Deviatoric Stress Levels Research Articles

Experimental investigation on the deformation characteristics of granular materials under drained rotational shear

Rotational shear is the type of loading path where samples are subjected to cyclic rotation of principal stress directions while the magnitudes of principal stresses are maintained constant. This paper presents results from an experimental investigation on the drained deformation behaviour of saturated sand in rotational shear conducted in a hollow cylinder apparatus. Two types of granular materials, Leighton Buzzard sand and glass beads are tested. A range of influential factors are investigated including the material density, the deviatoric stress level, and the intermediate principal stress. It is observed that the volumetric strain during rotational shear is mainly contractive and most of strains are generated during the first 20 cycles. The mechanical behaviour of sand under rotational shear is generally non-coaxial, i.e., there is no coincidence between the principal axes of stress and incremental strain, and the variation of the non-coaxiality shows a periodic trend during the tests. The stress ratio has a significant effect on soil response in rotational shear. The larger the stress ratio, the more contractive behaviour and the lower degree of non-coaxiality are induced. The test also demonstrates that the effect of the intermediate principal stress, material density and particle shape on the results is pronounced.

Finite element modelling for prediction of permanent strains in fine-grained subgrade soils

Roads are designed with good reliability to fulfil the long-term performance during the design period. In order to achieve an effective design, the long-term performance of pavements should be optimized during the design phase. One of the strategies is to develop models which are capable of predicting the long-term performance. This paper focuses on one of the most critical distress modes in flexible pavements, namely, rutting. The plastic strain of subgrade soils is modelled to quantify the amount of rut contributed from the subgrade. The deformation from the first loading cycle is incorporated in the elastoplastic theoretical framework based on the Drucker–Prager yield criterion. The proximity of deviator stress to the static failure limit of subgrade soils is considered to predict the amount of incremental plastic strains at each loading cycle. The model is implemented in the User Material Subroutine in the finite element program ABAQUS™. The prediction of plastic strains using the proposed model provides a good agreement with laboratory test with deviator stress level up to 50% of the static strength of the soil. The mobilisation of subgrade soils in pavements is normally low due to reduced stress magnitude at the subgrade level, which makes the proposed model in this study more appealing to understand the development of plastic strains in subgrade soils.

Experimental investigation of creep behavior of clastic rock in Xiangjiaba Hydropower Project

There are many fracture zones crossing the dam foundation of the Xiangjiaba Hydropower Project in southwestern China. Clastic rock is the main media of the fracture zone and has poor physical and mechanical properties. In order to investigate the creep behavior of clastic rock, triaxial creep tests were conducted using a rock servo-controlling rheological testing machine. The results show that the creep behavior of clastic rock is significant at a high level of deviatoric stress, and less time-dependent deformation occurs at high confining pressure. Based on the creep test results, the relationship between axial strain and time under different confining pressures was investigated, and the relationship between axial strain rate and deviatoric stress was also discussed. The strain rate increases rapidly, and the rock sample fails eventually under high deviatoric stress. Moreover, the creep failure mechanism under different confining pressures was analyzed. The main failure mechanism of clastic rock is plastic shear, accompanied by a significant compression and ductile dilatancy. On the other hand, with the determined parameters, the Burgers creep model was used to fit the creep curves. The results indicate that the Burgers model can exactly describe the creep behavior of clastic rock in the Xiangjiaba Hydropower Project.

Time-dependent behaviour of interactive marine and terrestrial deposit clay

A series of one-dimensional consolidation tests and triaxial creep tests were performed on Nansha clays, which are interactive marine and terrestrial deposits, to investigate their time-dependent behaviour. Based on experimental observations of oedometer tests, normally consolidated soils exhibit larger secondary compression than overconsolidated soils; the secondary consolidation coefficient (<TEX>$C_{\alpha}$</TEX>) generally gets the maximum value as load approaches the preconsolidation pressure. The postsurcharge secondary consolidation coefficient (<TEX>$C_{\alpha}$</TEX>') is significantly less than <TEX>$C_{\alpha}$</TEX>. The observed secondary compression behaviour is consistent with the <TEX>$C_{\alpha}/C_c$</TEX> concept, regardless of surcharging. The <TEX>$C_{\alpha}/C_c$</TEX> ratio is a constant that is applicable to the recompression and compression ranges. Compared with the stage-loading test, the single-loading oedometer test can evaluate the entire process of secondary compression; <TEX>$C_{\alpha}$</TEX> varies significantly with time and is larger than the <TEX>$C_{\alpha}$</TEX> obtained from the stage-loading test. Based on experimental observations of triaxial creep tests, the creep for the drained state differs from the creep for the undrained state. The behaviour can be predicted by a characteristic relationship among axial strain rate, deviator stress level and time.

Studies about Creep Characteristic of Silty Clay on Triaxial Drained Creep Test

The creep characteristic of saturated silty clay was studied by triaxial drained creep test through two stress paths of axial loading and lateral lightening. According to test data, some conclusions were submitted. First, the axial creep laws between the two stress paths were consistent on the drainage conditions. Volume strains were much smaller than axial strains. Volume strains presented shear dilatancy along with lightening confining pressure. The silty clay creep coefficient was put forward and its variation law was summarized. The silt soil creep coefficient was closely related to the deviatoric stress level. The two had a linear relationship. The silt soil creep coefficientincreased with deviatoric stress level and had no matter with the confining pressureand loading path.

Experimental investigation on the creep behavior of an unsaturated clay

To better understand the long-term deformation of landslides with consideration of the influence of water content variation, a series of triaxial creep tests with suction control was conducted on clay specimens taken from one large-scale landslide in the Three Gorges Reservoir area in China. Results indicate that, in the double-logarithmic coordinates, the axial strain increases linearly and the axial strain-rate decreases linearly with the elapsed time; the axial strain and strain rate increase with increasing deviator stress levels and decreasing matric suction. For theoretical analysis, based on the simulation of the test results by an empirical creep model developed for saturated soils, a linear relationship was established between suction and one of the parameters of the model. Then, a revised model with consideration of suction effects was developed. In the revised model, a power function was adopted for the description of the strain–time relationship and a hyperbolic function was employed for the stress–strain relationship. Verification indicated that the calculated results were in good agreement with the experimental ones.

Effects of fines and water contents on the mechanical behavior of interlayer soil in ancient railway sub-structure

In the ancient railway sub-structure in France, after years of operation, the inter-penetration of fine particles of sub-grade and ballast has created a new layer referred to as the interlayer. As it was naturally formed, the fines content and water content of the interlayer vary considerably. In this study, the effects of the fines and water contents on the mechanical behavior of interlayer soil were investigated by carrying out large-scale monotonic and cyclic triaxial tests. The results of the monotonic triaxial tests show that adding more fines in the interlayer soil does not significantly change the shear strength in the dry condition (water content w=4% and 6%), but drastically decreases the shear strength parameters (friction angle and cohesion) in the nearly saturated condition (w=12%). The cyclic triaxial tests were performed at various deviator stress levels. By considering the permanent axial strain at the end of application of each stress level, it was found that the higher the fines content in the nearly saturated condition (w=12%), the larger the permanent axial strain. In the case of lower water content (w=4% and 6%), the opposite trend was identified: adding fines decreases the permanent axial strain.

A viscoplastic model for rate-dependent hardening for asphalt concrete in compression

This paper presents a new type of viscoplastic model based on viscoelastic convolution integrals for explaining the behavior of asphalt concrete in compression under repeated loading. Triaxial compression cyclic tests carried out for long rest periods, with different loading times and two different pulse shapes, square and haversine, were used in developing and validating the model. These tests demonstrate that the evolution of permanent deformation depends on load history. This history-dependent behavior is not captured accurately by some of the existing Perzyna-type viscoplastic models in which permanent deformation evolution depends on the current values of stress and viscoplastic strain. Therefore, in this study, viscoelastic-like convolution integrals were used in the model to capture the effect of history. The proposed model is applicable to compressive creep and recovery experiments at 54°C with (1) several hundreds of cycles of loading including the secondary creep region, (2) haversine loading shapes at three different peak deviatoric stress levels, 620kPa, 827kPa, and 1034kPa, and square loading shapes at 827kPa peak deviatoric stress, and (3) long rest periods that allow complete viscoelastic recovery.

Noncoaxial Behavior of Sand under Various Stress Paths

In this paper, the results of three series of drained tests carried out on sands using hollow cylinder apparatus are presented. The noncoaxiality, defined as the difference between the major principal stress direction and the corresponding principal strain increment direction, is investigated. In the first series of tests, the sand was isotropically consolidated before being sheared with the fixed principal stress direction. In the other two series of tests, the sand specimens were isotropically consolidated and then sheared by rotating the major principal stress axes while the deviator stress level was either fixed (pure stress rotation) or increased continuously (combined shear loading). The experimental results provide clear evidence for material noncoaxiality when the rotation of principal stress direction is involved. The results from these series of tests show that the degree of noncoaxiality depends on the level of deviatoric stress and the stress increment direction. It tends to decrease when the specimen is approaching a failure state. It was also observed that the effect of soil density on noncoaxiality is more significant at lower shear stress levels. Test results on two different materials, Portaway sand and Leighton Buzzard sand, were also compared with the study of the influence of material anisotropy associated with sand particle characteristics. Numerical simulations of granular materials using the discrete element method (DEM) were conducted to understand the effect of the initial material anisotropy produced during sample preparation. The DEM results were consistent with those obtained from the hollow cylinder tests.

Permanent Deformation Characteristics and Prediction Model of Silty Subgrade Soils under Repeated Loading

AbstractBy using dynamic tri-axial testing, permanent plastic strain curves of silty subgrade soil under 104 repeated loading were tested with three water content levels, two compaction degree levels and three deviator stress levels. The effect of the above mentioned factors on permanent subgrade deformation were compared in quantity. A large number of literal investigation and testing data regression analysis show that Tseng and Lytton’s constitutive model can successfully predict accumulative permanent deformation of silty subgrade soil. Moreover, all above testing data were regressed to build the formation for calculating model coefficients of silty soil by using water content and resilient modulus. Hence the constructive model for predicting permanent deformation of silty soil subgrade was obtained, which can be used to analyze total permanent deformation of asphalt pavement.

Stiffness Degradation and Yielding of EPS Geofoam under Cyclic Loading

This paper summarizes major findings from a laboratory study based on stress-controlled cyclic uniaxial compression tests with initial deviator stress conducted on expanded polystyrene (EPS) geofoam. The experiments involved nonelasticized EPS cylinders of various densities subjected to various static deviator stresses and cyclic loading conditions to provide a detailed description of the geofoam cyclic stress-strain response in the viscoelastic and visco-elasto-plastic domains. Experimental results characterizing the viscoelastic behavior were compiled into a normalized Young’s modulus and damping ratio versus cyclic axial strain amplitude relationships. A unified formulation that can be used to determine the normalized modulus degradation curve for a given static deviator stress level and geofoam density (within 15–25 kg/m3 ) was developed. Examination of the yielding behavior of EPS geofoam under cyclic loading revealed a nonlinear increase in the accumulated plastic axial strain with the increasing n...

Effect of coarse aggregate size and cement paste volume on concrete behavior under high triaxial compression loading

When massive concrete structures (high-rise buildings, tunnels, dams, nuclear power plants, bridges, protection structures, …) are subjected to extreme loadings (aircraft shocks, rock falls, near-field detonations, ballistic impacts, …), the material undergoes triaxial compression loading at a high confinement. In order to reproduce high stress levels with well-controlled loading paths, static triaxial tests are carried out on concrete samples by mean of a very high-capacity triaxial press. It is a well-known fact that the cement paste volume and the coarse aggregate size are two important parameters of concrete formulation. This article focuses on identifying the effect of coarse aggregate size and cement paste volume on concrete behavior under high triaxial compression. This article shows that at low confinement, the concrete strength slightly increases as the coarse aggregate size increases. At high confinement, the coarse aggregate size has a slight influence on concrete deviatoric behavior and a significant influence on concrete strain limit-state. The higher the coarse aggregate size, the lower is the mean stress level corresponding to concrete strain limit-state. Furthermore, this article highlights that at low confinement, the concrete strength significantly increases with an increase in cement paste volume. Increasing confinement tends to reduce cement paste volume effect on concrete strength. At high confinement, contrary to what has been observed in unconfined compression, the cement paste volume has little effects on concrete deviatoric behavior. Otherwise, decreasing cement paste volume increases concrete deformation capacity. At very high confinement levels and at very high deviatoric stress levels, the axial tangent stiffness of concrete increases as the coarse aggregate size or the cement paste volume is reduced.

Resilient Moduli Response of Moderately Cement-Treated Reclaimed Asphalt Pavement Aggregates

The use of reclaimed asphalt pavement (RAP) aggregate materials in road construction reduces natural resource depletion and promotes the recycling of RAP materials for other applications. However, product variability and low resilient moduli characteristics often limit RAP applications in road bases. Stabilization of RAP materials with cement was hence attempted in a research study to evaluate the effectiveness of cement treatments in enhancing resilient characteristics of RAP aggregates. The present paper describes the results from a series of resilient modulus tests that were conducted in a laboratory environment using a repeated load triaxial test setup. The effects of three different cement dosages and various confining and deviatoric stress levels on the resilient modulus (MR) response of treated RAP materials were studied. MR values of untreated and cement-treated RAP aggregates ranged from 180 to 340 MPa and 200 to 515 MPa, respectively, which reveal the enhancements with cement treatment. Regressi...

Compressive Creep Behaviour of Asphalt Mixtures

The uniaxial and triaxial steady-state deformation behaviour of a gap graded and a continuously graded asphaltic mixture have been studied. Uniaxial creep and constant strain rate tests have been conducted over a range of stress levels, strain rates and temperatures, and triaxial creep tests have been conducted over a range of deviatoric stress levels and confining pressures. The steady-state deformation behaviour of both mixtures is found to be well captured by the Modified Cross Model which predicts linear viscous behaviour at low stress levels and non-linear viscous behaviour at high stress levels. The temperature dependency of the steady-state deformation behaviour is found to be well captured by the WLF equation. It is found that confinement has a stiffening effect on the steady-state deformation behaviour which is found to be higher for the continuously graded mixture. The volumetric strain is found to increase linearly with the shear strain with a gradient that is independent of stress level and confining pressure.

Triaxial mechanical creep behavior of sandstone

Based on laboratory results of time-dependent mechanical behavior tests, we investigated short-term and mechanical creep behavior of sandstone, observed in conventional triaxial compression experiments at room temperature, using a servo-controlled rheology testing machine. Given our short-term experimental test results, we confirmed deviatoric creep stress levels of sandstone. Multiple deviatoric stress levels were applied in steps to each sample. Each deviatoric stress level before the final failed deviatoric stress was maintained for 48 h or longer. Time-dependent variations of axial strains of sandstone samples are discussed and evaluated. During the creep tests, complete tertiary creep curves of sandstone were observed under failed deviatoric stress levels with different confining pressures. Slices of coal in sandstone samples can lead to distinct tertiary creep deformation failure.

Accommodation of volume changes in phase transition zones: Macroscopic scale

The volume changes associated with a phase transition need to be accommodated by creep. Otherwise, a pressure anomaly impeding the transformation is induced. Phase changes in mantle flows are therefore delayed by this process, which occurs not only on a microscopic scale but also, as shown in the present paper, on a macroscopic (i.e., kilometric) scale. The mechanism is illustrated first with the help of a simple analytical “pipe flow” model. The broadening and average deflection of the phase transition vary with the vertical velocity of the flow V, the viscosity in the zone of phase transition η, the density jump Δρ, and the pressure interval over which the phase change occurs Δ P. They are characterized by a nondimensional number: α = (4/3)ηgV (Δρ/ΔP2). For small α, the deflection of the phase transition is equal to α times the width of the transition loop. A numerical, one‐dimensional stationary model is then used to quantify how the flow is hampered by mass anomalies associated with the phase transition deflections. The response functions for harmonic loads in a self‐gravitating mantle are computed. Transition deflection is shown to have a significant influence in the case of a thin and viscous discontinuity. Conversely, it may be negligible if the material within transition zones is weakened. In an estimate where we link the viscosity in the transition zone to the level of deviatoric stress, we show that sizable (≈7 km) deflections of the 670 km discontinuity can be expected as a consequence of these macroscopic volume changes associated with phase transformations.

Prediction of Subgrade Resilient Modulus Using Genetic Algorithm and Curve-Shifting Methodology

This paper demonstrates the applicability of the genetic algorithm and curve-shifting methodology to the estimation of the resilient modulus at various stress states for subgrade soils by using the results of triaxial resilient modulus tests. This innovative methodology is proposed as an alternative to conventional nonlinear constitutive relationships. With the genetic algorithm, laboratory curves for different deviator stress levels at different confining pressures are horizontally shifted to form a final gamma distribution curve that can represent the stress–strain behavior of subgrade soils with the corresponding predicted shift factors. Resilient modulus values for a given stress state can be estimated on the basis of this curve and another gamma function that represents the variation of the shift values for different confining stresses. To compare the effectiveness of these two approaches, coefficients for the Uzan constitutive model were also determined for each laboratory test and compared with those determined by the approach described in this paper. Predicted resilient modulus values from each approach are separately compared with artificial neural network (ANN) model predictions to evaluate their efficiency and reliability for resilient response prediction. The results of the analysis indicated that the curve-shifting methodology gave superior estimates and a coefficient of determination 14% higher than the Uzan model predictions when the results were evaluated with the ANN model outputs. Thus, although it is not a constitutive model, use of the genetic algorithm and curve-shifting methodology is proposed as a promising technique for the evaluation of the stress–strain dependency of subgrade soils.

Talklüfte im Zentralen Aaregranit der Schöllenen-Schlucht (Kanton Uri, Schweiz)

The Schöllenen Gorge in the Reuss Valley of the Central Swiss Alps (Figs. 1 and 2) is a famous tourist attraction and ideal location for the study of the properties and formation mechanisms of uplift and post-uplift unloading joints. The gorge is situated in the southern part of the Central Aar Granite, a granitic batholith which intruded about 300 million years ago. The magmatic fabric of this batholith (Fig. 4) has only been locally modified during Alpine tectonic and metamorphic overprinting, mainly in the vicinity of ductile-brittle shear zones. The up to 600 m deep gorge provides an ideal opportunity to study the complex fracture systems of the batholith, and tunnels of the Göschenen hydropower system allow the study of the fracture patterns below ground surface.Outcrop, tunnel and remote mapping of fractures in the study area lead to the recognition of two probably syntectonic (Oligocene-Miocene) joint sets (S and Q joints) and three generations of uplift and post-uplift joints (unloading joints). The frequent S joints run nearly parallel to the Alpine schistosity, i.e. striking approximately E–W and dipping steeply to the south (Figs. 5 and 7). The less frequent Q joints dip steeply to SW; the angle between the two joint sets ranges between 60 and 80 degrees. The first generation of uplift joints (called L- joints) is subhorizontal and probably related to Alpine extensional veins filled with fissure quartz (Zerrklüfte). These veins formed during the late Alpine (Miocene) uplift of the Aar Granite (Mullis 1996). A first generation of post-uplift joints (T1 joints) strikes parallel to the valley axes and dip with 30–45 degrees towards the valley bottom. This set probably formed during an earlier stage of glacial valley erosion in the Pleistocene (Figs. 9–11). The youngest generation of post-uplift joints (T2 joints) is orientated parallel to the present ground surface of the Schöllenen Gorge and to erosional surfaces with glacial striations (Figs. 9–11 and 21). The frequency and size of these joints seems to decrease with depth below the ground surface. In one tunnel, post-uplift joints could be observed within a horizontal and vertical distance from the ground surface of 150 and 80 meters. Post-uplift joints only form in granites with a primary fabric that has not been intensively overprinted by brittle or ductile Alpine tectonic deformations.Fractographic investigations, i.e. investigations of crack propagation markers on joint surfaces, confirm this relative age of the fracture sets and give valuable insights into the formation mechanisms of post-uplift joints. Post-uplift joints show intense and 5–10 meter long plumose markings and only rarely arrest lines (Figs. 18a and 20). It can be shown that sets of post-uplift joints join at pre-existing (uplift and syntectonic) fractures to form large (50–100 m sized) curved exfoliation structures (Fig. 19). The growth direction of the post-uplift joints is mainly in subhorizontal directions (Figs. 19 and 20).Fractographic markings, spatial and depth distributions as well as the relative size of post-uplift fractures are explained within the mechanical framework of uniaxial and biaxial compression tests on intact granite samples and samples with artificial flaws. Most of these experiments have been carried out in the framework of studies related to brittle failure (spalling and rockbursting) around deep mining drifts and tunnels in hard rock’s (e.g. Hoek & Bieniawski 1965, Read et al. 1998, Eberhardt et al. 1999). As suggested already by Holzhausen & Johnson (1979), post-uplift fractures form as extension fractures in a compressive stress field with small confining stress. Laboratory tests carried out on artificial Griffith cracks suggest that the macroscopic fracture size is mainly controlled by the ratio of the smallest to the largest principal stress (σ3/σ1), the so-called spalling limit. In steep slopes this ratio should increase with depth below ground surface (Fig. 24c), leading to smaller exfoliation fractures with increasing depth. The spatial occurrence of post-uplift fractures along the surface topography is a function of the deviatoric stress level (Fig. 24a) and/or the development of local tensile stresses (Fig. 24d). Preliminary numerical simulations of these failure criteria in a multistage glacial erosion model (Fig. 23) allow some of the observed patterns of post-uplift fracture distributions to be reproduced.post-uplift joints in steep glacial valleys play an important role in valley erosion and in connection with the risk of rock falls, the safety of traffic corridors, and the inflow of water to near-surface tunnels and hydropower caverns. The depth dependant sizes, frequencies and hydraulic conductivities of these fractures can be directly related to the occurrence and magnitudes of the corresponding hazards.

Gravitational potential energy and regional stress and strain rate fields for continental plateaus: Examples from the central Andes and Colorado Plateau

The commonly observed extension in areas of elevated and thickened crust is an expected consequence of having excess gravitational potential energy (GPE) compared to the low GPE of the surrounding crust. While this conceptual model is well founded, it is less clear how well GPE-related stress orientations compare quantitatively to observed stress and strain rate orientations and what any inconsistency tells us about the presence of other competing forces. We estimate the GPE distribution for the central Andes and the greater Colorado Plateau area using topography and crustal thickness variations, respectively, and compare the related stress fields with the World Stress Map as well as with a geodetic strain rate field (for the Colorado Plateau only). In both areas, deviatoric stresses associated with GPE variations alone cannot fully account for the observed deformation rate field. For the central Andes only a combination of deviatoric stresses associated with GPE and relative plate motions can account for the near N–S tensional stress observed in the Peruvian Andes and the margin–normal compressional stress along the eastern Cordillera and sub-Andean fold-and-thrust belt. The observed deformation field around the Colorado Plateau shows E–W extension, largely inconsistent with the deviatoric stresses associated with GPE variations except for the area east of the Rio Grande Rift. The NE–SW oriented stress observed on the southwestern Colorado Plateau is consistent with the orientations of tensional deviatoric stresses associated with GPE variations. We argue that this consistency could be haphazard; stress observations may not reflect the current state of stress due to inherited structure, or could result from the relative high strength of Colorado Plateau that allows for regional GPE variations (and possibly basal shear) to be more significant forces than far-field plate interactions. For the central Andes and Colorado Plateau, stresses associated with GPE variations have a strong influence on the total stress field, and can thus be used to calibrate the overall level of deviatoric stress acting within the lithosphere.

Undrained dynamical behavior of Nanjing flake-shaped fine sand under cyclic loading

A series of dynamic behavior tests on Nanjing flake-shaped fine sand were performed by using the WFI cyclic triaxial apparatus made in England. The dynamic behaviors of Nanjing flake-shaped fine sand under different static deviator stress levels and cyclic stress ratios were studied. Through comparing the effective stress path under cyclic loading with static loading, the processes of liquefaction of saturated Nanjing flake-shaped fine sand with development of dynamic pore-water pressure, including the initial compact state, compression state and dilative state, were investigated. The variation of the shear stiffness with the number of cycles and cyclic strain was investigated by analyzing the secant shear modulus in each unload-reload loop of dynamic stress-strain relationship. And by means of the exponential function, the empirical equations of the relationship between secant shear modulus Gsec, shear modulus ratio Gsec/Gmax and cyclic strain e were established based on series of test results. The results show that according to different combinations of static deviator stress and cyclic stress, two kinds of failure patterns with deviator stress reversal or no deviator stress reversal are observed in the samples tested in this series, including cyclic mobility and the failure of accumulation residual strain. In addition, the degradation of dynamic shear modulus is due to the development of vibration pore-water pressure and it is observed that the shear modulus reduces with the progressive number of cycles.