Dam base metals deposit, South Australia, simulates the lithological rock-type units as categorical variables. Results show that the proportions of various rock-type units in the hard data are well reproduced when similar to those in the training image; when rock-type proportions between the training image and hard data differ, the results show a compromise between the two.     

On the assessment of maximum earthquakes in the alps and adjacent areas

Strong tectonic earthquakes within the crust always occur on already existing faults, and they have the property of a shear rupture. Such earthquakes with surface-wave magnitudes M < 7 obviously have a geometric similarity. Because of this similarity and the validity of the Gutenberg and Richter's energy—magnitude relation, the expression M = 2 log₁₀ L + const., with L = focal length, is valid.The expression L_maxL^* for the maximum focal length, is also valid if L^* is the length of the rectilinear extent of the seismic line on which the maximum earthquake occurs. The bounds of L^* may be given by sharp bends and/or by traversing deep faults. Thus the maximum imaginable earthquake on a seismic line with the length L^* has the magnitude M_max = 2 log₁₀ L^* + const.For the investigated region — the Alps and adjacent areas — from the data of recent and historical strong earthquakes, it follows that M_max = 2 log₁₀ L^* + 1.7, if L^* is measured in kilometres. These limiting values lie in the centre-field of the magnitude range for maximum earthquakes, published by Shebalin in 1970. By the aid of this equation it is also possible to assess the upper limiting value of the accompanying maximum scale intensity.     

Thin flow element and the problem of ill-conditioning

The problem of ill-conditioning in anisotropic and heterogeneous flow regions using plane and axisymmetric conditions is studied. A new concept, conditioning ratio, which covers all the possible factors significantly affecting the problem of ill-conditioning (e.g. aspect ratio, heterogeneity and anisotropy) is proposed. It has been shown that there is an upper limit for this conditioning ratio, beyond which the stiffness matrix of the modelled region will be ill-conditioned. Using this limiting value and considering the fact that flow behaviour in a single fracture is, basically, independent of the value of permeability normal to the plane of the fracture, k₁, a criterion is established to calculate the value of k₁ for thin elements. By adopting this criterion the problem of ill-conditioning could be avoided, regardless of the value of the aspect ratio. The reliability of the proposed criterion is examined by using thin elements with very large aspect ratio (up to 10⁶) in modelling the pumping problem from a well fully intersecting a vertical fracture. The comparison of the numerical results with the available analytical solutions is found to be very satisfactory.     

Drift loss cone instability in the ring current and plasma sheet

The drift loss cone instability, propagating nearly transverse to the ambient magnetic field, is studied in the ring current plasma taking into account the relative driftU between electrons and protons due to density gradients. The growth rates attain maxima and then decrease as the wave number parallel to the magnetic fieldk _II increases. The peak values of the growth rates, maximised with respect tok _II, are enhanced by the increase in number density, electron temperature and loss cone index, and by the decrease in β_t, the ratio of the proton thermal pressure to magnetic field pressure. The unstable frequencies fall in the range of 5 to 30Ω_p with the growth rate γ ≥Ω_p. In the ring current region betweenL=4 and 5, the instability will generate a strong turbulence in the frequency range between 5–500 Hz which can produce fluctuating electric fields 0. 5–5 mV/m and magnetic field 0.8–80mγ. This instability can also occur on the auroral field lines, which connect to the region of intense earthward plasma flow in the distant magnetotail and produce a broad band electrostatic noise.     

Nonlinear Response of Single Piles in Sand Subjected to Lateral Loads using k hmax Approach

This paper presents results of analysis of full-scale pile load test data of 14 piles embedded in either loose or medium dense sands. The analysis was performed using two methods, p–y curve approach and a more recently developed k_hmax approach. Comparison of the results obtained using both the methods is also presented. A step-by-step analysis procedure is presented for predicting lateral load deflection response of single piles in sand using the k_hmax approach. The results presented show that the k_hmax approach has promise over the p–y curve approach because of its simplicity and the fact that it provides upper- and lower-bound curves, which are valuable guides to making engineering decisions. For loose sands, a new range of k_hmax values is recommended to better predict the lateral load–deflection response of single piles.     

Statistical relations between source parameters for low and intermediate magnitudes (Friuli, 1976)

A data set of three-component short-period digital seismograms recorded in Friuli after the strong earthquake of 6th May 1976, allowed the local magnitude M_L and the seismic moment M₀ to be estimated in the range 0 < M_L < 2. The data set including the same parameters for the higher-magnitude Friuli events (M_L 5) shows two different slopes for the relation Log M₀ = CM_L + d for the two different ranges of M_L. One finds C ~ 1.0 (for 0 < M_L < 2) and C ~1.5 (for5 M_L 6.2), respectively.This implies that apparent stress release increases at low magnitudes, while it appears to be comparatively independent of the magnitude and to have an average value of about 100 bar for higher-magnitude earthquakes. Conversely, the fault dimensions do not appear to be magnitude-dependent for M_L < 2; for higher-magnitude events the linear fault dimensions range from about 1 km at M_L ~ 5 to about 12 km for the strong earthquake of 6th May 1976 (M_L = 6.2).