Stress‐dependent elastic wave velocity of microfractured sandstone

A model for the stress‐dependent elastic wave velocity response of fractured rock mass is proposed based on experimental evidence of stress‐dependent fracture normal and shear stiffness. Previously proposed models and previous experimental studies on stress‐dependent fracture stiffness have been reviewed to provide a basis for the new model. Most of the existing stress‐dependent elastic wave velocity models are empirical, with model parameters that do not have clear physical meanings. To propose the new model, the rock mass is assumed to have randomly oriented microscopic fractures. In addition, the characteristic length of microfractures is assumed to be sufficiently short compared to the rock mass dimensions. The macroscopic stress‐dependent elastic wave velocity response is assumed to be attributed to the stress dependency of fracture stiffness. The stress‐dependent fracture normal stiffness is defined as a generalized power law function of effective normal stress, which is a modification of the Goodman's model. On the other hand, the stress dependency of fracture shear stiffness is modeled as a linear function of normal stress based on experimental data. Ultrasonic wave velocity responses of a dry core sample of Berea sandstone were tested at effective stresses ranging from 2 to 55 MPa. Visual observation of thin sections obtained from the Berea sandstone confirms that the assumptions made for microstructure of rock mass model are appropriate. It is shown that the model can describe the stress‐dependent ultrasonic wave velocity responses of dry Berea sandstone with a set of reasonable material parameter values. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.     

Discrete element modeling of transversely isotropic rocks with non-continuous planar fabrics under Brazilian test

Acta Geotechnica - A new numerical approach based on the particle discrete element method (PDEM) is developed to investigate the mechanical behavior of transversely isotropic rocks with...     

Optimal location of piles in slope stabilization by limit analysis

Many studies have been conducted to establish the optimal location of a row of piles to reinforce and stabilize slopes. However, the results obtained are very different, and in some cases even inconsistent and contradictory. The factor of safety of piled slopes is determined by the magnitude of resistive forces exerted by the piles on the slope. At the same time, the maximum retaining forces provided by the piles are also affected by the pile position. In this paper, the problem of the optimal location of piles used to stabilize slopes is analyzed using a combination of limit slope stability analysis and the theory of Ito and Matsui (Soils Found 15:43?C59, 8) to calculate limit lateral loads on piles. Using an illustrative example slope, some of the issues including the most effective position, the most suitable position, and the position with the largest safety factor are discussed. The results show that the most effective pile position, the most suitable pile position, and pile position where the factor of safety can take maximum value are different from each other for a given slope.     

Comparison of testing techniques and models for establishing the SWCC of riverbank soils

The soil water characteristic curve (SWCC), also known as soil water retention curve (SWRC), describes the relationship between water content and soil suction in unsaturated soils. Water content and suction affect the permeability, shear strength, volume change and deformability of unsaturated soils. This paper presents results of the laboratory determination of the SWCC for soil samples obtained from the riverbank of the Lower Roanoke River in North Carolina. Six different testing methods were used to establish the SWCC including the filter paper, dewpoint potentiameter, vapor equilibrium, pressure plate, Tempe cell and osmotic methods. It is concluded that each suction measurement technique provides different measurable ranges of suction values, and the combined results from the different tests provide continuous SWCCs. Three widely available models were also shown to adequately fit the experimental SWCC data, particularly for matric suction values under 1500 kPa. These results will be valuable to practitioners in deciding which methods to use to establish the SWCC, and which empirical relationship to use for modeling the SWCC of riverbank soils.     

Molecular simulations of clay minerals: a study considering the change of cell size and shape

A molecular simulation study of dehydrated 2:1 clay minerals is carried out using a new MD simulation method that is capable of simulating a system under the most general applied stress conditions by considering the changes of MD cell size and shape. The tensor defining the cell size and shape is correlated with the atomic level stress tensors (both internal and external) through a Lagrangian formulation. In this paper, the static version of the method has been applied for the first time to the simulations of dehydrated mica sheets and has successfully revealed unforeseen structural transformations of clay minerals upon relaxation under different external stress conditions. Simulation results show that the degrees of freedom that the simulation cell possesses (i.e., whether the cell size or shape change is allowed) determines the final equilibrated crystal structure of clay minerals. When full allowance is given to the cell size and shape change, large shear distortions of clay minerals occur, resulting in the eliminations of interlayer spacing and internal shear stresses. However, when only the cell size change is allowed, interlayer spacing is retained, but large internal shear stresses also exist.     

Comment on the postulate of three plane strain mechanisms

This note discusses the inconsistencies that are inherent in the postulate of three plane strain mechanisms. It is shown that this postulate violates the principle of invariance and one obtains different results depending on the choice of the reference axes. If formulated in the principal stress space, this postulate requires that the principal stress and principal plastic strain increment directions be coaxial. Constitutive models based on this postulate cannot be used for general loading situations involving principal stress rotation where significant non-coaxiality is obtained.     

Nanoindentation approach characterizing strain rate sensitivity of compressive response of asphalt concrete

This paper presents the results of a study on the use of nanoindentation test to characterize the strain rate-dependent compressive response of asphalt concrete. Nanoindentation is now widely used for characterization and testing of composite as well as single-phase materials. Using a small piece of sample, nanoindentation tests can evaluate material behavior and structure in terms of the elasticity, time-dependent response, yield strength, damage, crack advance, debonding, and fatigues. In this study, a mixture of asphalt and calcium carbonate filler powder filling the intergranular void space of the asphalt concrete was characterized in terms of strain rate sensitivity at room temperature. The indentation hardness is observed to continuously decrease during constant indentation strain rates, but the hardness response clearly indicates positive strain rate dependency when compared at the same indentation depths. Following the constant strain rate tests, indentation creep response of the asphalt–filler mixture was tested at constant load conditions. The strain rate sensitivity values characterized from double logarithmic relationships between indentation hardness and strain rate during constant strain rate and constant load tests are comparable with that determined from uniaxial compression test of cylindrical asphalt concrete samples. The observed indentation size effect on hardness value was analyzed based on an existing size effect model. The size effect in the asphalt–filler mixture, which is stronger than that defined by the model, could be attributed to a plastically graded surface of asphalt–filler sample.     

Modeling of the simple shear deformation of sand: effects of principal stress rotation

The paper presents a simple constitutive model for the behavior of sands during monotonic simple shear loading. The model is developed specifically to account for the effects of principal stress rotation on the simple shear response of sands. The main feature of the model is the incorporation of two important effects of principal stress on stress–strain response: anisotropy and non-coaxiality. In particular, an anisotropic failure criterion, cross-anisotropic elasticity, and a plastic flow rule and a stress–dilatancy relationship that incorporate the effects of non-coaxiality are adopted in the model. Simulations of published experimental results from direct simple shear and hollow cylindrical torsional simple shear tests on sands show the satisfactory performance of the model. It is envisioned that the model can be valuable in modeling in situ simple shear response of sands and in interpreting simple shear test results.     

Determination of the poroelasticity of shale

Shales play important roles in various civil, energy and environmental engineering applications. Shales are categorized as poroelastic materials due to their tight and very stiff structure, and reliable poroelastic properties are required when dealing with shales. This paper presents simple procedures to determine the poroelastic properties of rocks using oedometer and triaxial consolidation tests. The procedures, which avoid the difficulty to perform determination of the unjacketed bulk modulus of the rock minerals, are demonstrated on a North Sea shale. The experimentally obtained Biot coefficient α and the drained bulk modulus K of the shale range from 0.95 to 0.99, and from 0.17 to 2.00 GPa, respectively. The Biot coefficient α and the drained bulk modulus K values determined from the oedometer and triaxial tests are compared and show good agreement and consistency between the two test procedures. The Skempton’s coefficient B-value of the triaxial samples was also experimentally measured prior to the triaxial consolidation tests. The theoretically predicted B-value varies from 0.81 to 0.96 which is, on the average, only about 10% higher than the experimentally obtained B-value which range from 0.80 to 0.85.

     

Viscoelastic damage model for asphalt concrete

The strain rate-dependent mechanical behavior of asphalt concrete was characterized using unconfined compression tests carried out at different loading rates. It was shown that at high strain rates, the elastic deformation and peak axial stress are highly sensitive to strain rate. Both increase as the strain rate increases. At very low strain rates, elastic response and unconfined compressive strength are relatively independent of the loading rate. Based on the experimental observations, a simple viscoelastic damage model is proposed for the strain rate-dependent unconfined compression behavior of asphalt concrete. In the model, strain rate response is modeled by a two-component viscoelastic model consisting of a constant elastic modulus and a viscous modulus that is related by a power-law function to the axial strain rate. Failure and strain softening are modeled via a damage formulation where damage evolution in the asphalt concrete is given by a simple form of the Weibull distribution function. The model was shown to be capable of describing the strain rate-dependent deformation, compressive strength, strain-softening and creep behavior of asphalt concrete. The model is relatively simple and requires only five material parameters.