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New mixed boundary true triaxial loading device for testing study on 3-D stress-strain-strength behaviour of geomaterials
Abstract
A brief review of the true triaxial apparatuses (TTA) developed in the past and their advantages and limitations are presented. Considering the limitations of previous designs, a new true triaxial loading device which provides mixed boundary conditions for a TTA is introduced. A three-dimensional finite element (FE) modelling study is carried out on the stress and strain distribution of a soil specimen subjected to loading from two different loading devices. It is found that the stresses and strains of the soil specimen subjected to loading from the new sliding plates are far more uniform than those subjected to loading from non-sliding plates with preset gaps. Finally, the applications of the present TTA with the new loading device for testing studies on a completely decomposed granite soil and a geofoam are introduced. Typical results are presented and discussed.
A test method is developed to simulate the deformation and strength characteristics of soils in real sites. This test method reveals the mechanism of seismic liquefaction of saturated sand under confined condition. A dynamic true triaxial test system is applied. This device provides mixed boundary conditions for samples and installation of advanced CATS test control system. The test results show that use of the dynamic true triaxial apparatus for sand liquefaction test research is feasible. Moreover, the mechanism of soil liquefaction under confined condition is investigated. Namely, the liquefaction will be generated when the axial and lateral pressures as well as the pore water pressure are equal to each other. It indicates that in the process of vibration load, the stress redistribution has a significant influence on the strength of sand liquefaction and the development mode of pore water pressure.
This paper presents (a) constitutive models such as hypo-elastic models and elastic visco-plastic models, (b) methods for calculating the settlement of clayey soils in one-dimensional (1D) straining, (c) equations for nonlinear creep and compression of clayey soils in 1D straining, (d) development of lab testing facilities such as a double cell triaxial apparatus, a true-triaxial loading device, a direct shear box for testing the interface of a structural element and an unsaturated soil with suction control, and a soil nail pullout box, and (e) development of optical fiber sensing technologies for geotechnical monitoring. From the above presentation, the main conclusions are summarized in this paper.
In order to study the influence of p, q and θσ on the deformation of coarse-grained soil, several tests in which only one of the three variables changes while the other two keep constant are performed on coarse-grained soil by using the TSW-40 type true triaxial apparatus in Hohai University. The results show that if p decreases with constant q and b, few deviatoric strain but some volumetric dilation will be generated at the preliminary stage. With the decrease of p, the volumetic dilation increases, which causes the increase of deviatoric strain that is smaller than the volumetric strain in absolute value. Later both the volumetric strain and the deviatoric strain will be accelerated until failure. It indicates that the decrease of p induces the volumetric dilation immediately, which loosens the particle structure, and then the deviatoric strain will be generated. If q increases with constant p and b, little volumetric dilation but some deviatoric strain will be produced at the preliminary stage. With the increase of q, the deviatoric strain increases, which causes the increase of the volumetric dilation that is smaller than the deviatoric strain in absolute value. Later both the deviatoric strain and the volumetric strain will be accelerated until failure. It demonstrates that the increase of q induces the deviatoric strain directly which causes particle dislocation, and then the volumetric dilation will be produced. If θσ changes with constant p and q, some but very small unrecoverable volumetric and deviatoric strains will be generated. Two parameters sp (sp =(p/q-p0/q0)/(1/Mf-p0/q0)) and sq (sp=(q/p-q0/p0)/(Mf-q0/p0)) are introduced, in which p0 and q0 are the initial spheric stress and the deviatoric stress respectively, Mf is the stress ratio at failure. The test results show that when p decreases with constant q and b, dεv/dp and 1/(1-sp)1/2-1 are in direct proportion; dεs/dp and -sp[1/(1-sp)1/2-1] are in direct proportion; stress-dilatancy equation is dεv/dεs= -1/sp. When q increases with constant p and b, dεs/dq and 1/(1-sq)1/2-1 are in direct proportion; dεv/dq and -sq[1/(1-sq)1/2-1] are in direct proportion; stress-dilatancy equation is dεv/dεs= -sq. Finally the characteristics of the flexibility matrix of coarse-grained soil are analyzed according to the test results. ©, 2015, Chinese Society of Civil Engineering. All right reserved.
A new type of cubical triaxial apparatus was used for an investigation of the influence of the intermediate principal stress on the drained stress-strain and strength characteristics of sand. For the same value of the minor principal stress and increasing value of the intermediate principal stress, both dense and loose specimens showed increasing slope of the stress-strain curve, decreasing strain-to-failure, and increasing rate of dilation.
The influence of the intermediate principal stress on the stress-strain, pore pressure, and strength characterstics of normally consolidated, remolded clay has been studied using conventional triaxial compression tests and cubical triaxial tests with independent control of the three principal stresses. For the same value of the minor principal stress, the specimens showed increasing slope of the effective stress ratio-strain curve with increasing value of the intermediate principal stress. The strain-to-failure decreased and the pore pressure increased initially and both remained approximately constant at high intermediate principal stresses. The effective strength of the clay increased from triaxial compression to a maximum before a slight decrease at triaxial extension. The undrained strength decreased slightly with increasing intermediate principal stress. Observations regarding the applicability of the normality condition of classical plasticity theory were made. Similarities and differences in behavior of clay and sand were examined.
The three-dimensional, drained stress-strain and strength behavior of Cambria Sand prepared in cubical specimens with cross-anisotropic fabric was studied using triaxial compression, plane strain, and cubical triaxial tests with independent control of the three principal stresses. The effects of initial cross-anisotropic fabric were mainly observed in the prefailure stress-strain behavior, whereas sufficient changes in the fabric had occurred at large strains to produce failure conditions which resembled those observed for isotropic sands. The three- dimensional failure surface could for practical purposes be modeled by an isotropic failure criterion.-from ASCE Publications Information
The influence of intermediate principal stress on the mechanical behavior of overconsolidated kaolin clay is investigated using three-dimensional true triaxial testing on cubical specimens. A flexible boundary, true triaxial setup with a real-time feedback control system was used to test soil specimens under stress and strain-control modes. Undrained tests on kaolin clay show that the following vary with intermediate principal stress: the stiffness at small strains, excess pore pressure generated during shear, and strength and strain to failure. Failure occurred at peak deviator stress followed by shear band formations and localized bulging. Prior theoretical formulations of bifurcation and undrained instability support these experimental observations. Analysis of data in the octahedral plane indicates that kaolin clay follows a nonassociative flow rule, which is described by a constant third stress invariant failure criterion with von Mises plastic potential surface.
The significance of material cross anisotropy in sands is underscored and experimentally evaluated in a series of true triaxial tests on Santa Monica beach sand in a cubical device. Failure patterns, initiation and development of shear banding, and complete stress-strain behavior are described for the entire range of the Lode angle under general three-dimensional loading conditions. Localized failure was found to govern the ultimate resistance of the sand for intermediate values of parameter b = (σ2-σ3)/(σ1-σ3) in each of the three sectors of the octahedral plane. Variations of the friction angle are fully described and show its significant dependence on the inherent cross-anisotropic material structure.
A stress-controlled, flexible boundary, true (or cubical) triaxial apparatus has been developed to investigate the behavior of cemented sand under various stress paths which are not achievable using conventional axisymmetric triaxial apparatus. The apparatus components, specimen preparation, and test procedure are described. Tests were performed on cemented sand along different stress paths which included hydrostatic compression, conventional triaxial compression , and along different directions on octahedral planes. The test results indicate that stress-strain and volumetric response of cemented sand depends on stress path.
Description
First publication of its kind in 25 years, this 900-page volume serves as an engineer’s guide for triaxial testing. Subjects include: equipment, test methods, and test interpretation and errors, and new test varieties.
The intermediate principal stress plays an important role for the stress-strain behavior of soils. The effect of the intermediate stress cannot be examined in the conventional triaxial apparatus since axisymmetric stress states are prescribed in it. Thus, other testing devices capable of producing asymmetric stress states are necessary for more accurate determination of the stress-strain behavior. This paper describes the Danish rigid boundary true triaxial apparatus developed at Aalborg University and the techniques employed to prepare and test specimens of clay and sand for effects of the intermediate stress. Three series of true triaxial tests are presented together with various conventional triaxial tests to illustrate the capabilities of the apparatus. The first series of tests was carried out on cross-anisotropic specimens from a natural clay deposit. The other two series were carried out on air-pluviated (frozen and unfrozen) specimens of sand that also showed cross-anisotropic behavior.
The Spatially Mobilized Plane (SMP) for frictional materials is extended to a plane for frictional and cohesive materials, which is named "Extended Spatially Mobilized Plane (Extended SMP)", by introducing a parameter of "bonding stress σ0". The "Extended SMP" includes the SMP applicable to frictional materials such as granular materials (σ0=0) and the octahedral plane applicable to cohesive materials such as metals (σ0→∞) at the two extremes. This corresponds to the fact that the two extremes of frictional and cohesive materials are granular materials and metals. The constitutive law is verified quantitatively using experimental data of triaxial compression, triaxial extension and true triaxial tests on cemented sands, which are selected as an intermediate material with both friction and cohesion. The experimental stress-strain relationship for the cemented sands under three-dimensional stress conditions are uniquely arranged on the "Extended SMP", and the strength of the cemented sands under three-dimensional stress conditions are well predicted by "Extended SMP" failure criterion.
A triaxial shear test box equipped with six rubber pressure bags was constructed to test cubical specimens of sand with a dimension of 100 mm multiplied by 100mm multiplied by 100mm. A series of drained tests was carried out on loose sand specimens prepared by depositing the sand under water. The tests employed different radial stress paths in which the major, intermediate and minor principal stresses were oriented independent of the direction of the specimen sedimentation. A number of tests were also carried out on specimens rotated by 90 degree about the horizontal axis after the specimens had been prepared by deposition.
Green (1967) has effectively stated the case regarding certain serious deficiencies of the Authors' new soil test box. Ko and Scott mention that small volumes of the sample at the corners and along the edges of the box may not be in a homogeneous stress state but did not consider this to be important. This would appear to represent simply an error in judgement. The Writer agrees with Green (1967) that the soil cube was appreciably restrained by the relatively
stiff stainless steel spacing frame. The Authors offer insufficient evidence to support the conclusion that the stress state generated in the sample contained within the new soil test box was found to be uniform or the opinion that the present equipment measures the true deformational behaviour of the soil tested. The opinions of Green (1967) and those of the Writer can easily be verified analytically or through the performance of simple experiments. The following brief and approximate analysis based on the theory of elasticity analytically demonstrates the possible importance of edge restraint for a particular stress path and a cylindrical specimen. Fig. 1 (a) represents a free cylinder with homogeneous triaxial compression while Fig. l (b) represents the same cylinder subjected to identical vertical loads but laterally fixed at four vertical edges.
This paper presents a recently developed true triaxial apparatus and a series of verification studies. The apparatus is capable of handling 241-mm cubical specimens providing the means for testing specimens under a wide variety of stress paths under drained and undrained conditions. It uses flexible boundaries to apply three independently controlled principal stresses with back pressure. The apparatus also uses a fully computer-controlled electro-pneumatic loading system with advanced technology for data control. A testing program is presented for the purpose of verification. Pea-gravel specimens with D 50=6.6 mm were tested under fully stress-controlled loading conditions. Stress paths used in this verification study include undrained and drained constant total mean stress paths and conventional triaxial compression and extension stress paths. Results from this study indicate that the newly developed apparatus is capable of capturing the stress-strain characteristics of coarse-grained soils.
The mechanical description of a new true triaxial apparatus for soil testing is presented. The design took into consideration flexibility in accommodating different specimen sizes, easy assembly procedure, and well-controlled boundary conditions. The apparatus can perform stress-controlled and strain controlled experiments. It is well instrumented with load, displacement, and pressure sensors and has the capabilities to capture strain localization and shear band development. Verification experiments were conducted on F-75 Ottawa sand to study the influence of b-value (b = (sigma(2) - sigma(3))/(sigma(1) - sigma(3))) on stress-strain and volumetric behavior of sand. The results show that the specimen stiffness increases, and the amount of post-peak softening increases as b-value increases. The peak and critical state friction angles and the rate of dilation increase as b-value increases from 0 to 0.25, followed by a smaller increase in the friction angles and no change in the rate of dilation as b-value increases. Specimens failure is characterized by nonuniform deformations that initiate during the hardening regime before the peak stress; however, shear bands become visible on the specimen surface during the post peak softening at which specimens' volumetric strain changes from dilative behavior to the constant volume condition.
A servo-controlled cuboidal shear device with automatic data acquisition system is described. Provisions are made for pore-pressure measurements with specially designed 'needle' piezometers. Complete stress-strain curves can be obtained with strains up to 20%. The application of servo-control in K//o consolidation and strain controlled loading is illustrated with flow charts and experimental data.
A flexible boundary electro-pneumatic true triaxial system has been developed for testing cohesive soil. The system is capable of applying principal stresses on each face of a cubical specimen using a Proportional-Integral-Differential (PID) based closed loop control algorithm. This device has the ability to measure both the internal and external pore pressures for a 102-mm cubical specimen and uses custom developed Butyl rubber membranes. Measurement of the internal pore pressure is accomplished using a needle piezometer. Appropriate software has been developed that can automatically perform saturation, isotropic or Ko consolidation, and shear testing under stress or strain control along various stress or strain paths. Using this system, results from isotropically consolidated triaxial compression and triaxial extension stress paths are presented for cubical kaolin specimens. Comparative tests using conventional cylindrical specimens using lubricated ends were also performed. Issues related to the interference of the flexible membranes, uniformity of strains and bifurcations, interpreted friction angles, and undrained shear strength are discussed.
An experimental study on the effects of nonplastic silt on the three-dimensional drained behavior of loose sand was performed employing a true triaxial testing apparatus. Laboratory experiments were performed on clean sand and on sand containing 20% nonplastic silt. The results indicate the failure stress levels and the overall trends of the stress-strain behavior were similar for both sands. However, the volume change behavior is significantly influenced by the presence of silt. The silty sand exhibited higher degrees of volumetric contraction during shearing than the clean sand. Relative density was used as the basis of comparison. The development of a shear band appears to have caused failure in all true triaxial testing performed, except in triaxial compression. This form of instability appears to increase its influence on the experimental results as the participation of intermediate principal stress increases. The formation of shear bands also appears to coincide with the cessation of contractive volumetric strain.
Drained true triaxial tests on dense Santa Monica Beach sand deposited with a cross-anisotropic fabric have been performed to study the failure condition in the principal stress space. The failure surface was assumed to be symmetric around the vertical axis (on the octahedral plane of the principal stress space), but varying as a function of the Lode angle. Data from previously performed consolidated-undrained true triaxial tests on San Francisco Bay Mud and data from triaxial compression, triaxial extension, and plane strain tests on Toyoura sand showed similar behavior in terms of effective stresses. A three-dimensional failure criterion is proposed for characterization of failure in cross-anisotropic soils, under commonly occurring conditions when loading and depositional directions coincide and no significant rotation of principal stresses occur. This cross-anisotropic criterion is developed using a coordinate rotation of the principal stress space and utilization of an existing isotropic failure formulation. Derivation of the three required parameters is explained and illustrated. The proposed criterion is compared with various experimental results; and it is demonstrated that the failure criterion for cross-anisotropic soils captures the experimental behavior with good accuracy.
In order to investigate the anisotropy in the deformation characteristics of gravel, a large-scale true triaxial apparatus that can control three principal stresses independently has been newly developed. One of the two horizontal stresses is applied by means of rigid vertical platens that confine the specimen, to induce a uniform horizontal strain over the height of the specimen in that one direction. A set of local deformation transducers and proximity transducers are used to measure strains to minimize the effects of specimen corners, bedding error, and system compliance. Specimens have a prismatic rectangular shape with dimensions of 50 cm high and 25 cm×22 cm in cross section. Using this apparatus, a couple of tests were conducted on gravel specimens prepared by manual compaction at a water content of 5.5 % to reach dry densities of 2.0 and 2.2 g/cm 3. At several stress states, during isotropic compression and subsequent triaxial loading, vertical and horizontal loading cycles of a very small stress amplitude were applied to evaluate the quasi-elastic deformation properties. The test results show that the small-strain quasi-elastic Young's modulus in a given direction is essentially a unique function of the normal stress in the same direction, regardless of the density of the specimen. Although this is contrary to some of the well-established models used in practice, it is consistent with results of relevant laboratory tests by others. Small-strain quasi-elastic vertical and horizontal Young's moduli exhibited effects of inherent and stress state-induced anisotropies. Performing cyclic loading tests of successively increased the stress amplitude, the strain-level dependency of the equivalent Young's modulus and hysteretic damping ratio in both the vertical and horizontal directions was obtained.
A new multiaxial cubical test apparatus is described. It uses fluid or pneumatically pressurized flexible cushions to transmit a three-dimensional, independently controlled, and compressive stress state to a 102-mm specimen of geologic material. The deformations in three orthogonal directions are detected by a set of linear variable differential transformers. The specimen preparation and apparatus assembly procedures are straightforward. The simplicity of the multiaxial cubical cell and its easy operating procedures are emphasized. Typical stress-strain curves for straight-line stress paths are discussed. The apparatus appears to operate especially well at low stress levels.
A suction-controlled true triaxial apparatus for unsaturated soil was developed from the existing true triaxial apparatus for sand by attaching a device to supply matric suction to specimens. Using the developed apparatus, true triaxial tests (σ1 σ2 σ3; where σ1, σ2, and σ3 are the three different principal stresses) on an unsaturated silty soil were carried out under constant suction using the negative pore-water pressure method (s = uw > 0; ua = 0) for applying the matric suction, s (s = ua uw; where ua is the pore-air pressure and uw is the pore-water pressure). It was found that the true triaxial test results under three different principal stresses are uniquely arranged on the "extended spatially mobilized plane (extended SMP)" for frictional and cohesive materials that is modified from the original SMP for frictional materials by introducing "a bonding stress, σ0 (= c·cot, where c is cohesion and is the internal friction angle)." It was also found that the shear strengths of the unsaturated silty clay obtained by the true triaxial apparatus nearly agree with the extended SMP failure criterion (Î1Î2/Î3 = constant, where Î1, Î2, and Î3 are the first, second, and third invariants of the translated stress tensor). The measured stress-strain-strength behaviour of the unsaturated soil in three-dimensional (3D) stresses can be well simulated by an elastoplastic model with the transformed stress based on the extended SMP criterion and a special hardening parameter.Key words: failure criterion, shear strength, special shear test, suction, stress path, unsaturated soil.
Expanded polystyrene (EPS) geofoam is increasingly being used as a construction material of choice in situations where its mechanical properties—such as its extremely low density, volume contraction under deviatoric compressive loading, and existence of post-yielding strain hardening—can be exploited. In this paper, a simple elastoplastic hardening constitutive model of EPS geofoam is formulated to model the mechanistic behaviour of EPS geofoam taking into account the characteristic properties of EPS. The model is based on experimental results from a series of triaxial tests performed on EPS samples for confining pressure ranging from 0 to 60 kPa at room temperature (23 °C). Behaviour under higher temperatures is currently under investigation and will be addressed in a future publication. The model has a total of six independent parameters and can be calibrated from data obtained from triaxial tests. It is shown that the constitutive model is able to correctly replicate the characteristic behaviour of the EPS geofoam under shearing. The model is relatively simple to incorporate into numerical codes for geotechnical analysis.
A general stress-strain relationship in incremental and invariant form is derived for sand on the basis of experimental evidence. The resulting expression does not include the yield condition but makes allowance for the direction of loading and the state of stress. Two new modified and dimensionless invariant functions are introduced and a detailed description and classification of stress paths presented. A new first yield criterion for sand stressed to yield along one stress path is developed from experimental evidence. The friction angle in triaxial compression was minimum and 14[degrees] less than that in triaxial extension. The Mohr-Coulomb yield criterion extended to three dimensions is rejected. Emphasis is placed on the importance of obtaining homogeneous stress in physical experiments. A new spherical compression apparatus was developed to study the behavior of sand under spherical compression. Disadvantages of former apparatuses were largely overcome by elimination of frictional loading, and a homogeneous state of stress was obtained. A new stress controlled three-dimensional compression apparatus capable of applying principal stresses to a rectangular, plate sample was developed to study the behavior of sand under a general stress state, particularly under deviatoric stress. This apparatus provided for the independent measurement of volumetric strain and allowed for the development of considerable deformation in obtaining yield.
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