A hybrid discrete–finite element model for numerical simulation of geomaterials

A hybrid discrete–finite element model is introduced for simulation of mechanical behavior of geomaterials. The soil or rock is modeled as a system of discrete balls that interact through normal and shear springs. The balls can be bonded at the contact points to withstand the applied deviatoric stresses. The important feature of this model is that the confining walls that can be imagined for example as the surrounding membrane or the mold in a physical test are modeled by deformable finite elements. This allows simulation of laboratory test features more realistically compared to the situations where the surrounding walls are rigid. The relationships between micro- and macro-properties are investigated in this paper as well. These relationships and the corresponding curves are helpful tools in calibration of the numerical model for the macroscopic elastic properties.     

Coupled transient saturated–unsaturated seepage and limit equilibrium analysis for slopes: influence of rapid water level changes

This study investigates the influence of the water level fluctuation on the stability of soil slopes using coupled seepage and slope stability analysis. A simulation framework was proposed and implemented seamlessly using Python code to seek insights into three factors that have not been thoroughly studied for this issue: soil unit weight variation in the unsaturated zone, unsaturated shear strength models, and velocity of water drawdown. For this purpose, the seepage analysis was carried out by discretizing a numerical seepage analysis model using a finite element analysis platform, FEniCS. The output of the seepage analysis, i.e., pore water pressure distribution, was used as input for the slope stability analysis. Limit equilibrium methods including the Bishop Simplified method and the Ordinary Method of Slices were modified to take into consideration the unsaturated shear strength, unit weight variation in the unsaturated zone, and hydrostatic pressure changes in response to the water level fluctuation of a reservoir. Both seepage and slope analysis modules were validated against commercial programs. Analysis results obtained with the validated framework clearly revealed the distinct influences of the three factors in representative silty and sandy slopes.

     

Consistent modeling of a catastrophic flowslide at the Shenzhen landfill using a hydro-elasto-plastic model with solid–fluid transition

Flow-type landslides are an important hazard that can cause great destruction due to the rapid flow velocity and large disaster area. This paper presents a catastrophic flowslide that recently occurred at a landfill in Shenzhen, China. This disaster involved an area about 1100 m in length and 630 m in maximum width, and caused the death of 77 people and the destruction of 33 buildings. The precise reason for the landfill’s failure is still unknown, and therefore we try to contribute an increased understanding of the event for future prevention. In this study, the failure mechanism of the studied slope was analyzed and described under partially saturated condition. The solid–fluid transition during the flowslide occurrence was described using a unified constitutive model. The model was used to perform the hydro-elasto-plastic modeling in the pre-failure stage, the viscous modeling in the post-failure stage, and the second-order work criterion was introduced in between to model the solid–fluid transition. The consistent evolution of the flowslide, including initiation, propagation, and deposit stages, was simulated and analyzed using the finite element method with Lagrangian integration points after careful calibration of the viscous parameters. The numerical results were compared with the real case and used to explain the failure mechanism.     

A comparative study of shallow groundwater level simulation with WA–ANN and ITS model in a coastal island of south China

Accurate and reliable prediction of shallow groundwater level is a critical component in water resources management. Two nonlinear models, WA–ANN method based on discrete wavelet transform (WA) and artificial neural network (ANN) and integrated time series (ITS) model, were developed to predict groundwater level fluctuations of a shallow coastal aquifer (Fujian Province, China). The two models were testified with the monitored groundwater level from 2000 to 2011. Two representative wells are selected with different locations within the study area. The error criteria were estimated using the coefficient of determination (R ²), Nash–Sutcliffe model efficiency coefficient (E), and root-mean-square error (RMSE). The best model was determined based on the RMSE of prediction using independent test data set. The WA–ANN models were found to provide more accurate monthly average groundwater level forecasts compared to the ITS models. The results of the study indicate the potential of WA–ANN models in forecasting groundwater levels. It is recommended that additional studies explore this proposed method, which can be used in turn to facilitate the development and implementation of more effective and sustainable groundwater management strategies.     

Thermal thickness of the Earth’s lithosphere: a numerical model

A technique is suggested and the thermal thickness of the lithosphere is calculated, as well as the temperature distribution in the lithosphere on the basis of data on topography, the age of the oceanic bottom, crustal composition and structure, gravity anomalies, and mean annual surface temperatures. The bottom of the lithosphere is determined as the 1300°C isotherm. The calculation resolution is 0.5°×0.5°. All first-order tectonic structures, such as mid-ocean ridges and plume areas in oceans, continental rifts, cratons, and orogenic belts, are expressed in the computed thermal thickness. The comparative analysis of the thermal thickness of oceanic and continental lithosphere, lithosphere of cratons and young platforms, ancient and young orogens, remnant oceanic basins and adjacent continental areas can be used in geodynamical analysis of the corresponding regions.     

Development and validation of a 3D numerical model for TBM–EPB mechanised excavations

A 3D numerical model for mechanised excavations is presented, which is capable of simulating the overall process of excavation and construction of a tunnel when a TBM EPB (Tunnel Boring Machine–Earth Pressure Balance) is used.The main construction aspects of a mechanised excavation are modelled. Their influence on calculated ground displacements are investigated by means of a series of parametric analyses.With the aim of testing the performance of the proposed 3D numerical model, a series of 25 Class C predictions has been carried out. Case Histories related to the construction of the 1995–2003 Madrid Metro Extension Project were considered for this purpose.As a general rule, the results obtained with the Modified Cam–Clay model closely fit in situ measurements. When the Linear-Elastic or the Mohr–Coulomb models are used, it is not as easy to summarise the results obtained, as higher fluctuations are observed around in situ measured data. A good agreement is also shown when the distribution of horizontal displacements along depth is considered.For some sections, the mechanised excavation model is not capable of reproducing the high values of the surface settlements measured in situ. A closer look at the results shows that mixed face conditions are found for these cases, with the TBM excavating through layered soil formations having sharply different mechanical behaviour.     

A review of the pressure–temperature–time evolution of the Limpopo Belt: Constraints for a tectonic model

Published literature argues that the Limpopo Belt can be subdivided into three zones, each with a distinctive geological character and tectono-metamorphic fingerprint. There are currently two contrasting schools of thought regarding the tectono-metamorphic evolution of the CZ. One camp argues that geochronological, structural and prograde pressure–temperature (P–T) evidence collectively indicate that the CZ underwent tectono-metamorphism at ca. 2.0 Ga which followed a clockwise P–T evolution during a transpressive orogeny that was initiated by the collision of the Kaapvaal and Zimbabwe cratons. Deformation and metamorphism consistent with this scenario are observed in the southern part of the NMZ but are curiously absent from the whole of the SMZ. The opposing view argues that the peak metamorphism associated with the collision of the Kaapvaal and Zimbabwe cratons occurred at ca. 2.6 Ga and the later metamorphic event is an overprint associated with reactivation along Archean shear zones. Post-peak-metamorphic conditions, which at present cannot be convincingly related to either a ca. 2.6 or 2.0 Ga event in the CZ reveal contrasting retrograde paths implying either near-isothermal decompression and isobaric cooling associated with a ‘pop-up’ style of exhumation or steady decompression–cooling linked to exhumation controlled by erosion. Recent data argue that the prograde evolution of the ca. 2.0 Ga event is characterised by isobaric heating prior to decompression–cooling. Contrasting P–T paths indicate that either different units exist within the CZ that underwent different P–T evolutions or that some P–T work is erroneous due to the application of equilibrium thermobarometry to mineral assemblages that are not in equilibrium. The morphology of the P–T path(s) for the ca. 2.6–2.52 Ga event are also a matter of dispute. Some workers have postulated an anticlockwise P–T evolution during this period whilst others regard this metamorphic event as following a clockwise evolution. Granitoid magmatism is broadly contemporaneous in all three zones at ca. 2.7–2.5 suggesting a possible causal geodynamic link. P–T contrasts between and within the respective zones prevent, at present, the construction of a coherent and inter-related tectonic model that can account for all of the available evidence. Detailed and fully-integrated petrological and geochronological studies are required to produce reliable P–T–t paths that may resolve some of these pertinent issues.     

Formation of the Olyutorsky–Kamchatka foldbelt: a kinematic model

The Olyutorsky–Kamchatka foldbelt formed as a result of two successive collisions of the Achaivayam–Valaginsky and Kronotsky–Commander island arcs with the Eurasian margin where the two terranes docked after a long NW transport. We model their motion history from the Middle Campanian to Present and illustrate the respective plate margin evolution with ten reconstructions. In this modeling the arcs are assumed to travel on the periphery of the large plates of Eurasia, North America, Pacific, and Kula, for which the velocities and directions of motion are known from published data. The model predicts that the Achaivayam–Valaginsky arc was the leading edge of the Kula plate from the Middle Campanian to the Middle Paleocene and then moved slowly with the Pacific plate as long as the Middle Eocene when it accreted to Eurasia. The Kronotsky arc initiated in the Middle Campanian on the margin of North America and was its part till the latest Paleocene when the terrane changed polarity to move northwestward with the Pacific plate and eventually to collide with Eurasia in the Late Miocene. The predicted paleolatitudes of the Achaivayam–Valaginsky and Kronotsky–Commander island arcs for the latest Cretaceous and Paleogene are consistent with nine (out of eleven) reliable paleomagnetic determinations for samples from the two arcs. Additional changes imposed on the initial model parameters (kinematics of the large plates, relative position of the Kula–Pacific Ridge and the Emperor seamount chain, or time of active volcanism within the arcs) worsen the fit of the final reconstructions to available geological and paleomagnetic data. Therefore, the suggested model appears to be the most consistent one at this stage of knowledge.     

Evaluation of numerical stress-point algorithms on elastic–plastic models for unsaturated soils with hardening dependent on the degree of saturation

Constitutive models of unsaturated soils, and in particular those based on constitutive variables which include both degree of saturation and suction, are characterised by strong non linearities due to hydromechanical coupling. In this paper, a refined Runge–Kutta–Dormand–Prince explicit algorithm and a fully implicit Euler scheme are compared for the integration of the latter class of models. The explicit and implicit procedures have been tested along different hydromechanical paths, involving various hydraulic and mechanical external control conditions. Accuracy and efficiency of the algorithms have been investigated. The results confirm that substepping is mandatory for the explicit algorithm to converge regardless the initial step size and to remain sufficiently accurate. The value of the incremental hydromechanical work per unit volume was calculated during the explicit integration procedure. The numerical results show that the maximum size of the substep which can be adopted to meet a given tolerance depends on the gradient of the incremental work per unit volume. Therefore, the latter appears a good candidate to identify problematic integration steps in terms of convergence. Accuracy of the implicit algorithm also depends on the chosen step size, although the algorithm proved to be convergent in all the paths analysed.     

Exploring the magnitude–frequency distribution: a cellular automata model for landslides

Landslide magnitude–frequency curves allow for the probabilistic characterization of regional landslide hazard. There is evidence that landslides exhibit self-organized criticality including the tendency to follow a power law over part of the magnitude–frequency distribution. Landslide distributions, however, also typically exhibit poor agreement with the power law at smaller sizes in a flattening of the slope known as rollover. Understanding the basis for this difference is critical if we are to accurately predict landslide hazard, risk or landscape denudation over large areas. One possible argument is that the magnitude–frequency distribution is dominated by physiographic controls whereby landslides tend to a larger size, and larger landslides are landscape limited according to a power law. We explore the physiographic argument using first a simple deterministic model and then a cellular automata model for watersheds in coastal British Columbia. The results compare favorably to actual landslide data: modeled landslides bifurcate at local elevation highs, deposit mass preferentially where the local slopes decrease, find routes in confined valley or channel networks, and, when sufficiently large, overwhelm the local topography. The magnitude–frequency distribution of both the actual landslides and the cellular automata model follow a power law for magnitudes higher than 10,000–20,000 m² and show a flattening of the slope for smaller magnitudes. Based on the results of both models, we argue that magnitude–frequency distributions, including both the rollover and the power law components, are a result of actual physiographic limitations related to slope, slope distance, and the distribution of mass within landslides. The cellular automata model uses simple empirically based rules that can be gathered for regions worldwide.     

Geostatistical analysis of spatiotemporal variability of groundwater level fluctuations in Amman–Zarqa basin,Jordan: a case study

The main objective of this study was to assess the spatial and temporal variability of groundwater level fluctuations in the Amman–Zarqa basin, during the period 2001–2005. In the year 2003, as a consequence of war, there was a sudden increase in the population in this basin. Knowing that the basin is already heavily populated and witnesses most of the human and industrial activities in Jordan, this study was prompted to help make wise water resources management decisions to cope with the new situation. Data from 31 fairly distributed wells in the upper aquifer of the basin were subjected to geostatistical treatment. Kriging interpolation techniques have indicated that the groundwater flow directions remained almost constant over the years. The two main directions are SW–NE and E–W. Kriging mapped fluctuations have also showed that drop and rise events are localized in the basin. Forecasting possibilities for management purposes were tackled using autocorrelation analysis. The constructed autocorrelograms indicated, in general, the temporal dependence of seasonal water level fluctuations, and that forecasting can be carried out within a period of 3–21 months. Several suggestions were made to mitigate the drop and rise hazards in the detected sites.     

Computational simulation of time-dependent behavior of soil–structure interaction by using a novel creep model: Application to a geosynthetic-reinforced soil physical model

In this paper, a model geosynthetic-reinforced soil retaining walls (GRS-RW) is tested by vertically loading it through a rough footing on the top near the retaining wall and the results are simulated by a sophisticated nonlinear Finite Element Method (FEM) having a novel rate dependent constitutive model for both the backfill material and the geosynthetic reinforcement. Usually, polymer geosynthetic reinforcement is known to exhibit more-or-less rate-dependent stress–strain or load–strain behavior due to their viscous properties. The geomaterials (i.e., clay, sand, gravel and soft rock) also exhibit viscous properties. The viscous behavior of geometrials are quite different from that of the polymer based geosynthetic-reinforcements. It has been revealed recently that viscous behavior of sand is a kind of temporary effect, which vanishes with time. So the rate-dependent deformation of backfill reinforced with polymer geosynthetic reinforcement becomes highly complicated due to interactions between the elasto-viscoplastic properties of backfill and reinforcement. In the present study, a scaled model geosynthetic-reinforced soil retaining wall is tested with a vertically loaded rough rigid footing. The results of the model test are simulated by using an appropriate elasto-viscoplastic constitutive model of both sand and geogrid embedded in a nonlinear plane strain FEM.     

Calibration of the parameters for a hardening–softening constitutive model using genetic algorithms

The present paper introduces a genetic algorithm-based optimization technique to calibrate a nonlinear strain hardening–softening constitutive model for soils using five material parameters. The efficiency of the proposed technique is analyzed through the use of different GA techniques. The effects of elitism, crossover, and mutation, as well as population size, on the performance of the conventional GAs for this problem are investigated. Micro-genetic algorithms (mGAs) are chosen and tested for different population sizes. The mGAs with a population size of five yields the optimal parameter values after fewer function evaluations and capture the overall simulated or experimental behavior at every point in stress–strain and strain paths in triaxial compression. The proposed calibration technique is validated through comparison with the traditional calibration technique.     

Flow in the unsaturated zone around a shallow subsurface radioactive waste trench: Interpretation of an infiltration–drainage test at the Chernobyl Pilot Site

This article describes an infiltration–drainage test carried out in the unsaturated zone (UZ) at the Chernobyl Pilot Site during October 2008; this is an international radioecology study site and is the subject of several papers in this special issue. The test has to be seen in the larger context of radionuclide transport from a waste trench. The conducted experiment consisted of infiltrating a layer of 9.5 cm of water in a circular area of 5.51 m² over 5 h. Its main objective was to create a larger range of water content values (and hence suction pressure values), not only at the top of the soil profile but also at greater depths, in this case up to 1.50 m. Observations of water content and suction pressure were carried out continuously at seven different depths during infiltration, drainage and during the return to natural conditions over a period of several months. This allowed deriving UZ parameter values with greater confidence than those derived from monitoring small natural water content changes over periods of years.     

Factors controlling the configuration of the fresh–saline water interface in the Dead Sea coastal aquifers: synthesis of TDEM surveys and numerical groundwater modeling

TDEM (time domain electromagnetic) traverses in the Dead Sea (DS) coastal aquifer help to delineate the configuration of the interrelated fresh-water and brine bodies and the interface in between. A good linear correlation exists between the logarithm of TDEM resistivity and the chloride concentration of groundwater, mostly in the higher salinity range, close to that of the DS brine. In this range, salinity is the most important factor controlling resistivity. The configuration of the fresh–saline water interface is dictated by the hydraulic gradient, which is controlled by a number of hydrological factors. Three types of irregularities in the configuration of fresh-water and saline-water bodies were observed in the study area: 1. Fresh-water aquifers underlying more saline ones ("Reversal") in a multi-aquifer system. 2. "Reversal" and irregular residual saline-water bodies related to historical, frequently fluctuating DS base level and respective interfaces, which have not undergone complete flushing. A rough estimate of flushing rates may be obtained based on knowledge of the above fluctuations. The occurrence of salt beds is also a factor affecting the interface configuration. 3. The interface steepens towards and adjacent to the DS Rift fault zone. Simulation analysis with a numerical, variable-density flow model, using the US Geological Survey's SUTRA code, indicates that interface steepening may result from a steep water-level gradient across the zone, possibly due to a low hydraulic conductivity in the immediate vicinity of the fault. Electronic Publication     

Influence of diesel fuel contamination on the electrical properties of unsaturated soil at a low frequency range of 100 Hz–10 MHz

In this study, the effect of diesel fuel contamination on the electrical properties of unsaturated soils was estimated in the low frequency ranges. For the soils having 5% water content, the electrical resistivity increased with the diesel fuel contents while the permittivity decreased at higher diesel contents. However, at 15% water content, the variation of electrical properties was not significant possibly because most of the electric currents should occur through the pore water. The linear relationship between the electrical resistivity and the diesel fuel contents in soil was developed at 5% water content, which implied that the electrical resistivity could be used to quantify the extent of diesel fuel contamination in soil. The results indicated that the electrical properties including the resistivity and the permittivity could give the reliable estimation on the diesel contamination with the low water content in soil and the frequency applied below 1 MHz.     

Hydrochemical evolution of groundwater in a riparian zone affected by acid mine drainage (AMD), South China: the role of river–groundwater interactions and groundwater residence time

Investigations were undertaken in the riparian zone near Shangba village, an AMD area, in southern China to determine the effects that river–groundwater interactions and groundwater residence time have had on environmental quality and geochemical evolution of groundwater. Based on the Darcy’s law and ionic mass balances as well as the method of isotopic tracer, the results showed that there were active interactions between AMD-contaminated river water and groundwater in the riparian zone in the study area. River water was found to be the main source of groundwater recharge in the northwestern part of the study area, whereas groundwater was found to be discharging into the river in the southeastern part of the study area throughout the year. End-member mixing analysis quantified that the contributions of river water to groundwater decreased gradually from 35.9% to negligible levels along the flow path. The calculated mixing concentrations of major ions indicated that water–rock reactions were the most important influence on groundwater quality. The wide range of Ca²⁺?+?Mg²⁺ and HCO₃^? ratios and the change of groundwater type from Ca²⁺–SO₄^2? type to a chemical composition dominated by Ca²⁺–HCO₃^? type indicated a change of the major water–rock reaction process from the influence of H₂SO₄ (AMD) to that of CO₂ (soil respiration) along a groundwater flow path. Furthermore, the kinetics interpretation of SO₄^2? and HCO₃^? concentrations suggested that the overlapping time of their kinetics triggered the hydrochemical evolution and the change of major weathering agent. This process might take approximately 8 years and this kinetic time will be continued when a steady source of contamination enter the aquifer.