Sandbox Experiments Research Articles

Digital sandbox modelling of Indian collision to Eurasia

Summary Discrete Element Method (DEM) is a powerful tool as a digital sandbox simulator to numerically reproduce fault related structures and to analyse the deformation quantitatively. Similar to analogue sandbox experiments, DEM approximates the geologic body as an assembly of particles that can properly simulate the brittle behaviour of the upper crust. We examined the collision process of the Indian sub-continent to the Eurasian Plate by using the DEM. The simulations reproduced the deformation geometry similar to published analogue experiments. Velocity and stresses of each particle extracted from the simulation were quite unstable showing a characteristic feature of the brittle behaviour of the upper crust. A comparison of these results with GPS and in-situ stress data of the eastern Asia suggests that the ductile deformation of the lower crust and mantle may have major roles to control the real deformation. The results also suggest that Tapponnier’s tectonic model may have a strong boundary effect, particularly to the stress field within the model.

Redox potential distribution inferred from self‐potential measurements associated with the corrosion of a burden metallic body

ABSTRACTNegative self‐potential anomalies can be generated at the ground surface by ore bodies and ground water contaminated with organic compounds. These anomalies are connected to the distribution of the redox potential of the ground water. To study the relationship between redox and self‐potential anomalies, a controlled sandbox experiment was performed. We used a metallic iron bar inserted in the left‐hand side of a thin Plexiglas sandbox filled with a calibrated sand infiltrated by an electrolyte. The self‐potential signals were measured at the surface of the tank (at different time lapses) using a pair of non‐polarizing electrodes. The self‐potential, the redox potential, and the pH were also measured inside the tank on a regular grid at the end of the experiment. The self‐potential distribution sampled after six weeks presents a strong negative anomaly in the vicinity of the top part of the iron bar with a peak amplitude of −82 mV. The resulting distributions of the pH, redox, and self‐potentials were interpreted in terms of a geobattery model combined with a description of the electrochemical mechanisms and reactions occurring at the surface of the iron bar. The corrosion of iron yields the formation of a resistive crust of fougerite at the surface of the bar. The corrosion modifies both the pH and the redox potential in the vicinity of the iron bar. The distribution of the self‐potential is solved with Poisson's equation with a source term given by the divergence of a source current density at the surface of the bar. In turn, this current density is related to the distribution of the redox potential and electrical resistivity in the vicinity of the iron bar. A least‐squares inversion method of the self‐potential data, using a 2D finite difference simulation of the forward problem, was developed to retrieve the distribution of the redox potential.

Detection and localization of hydromechanical disturbances in a sandbox using the self‐potential method

Four sandbox experiments were performed to understand the self‐potential response to hydro‐mechanical disturbances in a water‐infiltrated controlled sandbox. In the first two experiments, ∼0.5 mL of water was abruptly injected through a small capillary at a depth of 15 cm using a syringe impacted by a hammer stroke. In the second series of experiments, ∼0.5 mL of pore water was quickly pumped out of the tank, at the same depth, using a syringe. In both type of experiments, the resulting self‐potential signals were measured using 32 sintered Ag/AgCl medical electrodes. In two experiments, these electrodes were located 3 cm below the top surface of the tank. In two other experiments, they were placed along a vertical section crossing the position of the capillary. These electrodes were connected to a voltmeter with a sensitivity of 0.1 μV and an acquisition frequency of 1.024 kHz. The injected/pumped volumes of water produced hydro‐mechanical disturbances in the sandbox. In turn, these disturbances generated dipolar electrical anomalies of electrokinetic nature with an amplitude of few microvolts. The source function is the product of the dipolar Green's function by a source intensity function that depends solely on the product of the streaming potential coupling coefficient of the sand to the pore fluid overpressure with respect to the hydrostatic pressure. Numerical modeling using a finite element code was performed to solve the coupled hydro‐mechanical problem and to determine the distribution of the resulting self‐potential during the course of these experiments. We use 2D and 3D algorithms based on the cross‐correlation method and wavelet analysis of potential fields to show that the source was a vertical dipole. These methods were also used to localize the position of the source of the hydromechanical disturbance from the self‐potential signals recorded at the top surface of the tank. The position of the source agrees with the position of the inlet/outlet of the capillary showing the usefulness of these methods for application to active volcanoes.

Underthrusting‐accretion cycle: Work budget as revealed by the boundary element method

Sandbox models of accretionary wedges have demonstrated that fault systems grow episodically via cycles of alternating wedge thickening, which is accommodated by slip along faults within the wedge (underthrusting), and wedge lengthening, which is accommodated by growth of new faults at the wedge toe (accretion). The transition between these two modes of deformation is controlled by the interplay of work against gravity, frictional heating, the work of deformation around faults, and the work of fault propagation and seismic/acoustic energy. Using numerical mechanical models based on the boundary element method, we have simulated the deformation observed in sandbox experiments, providing a mechanical analysis of the underthrusting/accretion transition. Our results show that the total work done by the contracting wedge increases during the underthrusting stage up to a critical value when the propagation of a new frontal thrust significantly reduces the work required for further deformation. The numerical models also predict the location of the maximum shear along the basal décollement during underthrusting as well as the energetically most viable position and vergence for the nucleation of a new thrust. These locations do not coincide, and the match of the energetically most favorable position with the experimental results suggests that the new thrust ramps develop first ahead and then link down and backward to the propagating basal décollement. The shear localization producing a new thrust ramp will occur where the energy spent by the deforming wedge is minimized due to an optimal combination of gravitational, frictional, internal, and propagation work terms.

Modeling the shortening history of a fault tip fold using structural and geomorphic records of deformation

We present a methodology to derive the growth history of a fault tip fold above a basal detachment. Our approach is based on modeling the stratigraphic and geomorphic records of deformation, as well as the finite structure of the fold constrained from seismic profiles. We parameterize the spatial deformation pattern using a simple formulation of the displacement field derived from sandbox experiments. Assuming a stationary spatial pattern of deformation, we simulate the gradual warping and uplift of stratigraphic and geomorphic markers, which provides an estimate of the cumulative amounts of shortening they have recorded. This approach allows modeling of isolated terraces or growth strata. We apply this method to the study of two fault tip folds in the Tien Shan, the Yakeng and Anjihai anticlines, documenting their deformation history over the past 6–7 Myr. We show that the modern shortening rates can be estimated from the width of the fold topography provided that the sedimentation rate is known, yielding respective rates of 2.15 and 1.12 mm/yr across Yakeng and Anjihai, consistent with the deformation recorded by fluvial and alluvial terraces. This study demonstrates that the shortening rates across both folds accelerated significantly since the onset of folding. It also illustrates the usefulness of a simple geometric folding model and highlights the importance of considering local interactions between tectonic deformation, sedimentation, and erosion.

Kinematics of fault‐related folding derived from a sandbox experiment

We analyze the kinematics of fault tip folding at the front of a fold‐and‐thrust wedge using a sandbox experiment. The analog model consists of sand layers intercalated with low‐friction glass bead layers, deposited in a glass‐sided experimental device and with a total thickness h = 4.8 cm. A computerized mobile backstop induces progressive horizontal shortening of the sand layers and therefore thrust fault propagation. Active deformation at the tip of the forward propagating basal décollement is monitored along the cross section with a high‐resolution CCD camera, and the displacement field between pairs of images is measured from the optical flow technique. In the early stage, when cumulative shortening is less than about h/10, slip along the décollement tapers gradually to zero and the displacement gradient is absorbed by distributed deformation of the overlying medium. In this stage of detachment tip folding, horizontal displacements decrease linearly with distance toward the foreland. Vertical displacements reflect a nearly symmetrical mode of folding, with displacements varying linearly between relatively well defined axial surfaces. When the cumulative slip on the décollement exceeds about h/10, deformation tends to localize on a few discrete shear bands at the front of the system, until shortening exceeds h/8 and deformation gets fully localized on a single emergent frontal ramp. The fault geometry subsequently evolves to a sigmoid shape and the hanging wall deforms by simple shear as it overthrusts the flat ramp system. As long as strain localization is not fully established, the sand layers experience a combination of thickening and horizontal shortening, which induces gradual limb rotation. The observed kinematics can be reduced to simple analytical expressions that can be used to restore fault tip folds, relate finite deformation to incremental folding, and derive shortening rates from deformed geomorphic markers or growth strata.

Kinematic analysis of the Pakuashan fault tip fold, west central Taiwan: Shortening rate and age of folding inception

The Pakuashan anticline is an active fault tip fold that constitutes the frontal most zone of deformation along the western piedmont of the Taiwan Range. Assessing seismic hazards associated with this fold and its contribution to crustal shortening across central Taiwan requires some understanding of the fold structure and growth rate. To address this, we surveyed the geometry of several deformed strata and geomorphic surfaces, which recorded different cumulative amounts of shortening. These units were dated to ages ranging from ∼19 ka to ∼340 ka using optically stimulated luminescence (OSL). We collected shallow seismic profiles and used previously published seismic profiles to constrain the deep structure of the fold. These data show that the anticline has formed as a result of pure shear with subsequent limb rotation. The cumulative shortening along the direction of tectonic transport is estimated to be 1010 ± 160 m. An analytical fold model derived from a sandbox experiment is used to model growth strata. This yields a shortening rate of 16.3 ± 4.1 mm/yr and constrains the time of initiation of deformation to 62.2 ± 9.6 ka. In addition, the kinematic model of Pakuashan is used to assess how uplift, sedimentation, and erosion have sculpted the present‐day fold topography and morphology. The fold model, applied here for the first time on a natural example, appears promising in determining the kinematics of fault tip folds in similar contexts and therefore in assessing seismic hazards associated with blind thrust faults.

Detecting and Quantifying Leakage Through Defective Borehole Seals: A New Methodology and Laboratory Verification

Abstract A new method for quantifying leakage through poorly sealed boreholes is presented and verified using a laboratory scale sandbox experiment. The method applies to a leaky borehole between two aquifers separated by an aquitard. A nonreactive tracer is injected into an upper aquifer piezometer, and the lower aquifer is pumped at a fixed rate. First, the presence of the tracer in the recovered water indicates the existence of the hydraulic short-circuit and cross-contamination. The leakage rate associated with the pumping rate can then be determined by measurement of the recovered tracer concentration. By correlating the leakage rate with the pumping rate, the hydraulic properties of the defective seal can be determined and the degree of cross-contamination can be predicted for any pumping rate. The method will be useful for practitioners who need to evaluate the quality of a borehole seal. The method is successfully tested using a laboratory sandbox experiment.

Fault growth and coalescence: insights from numerical modelling and sandbox experiments

ABSTRACT Displacement of strata varies along the strike of faults. This has important implications for the hydrocarbon industry, since for example this affects the occurrence and distribution of fractures along faults in a reservoir and can influence the sealing capacity of faults. As faults grow, neighbouring faults will interact with each other and eventually connect or coalesce. Geometrical fault growth models for coalescence are used to explain a large part of the observed spread of one order of magnitude in Length and Maximum Throw in natural examples of fault populations. Numerical modelling indicates that coalesced (merged) faults tend to return to their steady state growth evolution by accumulating displacement more rapidly than increasing in length, if no further coalescence occurs. Therefore, repetitive coalescence leaves faults “under-displaced” and results in a considerable spread in Length and Maximum Throw. To confirm and support these observations, a series of sandbox experiments was performed, which help improve our understanding of fault growth processes. The fault geometries observed in these models reflect geometries in natural examples, for example in the Natih Formation of Al Jabal al Akhdar in Oman. With increasing strain, repetitive coalescence takes place at all scales. After linkage, a new, coalesced fault behaves as a single, linked segment and accumulates more displacement than increasing length during an increment of strain. The slope of the best fit line of Length vs. Maximum Throw data for the fault population, in double logarithmic space, steepens with increasing strain and stabilises at about one.

Have the southernmost Andes been curved since Late Cretaceous time? An analog test for the Patagonian Orocline

The kinematic evolution of the enigmatic arc-shaped southernmost Andes of Patagonia and Tierra del Fuego has been a subject of debate for most of the past century. We compared the results from analog sandbox experiments with the tectonic evolution and actual configuration of the mountain chain in order to elucidate whether oroclinal bending took place during the Tertiary, or if the southernmost Andes have been a curved orogen since at least Late Cretaceous time. Experiments simulating oroclinal rotation produced strong along-strike variations in shortening and failed to account for structural data compiled from the Fuegian Andes. Results from experiments simulating an L-shaped, concave-to-foreland indenter were in agreement with the known Tertiary structural evolution of the southernmost Andes. The diachronicity of principal shortening events previously recognized in Patagonia and Tierra del Fuego could only be reproduced by moving the indenter in two successive orthogonal directions: first approximately northward to form the Fuegian fold-and-thrust belt, and then approximately eastward to propagate thrusting in the Patagonian Andes. This two-phase evolution is consistent with a recorded change in the convergence direction of the Farallon-Nazca plate that occurred at ca. 27 Ma.

The influence of the stress–strain behavior of non-cohesive soils on the geometry of shear band systems under extensional strain

The influence of the stress–strain behavior of granular non-cohesive materials on the geometry of shear band systems, specified by the spacing and the inclination of the shear bands, is investigated. Sandbox experiments on quartz sand in natural as well as in increased gravity are performed by applying extensional strain to specimens with different densities in initial state. Radiography is used to determine the spacing and the inclination of the developing shear zones, Digital Image Correlation (DIC) is applied to identify the deformation mechanism and the point of localization. Triaxial extension tests with respective densities are performed in order to determine the stress–strain behavior of the sand. It is found that the shear band spacing can be correlated with the initial density of the specimen.

Polygonal fault systems and channel boudinage: 3D analysis of multidirectional extension in analogue sandbox experiments

A systematic set of analogue models has been carried out to study the structural evolution of a sedimentary pile consisting of superposed brittle and ductile lithologies in a regional context of passive margins. The models are composed of silicone representing a ductile basal layer of evaporites or overpressured shales, and sand progressively sedimented on top to simulate brittle overburden sediments. Channels with various shapes are embedded in the silicone. Deformation is triggered by gravitational instability of the growing sedimentary pile and basal slope angles ranging from 0 to 5°. The main results follow. • A polygonal fault pattern developed, due to the 3D boudinage of the overburden sand above the silicone layer during multidirectional extension. • If a sandy channel was embedded in the ductile base, it was immediately cut by faults, which were perpendicular to the channel boundaries, no matter what the angle between channel and slope direction. • The boundaries of the channel preferentially localised faults, which propagated through the sedimentary pile above. Ongoing deformation along these faults therefore strongly influenced further accumulation of sediments.

Transport of Edible Oil Emulsions in Clayey Sands: 3D Sandbox Results and Model Validation

Injection of edible oils into the subsurface can provide an effective, low-cost alternative for stimulating anaerobic bioremediation processes. However, concerns have been raised about the effects of oil buoyancy and variations in aquifer permeability on the final distribution of oil in the subsurface. Three-dimensional (3D) sandbox experiments (1.2m×0.98m×0.98m) were conducted to study the distribution of edible oil emulsions under homogeneous and heterogeneous conditions. A fine emulsion was first injected followed by chase water to distribute the emulsion throughout the sandbox. This approach was very effective, resulting in a reasonably uniform volatile solids distribution in the top, middle, and bottom layers, measured 5 and 7weeks after the completion of emulsion injection. A standard colloidal transport model that includes a Langmuirian blocking function was used to simulate emulsion transport and retention in the 3D sandbox. All parameters for the emulsion transport model were measured independently. Simulations results generally matched observed values for both the homogeneous and heterogeneous injection tests demonstrating that this approach can be used to describe the transport and distribution of emulsified oil in sandy sediments.

Predictive modelling of structure evolution in sandbox experiments

In this paper a computational approach is presented that is able to forward model complex structural evolution with multiple intersecting faults that exhibit large relative movement. The approach adopts the Lagrangian method, complemented by robust and efficient automated adaptive meshing techniques, a constitutive model based on critical state concepts and global energy dissipation regularized by inclusion of fracture energy in the equations governing state variable evolution. The efficacy of the approach is benchmarked by forward simulation of two extensional analogue experiments that exhibit the development of a roll-over anticline with a series of superimposed crestal collapse graben systems. These sandbox experiments are excellent benchmarks for computational models, as both intersecting localisations with different rates of slip and large relative movement on localisations must be represented, while other complex phenomena associated with structural evolution over geological timeframes are not present.

Sandbox experiments on gravitational spreading and gliding in the presence of fluid overpressures

Whereas in previous analogue experiments on gravitational spreading and gliding, detachment occurred on a ductile layer, we have used a relatively new technique of injecting compressed air into sand packs so as to simulate the effects of fluid overpressures in sedimentary strata and to trigger slope instabilities. In our experiments, the governing equations yield scales for dimensions, stresses and fluid pressure. However, the more transitory phenomena of production and decrease of overpressure cannot be suitably scaled. By using layers of differing permeability, we are able to produce sharp detachments in models made of sand alone. The experiments involve gravity spreading or gravity gliding. In gravity spreading, propagation of the detachment and of extensional deformation depends on the fluid pressure. For medium values of fluid overpressure, normal faults are closely spaced, numerous and bound rotated blocks. They propagate progressively toward the back of the model. For the highest pressures, the deformation propagates very fast and faults bound non-rotated blocks, which slide on an efficient basal detachment. Fault dips are also controlled by fluid pressure and by frictional resistance at the base. To model gravitational gliding required an apparatus with a more complex system of air injection. We did a series of experiments using injection windows of various lengths and compared the results with predictions from a quasi-3D analytical model of sliding. In contrast with predictions for an infinite slope, sliding depends on (1) the fluid overpressure on the detachment, (2) the fluid overpressure in the body of the sliding sheet, and (3) the shape of the detachment surface. In particular, we show that frictional resistance at the lower edge is a primary control on the dynamics of gliding.

Sandbox Experimental Study on the Influence of Rock Strength and Gravity on Formation of Thrusts

ABSTRACT A sandbox experiment model was designed to simulate how differences in rock strength and gravity between two blocks can influence the formation characteristics of thrusts. In the experiment the compression was from one direction with basement shortening and the initial surfaces of the model were oblique. The results show that if the initial surface was horizontal or the slope angle was smaller than 7°, the compression induced two groups of thrusts with opposite dip orientations. If the slope angle of the initial surface was greater than 7°, the compression induced only one group of thrusts with a dip orientation contrary to the original compression direction. This result is similar to the actual section of a collision zone between two continental blocks. By applying stress analysis, rock strength is shown to be an important factor in deformation. As other boundary conditions are changeless, it is the change of gravitational potential energy that leads to different deformation styles.

The numerical sandbox: comparison of model results for a shortening and an extension experiment

Abstract We report results of a study comparing numerical models of sandbox-type experiments. Two experimental designs were examined: (1) A brittle shortening experiment in which a thrust wedge is built in material of alternating frictional strength; and (2) an extension experiment in which a weak, basal viscous layer affects normal fault localization and propagation in overlying brittle materials. Eight different numerical codes, both commercial and academic, were tested against each other. Our results show that: (1) The overall evolution of all numerical codes is broadly similar. (2) Shortening is accommodated by in-sequence forward propagation of thrusts. The surface slope of the thrust wedge is within the stable field predicted by critical taper theory. (3) Details of thrust spacing, dip angle and number of thrusts vary between different codes for the shortening experiment. (4) Shear zones initiate at the velocity discontinuity in the extension experiment. The asymmetric evolution of the models is similar for all numerical codes. (5) Resolution affects strain localization and the number of shear zones that develop in strain-softening brittle material. (6) The variability between numerical codes is greater for the shortening than the extension experiment. Comparison to equivalent analogue experiments shows that the overall dynamic evolution of the numerical and analogue models is similar, in spite of the difficulty of achieving an exact representation of the analogue conditions with a numerical model. We find that the degree of variability between individual numerical results is about the same as between individual analogue models. Differences among and between numerical and analogue results are found in predictions of location, spacing and dip angle of shear zones. Our results show that numerical models using different solution techniques can to first order successfully reproduce structures observed in analogue sandbox experiments. The comparisons serve to highlight robust features in tectonic modelling of thrust wedges and brittle-viscous extension.

A sandbox experiment to investigate bacteria‐mediated redox processes on self‐potential signals

We investigated the influence of microbial processes on self‐potential signals in a Plexiglas tank filled with a water‐saturated quartz sand. A small region of the tank was treated with sulfato‐reducer bacteria and organic nutrients. Redox potential measurements were performed both in the treated portion containing the bacteria and in the non‐treated portion of the tank. Self‐potential signals were recorded at the upper (free‐air) surface of the tank to monitor biodegradation. We observed a linear correlation between the temporal variation of these self‐potential signals and the redox potential difference between the treated and the non‐treated portion of the tank. Self‐potential signals can therefore be used as a non‐intrusive redox sensor. In addition, we propose a geobattery concept in which biofilms and the possible precipitation of metallic particles (biominerals) at the redox front allow electron transfer (therefore a net driving current density) between the reduced and oxidized parts of the system. In turn, this current is responsible for an electrical field in the Maxwell equations.

Sandbox models of downward-steepening normal faults

Two deformational styles resulted from sandbox experiments examining the hanging-wall deformation above a downward-steepening normal-fault bend comprised of two planar segments dipping at 40 and 60. In the first, hanging-wall layer-parallel extension dominated, with synthetic normal faults forming an upward-widening fault-bound wedge above the fault bend. Early forming, arcuate, vertical-to-reverse faults bound the wedge on its downthrown side and were followed by a planar, large-displacement synthetic normal fault bounding the wedge on the upthrown side. This later fault accommodated almost all of the subsequent displacement that occurred on the underlying 60 fault. Slip variably occurred along the 40 segment of the fault. Good analogs in nature exist for this deformation geometry. In the second deformational style, hanging-wall layer-parallel compression dominated, forming a monocline with antithetic hinge surfaces dipping downward to the fault-bend surface. Antithetic reverse faults formed in the limb of the monocline. The upper hinge of the monocline intersected the footwall at the fault bend, whereas its lower hinge intersected the 60 fault below the fault bend. The lower hinge was older and formed near the location of the fault bend prior to its being translated down the 60 master fault as part of the hanging wall. Elements of this geometry correlate well with the results of some geometric-based numerical models, but strong analogs in nature are elusive.

Discrete element simulations of continental collision in Asia

Analogue physical modelling using granular materials (i.e., sandbox experiments) has been applied with great success to a number of geological problems at various scales. Such physical experiments can also be simulated numerically with the Discrete Element Method (DEM). In this study, we apply the DEM simulation to the collision between the Indian subcontinent and the Eurasian Plate, one of the most significant current tectonic processes in the Earth.DEM simulation has been applied to various kinds of dynamic modelling, not only in structural geology but also in soil mechanics, rock mechanics, and the like. As the target of the investigation is assumed to be an assembly of many tiny particles, DEM simulation makes it possible to treat an object with large and discontinuous deformations. However, in DEM simulations, we often encounter difficulties when we examine the validity of the input parameters, since little is known about the relationship between the input parameters for each particle and the properties of the whole assembly. Therefore, in our previous studies (Yamada et al., 2002a, 2002b, 2002c), we were obliged to tune the input parameters by trial and error.To overcome these difficulties, we introduce a numerical biaxial test with the DEM simulation. Using the results of this numerical test, we examine the validity of the input parameters used in the collision model. The resulting collision model is quite similar to the real deformation observed in eastern Asia, and compares well with GPS data and in-situ stress data in eastern Asia.