Range Of Effective Stresses Research Articles

Experimental and numerical investigations of permeability in heterogeneous fractured tight porous media

Analyzing gas flow behavior is important for production prediction in heterogeneous fractured shale reservoirs, which is complex due to the presences of nanopores and high-degree heterogeneity in these complex flow network. First, we applied the discrete fracture model to simulate gas pulse-decay experiments in core plugs with different configurations. The effective permeability ratio was proposed to evaluate the effects of heterogeneity, fracture, and vug on the flow behavior. Second, we performed pulse-decay experiments on one intact fractured shale core to examine the effects of pore pressure and effective stress on permeability variations. The measured pressure profiles were history matched by numerical methods to obtain the porosity and permeability of matrix and fracture. The matching degree is evaluated by the Global Matching Error (GME). Our results highlight the positive impact of dense fracture network to improve flow capacities in the tight reservoir: effective permeability of the fractured core with 8 pairs of 1.3-cm connected fractures increases 4.07 times that of the un-fractured core. Vugs might be important as well if they connect adjacent fracture networks, but their own contribution to flow capacity is negligible: effective permeability increases only 1.00 to 1.02 times when the number of vugs increase from 3 to 35. The GME ranges from 0.04% to 0.2% for history matching of the fractured core. Core heterogeneity is exhibited more obviously when gas flows through under low pressure than under high pressure, which can be used to guide the design of pulse-decay experiment properly depending on the purpose. The main contributions of this study are that we constructed the finite-element based numerical model to simulate the pulse-decay experiment, proposed a methodology to upscale core permeability when fractures and vugs are present, and measured porosity and permeability for the matrix and fracture simultaneously in one fractured core over a wide range of pressure and effective stress.

Frictional properties and 3-D stress analysis of the southern Alpine Fault, New Zealand

New Zealand's Alpine Fault (AF) ruptures quasi-periodically in large-magnitude earthquakes. Paleoseismological evidence suggests that about half of all recognized AF earthquakes terminated at the boundary between the Central and South Westland sections of the fault. There, fault geometry and the polarity of uplift change. The South Westland AF exhibits oblique-normal fault motion on a structure oriented 052°/82°SE that, for at least 35 km along strike, contains saponite-rich principal slip zone gouges. New hydrothermal friction experiments reveal that the saponite fault gouge is frictionally weak, exhibiting friction coefficients between μ = 0.12 and μ = 0.16 for a range of temperatures (T = 25–210 °C) and effective normal stresses (σn' = 31.2–93.6 MPa). The saponite gouge is rate-strengthening in all velocity steps performed at velocities between 0.01 and 3.0 μm/s, behavior conducive to aseismic creep. A three-dimensional stress analysis shows that the South Westland AF is favorably oriented with respect to the regional stress field for slip within the frictionally weak saponite fault gouge. Geometrically, the fault is severely misoriented for slip in any fault-forming materials with friction coefficients exceeding μ∼0.5. The combination of weak gouges prone to aseismic creep, strong asperities, and low resolved shear stress may impede earthquake rupture propagation along the South Westland Alpine Fault.

Stress dependent permeability and porosity of low-permeability rock

The seepage property of low-permeability rock is of significant importance for the design and safety analysis of underground cavities. By using a self-developed test system, both permeability and porosity of granite from an underground oil storage depot were measured. In order to study the influence of rock types on permeability, a tight sandstone was selected as a contrast. The experimental results suggested that the porosity of this granite is less than 5% and permeability is low to 10–20 m2 within the range of effective stress. During the loading process, both exponential relationship and power law can be utilized to describe the relationship between effective stress and permeability. However, power law matches the experimental data better during the unloading condition. The stress dependent porosity of granite during loading process can be described via an exponential relationship while the match between the model and experimental data can be improved by a power law in unloading paths. The correlation of permeability and porosity can be described in a power law form. Besides, granite shows great different evolution rules in permeability and porosity from sandstone. It is inferred that this difference can be attributed to the preparing of samples and different movements of microstructures subjected to effective stress.

Effect of Water and Leachate on Hydraulic Behavior of Compacted Bentonite, Calcareous Sand and Tuff Mixtures for Use as Landfill Liners

Compacted soil–bentonite liners, consisting of a sandy soil mixed with bentonite as backfill, are used extensively as engineered barriers for contaminant containment. This paper studies the valorization of local materials containing calcareous sand, tuff obtained from Laghouat region (in the South Algeria), to associate with bentonite in order to improve their hydraulic characteristics for use as landfill liner material. Firstly, a geotechnical characterization of mixtures chooses from a fixed percentage to 10% bentonite and different percentages of calcareous sand and tuff so that they are complementary to 90% by not 10%. Thereafter, the determination of saturated hydraulic conductivity at falling-head permeability (Kv) and oedometer (Kid, indirect Measure) tests of all compacted mixtures at Optimum Normal Proctor have been carried out using both permeates by tap water and a landfill leachate in order to simulate long-term conditions. The results showed that the saturated hydraulic conductivity of tap water is relatively lower than the one saturated by leachate in the falling-head test, unlike the oedometer test. The B10CS20T70 mixture has satisfied the hydraulic conductivity criterion of bottom barriers (i.e. water permeated: kv20° = 1.97 × 10−9 and kid from 7 × 10−9 to 1.83 × 10−10 < 10−9m/s; leachate permeated: kv20° = 2.91 × 10−9 and kid from 7 × 10−9 at 1.44 × 10−10 < 10−9 m/s). Finally, a comparison between direct measurements of the saturated hydraulic conductivity by triaxial (Kd) test and oedometer test (Kid) in the range of effective stress applied 100–800 kPa led to propose equations of correlations between these two methods. In conclusion, adopted formulation B10CS20T70 perfectly meets the regulatory requirements in force and constitutes an economic product based on available local materials for engineers barriers.

Laboratory assessment of the effects of polymer treatment on geotechnical properties of low-plasticity soil slurry

A laboratory study was undertaken to assess the effects of polymer treatment (PT) on the geotechnical behaviour of a low-plasticity slurry. PT was undertaken on the material using a high molecular weight polyacrylamide polymer. Slurry consolidometer and triaxial testing were undertaken to compare the geotechnical behaviour of the material following PT, compared to an untreated (UT) condition. The material was prepared from a slurry state in a nonsegregating condition, to enable comparison of uniform samples. Testing indicated that PT resulted in lower final consolidated densities at a given magnitude of effective stress, while increasing the rate of consolidation and hydraulic conductivity. Triaxial testing indicated that PT material, when sheared, appeared to exhibit a different critical state line (CSL) than UT material. The PT CSL was higher in void ratio terms than the UT CSL, and with an increased compressibility. Both PT and UT material exhibited undrained shear strengths consistent with the state of the specimen with respect to that material’s CSL. PT material exhibited higher undrained shear strengths at a given density. All the effects observed following PT appeared to persist across a wide range of effective stresses.

Fully Softened Shear Strength for Soil Slope Stability Analyses

AbstractThe fully softened shear strengths of soils, mudstones, and shales of different plasticities and gradations were measured at low (10 and 25 kPa), intermediate (50 and 100 kPa), and high (200, 300, and 400 kPa) effective normal stresses. A torsional ring shear apparatus was used for the strength measurement. The effects of the change in nonlinearity of the fully softened shear strength envelope over the utilized normal stress ranges on slope stability analyses were investigated. An empirical correlation was developed to predict the fully softened shear strength as a function of plasticity index and a wide range of effective normal stresses. The correlation is presented as a revised version of those previously developed for a limited number of normal stresses that do not cover the range mobilized in the vast majority of reported long-term first-time landslides. A numerical expression was also introduced to allow for direct incorporation of the fully softened shear strength correlation in slope stabi...

Drained residual shear strength at effective normal stresses relevant to soil slope stability analyses

An extensive torsional ring shear testing program has been conducted to measure the drained residual shear strength of soils at the wide range of effective normal stress (10 to 700kPa) usually mobilized in reactivated and first-time landslides. Soils, mudstones and shales of different plasticity and gradation were tested in the program. The effects of the change in nonlinearity of shear strength envelope over the utilized normal stress ranges on slope stability analyses were investigated. Using this data, new empirical residual shear strength correlations were developed as a function of soil index parameters and wide range of effective normal stresses. In essence, the correlations are presented as revised versions of those previously developed for a limited number of normal stresses utilizing the same soil index parameters. Comparisons were made with a considerable amount of back-calculated shear strength data reported in the literature for reactivated landslides as well as results predicted from existing shear strength correlations to verify the increased suitability of the new correlations for use in slope stability analyses. A numerical expression was also introduced to express the residual shear strength correlations for direct incorporation in slope stability software.

Near-exponential relationship between effective stress and permeability of porous rocks revealed in Gangi's phenomenological models and application to gas shales

A number of theoretical models, as well as empirical equations obtained by fitting specific experimental data, have been developed to describe the relationship between effective stress and permeability of intact and fractured porous rocks. It has been found that most experimental data can be fitted using exponential equations. In this study the modified power law equations by Gangi for intact and fractured rocks are revisited to evaluate their applicability for modeling experimental permeability data which display exponential or near-exponential effective stress dependency. It has been shown that Gangi's power law equations for both intact and fractured rocks can be approximated, over the range of effective stresses of practical interest, by exponential equations with compressibilities that are related to the physical properties of the rock. The significance of this work is that it has provided further theoretical evidence for the apparent exponential relationship between effective stress and permeability. Moreover, it allows for more vigorous theoretical equations to be applied with the easiness of empirical exponential equations. This is demonstrated by applying the models to the experimental permeability data for six gas shales reported recently.

Evidence for a Highly Conductive Fracture after Water Fracturing in the GeneSys Project

AbstractThe GeneSys project aims to develop a low-permeability, sedimentary reservoir of the Northern German Basin for the provision of geothermal energy to heat the Federal Institute for Geosciences and Natural Resources (BGR) located at the Geo Center in Hanover, Germany. In May 2011, a massive fracturing (frac) operation was performed to create a large heat exchanger at a depth of 3,700 m. Subsequent to the frac operation, two low-rate injection tests were conducted below fracture-closure pressure. The injection phases of the two tests provide evidence for a large and highly conductive fracture, although proppants were not used during the frac operation, indicating that the fracture stays open because of self-propping effects, at least in the explored range of effective stress. Hydraulically active fracture areas of more than 0.5 km2 were calculated from an analysis of the pressure transient during the low-rate injection tests relying on matrix permeabilities determined in laboratory experiments. In pr...

An Evaluation of Three Triaxial Systems With Results From 0.1 to 100 MPa

Abstract This paper evaluates the results of triaxial tests carried out over a very wide range of effective stresses using custom-built triaxial systems specially developed for testing at low, medium, and high pressures. These tests were performed on samples of resedimented Boston Blue Clay, and good reproducibility is demonstrated across testing devices. A novel approach was taken to evaluate the effect of apparatus compressibility of the drainage system on the measured undrained shear behavior, as this issue becomes increasingly important for triaxial testing at high stresses. The effect of apparatus compressibility on triaxial shear results was evaluated by comparing the volume of pore fluid necessary to develop the drained strength of a specimen to the volume of flow caused by apparatus compressibility. This method is more illustrative and intuitive for undrained triaxial testing of saturated specimens than the traditional approach of using a specimen's B-value. Triaxial test results show a consistent decrease in both undrained strength ratio and critical state friction angle over the effective stress range of 0.1 to 100 MPa for each overconsolidation ratio investigated. The conventional assumption made in soil models that fine-grained soils exhibit constant normalized strength properties is therefore shown to be invalid when these properties are viewed over a significant range of effective stresses.

Undrained Behavior of Sand-Fines Mixtures and Their State Parameter

AbstractThe influence of fines on the undrained behavior of sand was investigated experimentally over a range of fines content and effective mean stress. The role of fines on compressibility and formation of meta-stable soil fabric was analyzed. For a fines content in the range of 5–30%, most of the specimens manifested reverse behavior opposed to the normal behavior of clean sand. The addition of fines led to shifting of both the isotropic consolidation line and the steady-state line, increased compressibility, and occurrence of reverse behavior. All these behavior attributes are linked when the test results are interpreted in the context of the critical-state soil mechanics framework. In particular, reverse behavior is associated with an isotropic consolidation line that locates above the steady-state line. Several quantitative measures for characterizing the undrained deviator stress-strain responses were proposed, and these measures manifested correlation with the state parameter at the start of undra...

Fault transmissibility in clastic-argillaceous sequences controlled by clay smear evolution

The continuity of clay smears evolving in sealed direct shear experiments of initially intact sandstone-mudrock sequences was quantified to large displacements up to more than ten times the thickness of the sealing layer. The sample blocks consisted of a preconsolidated clay-rich seal layer, which was embedded and synthetically cemented in quartz sand. The mineralogy and mechanical properties of the clay layer and the reservoir sandstones were varied systematically to mimic a range of natural clastic rock sequences. The fluid-flow response across the fault zone was monitored continuously during deformation using a new type of direct shear cell. The displacement at which seals break down is closely linked to the amount of phyllosilicates in the seal layer. Contrary to expectations, softer seal layers do not seal better than stiff seal layers for a given clay content. In the testing range of normal effective stresses between 4 to 24 MPa (580–3481 psi) covering maximum burial depth conditions of approximately 800 m (2625 ft) to approximately 4 km (2 mi) (assuming normal fault tectonics), a systematic trend is also observed, indicating better smear continuity by increasing the effective normal stress. Predominantly brittle processes such as slicing and wear, and not ductile drag or plastic flow, appear to be responsible for the generation of clay smears. The test results offer the prospect of incorporating critical shale smear factors (i.e., normalized displacement at which seal breakdown occurs) into probabilistic fault seal algorithms that consider important properties that can be measured or estimated, namely, clay content and fault-normal effective stress.

Arrest and recovery of frictional creep on the southern Hayward fault triggered by the 1989 Loma Prieta, California, earthquake and implications for future earthquakes

[1] Theodolite measurements across the right-lateral Hayward fault, San Francisco Bay, California, show a dramatic reduction in surface creep rate from 5 to 10 mm/yr before the 1989 Loma Prieta earthquake to nearly zero creep rate after the earthquake. A ∼6 year period of nearly zero surface creep was followed by sudden fault creep that accumulated about 20–25 mm of right-lateral displacement followed by an eventual return to a steady creep by year ∼2000. This creep behavior can be explained as a result of a sudden shear stress reduction on the fault and is consistent with model predictions for a fault imbedded in an elastic medium with slip governed by laboratory-derived friction laws. We infer friction parameters on the fault using a spring-slider model and a boundary element model with the rate- and state-dependent friction laws. The state (healing) term in the friction law is critical for reproducing the observed evolution of surface creep; a popular simplified rate-dependent friction law is insufficient. Results suggest that the creep event extended to a depth of ∼4–7.5 km. The inferred critical slip distance, dc, is 1–2 orders of magnitude larger than lab values, and inferred aσ values imply low effective fault-normal stresses of 5–30 MPa. This range of effective normal stress and inversion results for (a − b)σ imply very small values for a − b of 10−5 to 10−3, suggesting the fault has nearly velocity-neutral frictional properties. Earthquake simulations with such small a − b values show that creeping areas on the Hayward fault may be capable of rupturing during earthquakes.

Pore pressure development beneath the décollement at the Nankai subduction zone: Implications for plate boundary fault strength and sediment dewatering

Despite its importance for plate boundary fault processes, quantitative constraints on pore pressure are rare, especially within fault zones. Here, we combine laboratory permeability measurements from core samples with a model of loading and pore pressure diffusion to investigate pore fluid pressure evolution within underthrust sediment at the Nankai subduction zone. Independent estimates of pore pressure to ∼20 km from the trench, combined with permeability measurements conducted over a wide range of effective stresses and porosities, allow us to reliably simulate pore pressure development to greater depths than in previous studies and to directly quantify pore pressure within the plate boundary fault zone itself, which acts as the upper boundary of the underthrusting section. Our results suggest that the time‐averaged excess pore pressure (P*) along the décollement ranges from 1.7–2.1 MPa at the trench to 30.2–35.9 MPa by 40 km landward, corresponding to pore pressure ratios of λb = 0.68–0.77. For friction coefficients of 0.30–0.40, the resulting shear strength along the décollement remains &lt;12 MPa over this region. When noncohesive critical taper theory is applied using these values, the required pore pressure ratios within the wedge are near hydrostatic (λw = 0.41–0.59), implying either that pore pressure throughout the wedge is low or that the fault slips only during transient pulses of elevated pore pressure. In addition, simulated downward migration of minima in effective stress during drainage provides a quantitative explanation for down stepping of the décollement that is consistent with observations at Nankai.

Integrating laboratory creep compaction data with numerical fault models: A Bayesian framework

We developed a robust Bayesian inversion scheme to plan and analyze laboratory creep compaction experiments. We chose a simple creep law that features the main parameters of interest when trying to identify rate‐controlling mechanisms from experimental data. By integrating the chosen creep law or an approximation thereof, one can use all the data, either simultaneously or in overlapping subsets, thus making more complete use of the experiment data and propagating statistical variations in the data through to the final rate constants. Despite the nonlinearity of the problem, with this technique one can retrieve accurate estimates of both the stress exponent and the activation energy, even when the porosity time series data are noisy. Whereas adding observation points and/or experiments reduces the uncertainty on all parameters, enlarging the range of temperature or effective stress significantly reduces the covariance between stress exponent and activation energy. We apply this methodology to hydrothermal creep compaction data on quartz to obtain a quantitative, semiempirical law for fault zone compaction in the interseismic period. Incorporating this law into a simple direct rupture model, we find marginal distributions of the time to failure that are robust with respect to errors in the initial fault zone porosity.

Radial Deformations Induced by Groundwater Flow on Deep Circular Tunnels

The magnitude and distribution of ground deformations around a tunnel are often monitored during construction and provide key information about ground-support interaction and ground behavior. Thus it is important to determine the effects of different parameters on ground deformations to accurately and effectively evaluate what contributes to ground and support behavior observed during excavation. This paper investigates one such relation: the effects of seepage on radial deformations. A number of numerical analyses have been conducted with the following assumptions: deep circular unsupported tunnel, elastic ground, isotropic far field stresses, dry ground or saturated ground with steady-state water seepage. The analyses cover a wide range of tunnel sizes, effective stresses, and pore pressures. Results from the numerical simulations confirm previous analytical solutions for normalized radial deformations behind the face (i.e. on the tunnel side of the face) of a tunnel excavated in dry ground, and have been used to propose a new analytical formulation for normalized radial displacements ahead and behind the tunnel face for both dry and saturated ground with water flow. Water seepage substantially increases the magnitude and distribution of the normalized radial deformations ahead of the face and at the tunnel face, but does not change much the displacement distribution behind the tunnel face.

The effects of disseminated methane hydrate on the dynamic stiffness and damping of a sand

Methane hydrates are ice-like compounds that can exist only under restricted thermobaric conditions, at low temperatures or under high ambient pressure. They are important because of their potential contributions as a future source of energy, to global warming, and as a possible trigger for long run-out submarine slope instability. This paper describes laboratory experiments to synthesise disseminated methane hydrates and to characterise them under small-strain dynamic loading in the resonant column apparatus. The effects of depositing varying quantities of methane hydrate within a sand are investigated by reference to their shear and bulk modulus, and damping, over a range of isotropic effective stress. Results are compared with those obtained on the same sand without hydrate bonding and after dissociation.

Lower-bound shear strength for geosynthetic clay liners in base liners

The objective of this paper is to establish the minimum available shear strength for any type of geosynthetic clay liner (GCL) in a base liner. Direct shear tests are conducted on very thin (nominally 1 mm thick) specimens of reconstituted bentonite placed against a smooth geomembrane to measure the drained, residual strength of this interface. The use of thin specimens minimizes the time required to achieve drained conditions, and also minimizes the shear displacement required to mobilize the residual strength; testing times were several weeks and residual strengths were mobilized within 10 mm of shear displacement. The Mohr–Coulomb strength envelope developed from these test results corresponds to a secant friction angle of 4.7° over a range of effective normal stresses from 250 to 1500 kPa. Limited published information for the shear strength of bentonite and GCLs at these effective normal stresses supports the use of this envelope as a lower-bound strength for all types of GCL. This envelope establishes a conservative design check for slope stability and a benchmark for evaluating product-specific and project-specific test results with GCLs.

Compressibility and Permeability Correlations for Fine-Grained Dredged Materials

New correlations are presented for the compressibility and permeability of normally consolidated, fine-grained, marine and riverine dredged materials that are based on the liquid limit alone. They are simpler, statistically stronger, and applicable over a wider range of effective stress and permeability than comparable, earlier correlations based on the liquid limit, plasticity index, and activity of fine-grained dredged materials, mine tailings, and similar soils. However, like the latter, they must be applied with caution to sandy materials and to materials with high organic contents or that contain atypical clays with fibrous particles.

Shear Heating in Granular Layers

—Heat-flow measurements imply that the San Andreas Fault operates at lower shear stresses than generally predicted from laboratory friction data. This suggests that a dramatic weakening effect or reduced heat production occur during dynamic slip. Numerical studies intimate that grain rolling or localization may cause weakening or reduced heating, however laboratory evidence for these effects are sparse. We directly measure frictional resistance (μ), shear heating and microstructural evolution with accumulated strain in layers of quartz powder sheared at a range of effective stresses (σ n = 5 - 70 MPa) and sliding velocities (V = 0.01 - 10 mm/s). Tests conducted at σ n ≥ 25 MPa show strong evidence for shear localization due to intense grain fracture. In contrast, tests conducted at low effective stress (σ n = 5 MPa) show no preferential fabric development and minimal grain fracture hence we conclude that non-destructive processes such as grain rolling/sliding, distributed throughout the layer, dominate deformation. Temperature measured close to the fault increases systematically with σ n and V, consistent with a one-dimensional heat-flow solution for frictional heating in a finite width layer. Mechanical results indicate stable sliding $(\mu \sim 0.6)$ for all tests, irrespective of deformation regime, and show no evidence for reduced frictional resistance at rapid slip or high effective stresses. Our measurements verify that the heat production equation $(q =\mu \sigma_n V)$ holds regardless of localization state or fracture regime. Thus, for quasistatic velocities (V≤ 10 mm/s) and effective stresses relevant to earthquake rupture, neither grain rolling/sliding or shear localization appear to be a viable mechanism for the dramatic weakening or reduced heating required to explain the heat flow paradox.