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New mixed boundary true triaxial loading device for testing study on 3-D stress-strain-strength behaviour of geomaterials

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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.

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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.
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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.
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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.
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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.
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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.
Article
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.
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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.
Article
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.
Strength and deformation of sand measured in an independent stress control cell
  • G E Green
Green, G.E. 1971. Strength and deformation of sand measured in an independent stress control cell. In Stress-Strain Behaviour of Soils, Proceedings of the Roscoe Memorial Symposium, Cambridge, UK, 29-31 March 1971. Edited by R.H.G. Parry. G.T. Foulis and Co. Ltd., Henley-on-Thames, UK. pp. 285-323.
A new true triaxial apparatus
  • J A Pearce
Pearce, J.A. 1971. A new true triaxial apparatus. In Stress-Strain Behaviour of Soils, Proceedings of the Roscoe Memorial Symposium, Cambridge, UK, 29-31 March 1971. Edited by R.H.G. Parry. G.T. Foulis and Co. Ltd., Henley-on-Thames, UK. pp. 330-339.
Strength and compressibility of granular materials under generalized strain conditions
  • G E Green
Green, G.E. 1969. Strength and compressibility of granular materials under generalized strain conditions. Ph.D. thesis, University of London, London.
Small strain deformation characteristics of sedimentary soft mudstone from true triaxial tests
  • K Hayno
  • J Koeski
  • T Sato
  • F Tatsuoka
Hayno, K., Koeski, J., Sato, T., and Tatsuoka, F. 1999. Small strain deformation characteristics of sedimentary soft mudstone from true triaxial tests. In Pre-failure deformation characteristics of geomaterials. Edited by M. Jamiolkowski, R. Lancellotta, and D.C.F. Lo Presti. A.A. Balkema, Lisse, the Netherlands. Vol. 1, pp. 191-198.
  • J M Bell
Bell, J.M. 1965. Stress–strain characteristics of cohesionless
Multiaxial testing at Boulder and elsewhere
  • D M Wood
Wood, D.M. 2008. Multiaxial testing at Boulder and elsewhere. In Proceedings of the Inaugural International Conference of the Engineering Mechanics Institute (EM08), 19–21 May 2008, Minneapolis, Minn. American Society of Civil Engineers (ASCE), Reston, Va. p. 31. [Abstr.]
An investigation of EPS Geofoam behaviour in compression
  • D K Atmatzidis
  • E G Missirlis
  • D A Chrysikos
Atmatzidis, D.K., Missirlis, E.G., and Chrysikos, D.A. 2001. An investigation of EPS Geofoam behaviour in compression. In Proceedings of EPS Geofoam 2001 -3rd International Conference, Salt Lake City, Utah, 10-12 December 2001.
ABAQUS user's manuals
  • D Hibbitt
  • B Karlsson
  • P Sorensen
Hibbitt, D., Karlsson, B., and Sorensen, P. 2005. ABAQUS user's manuals. Version 6.5 [computer program].
Curves of normalized deviator stress versus major principal strain for b values of 0.5 from true triaxial tests on geofoam specimens with two different constant mean stresses of p' = 40 and 60 kPa. lar materials subjected to statically applied homogeneous loads in an open system
  • Fig
Fig. 13. Curves of normalized deviator stress versus major principal strain for b values of 0.5 from true triaxial tests on geofoam specimens with two different constant mean stresses of p' = 40 and 60 kPa. lar materials subjected to statically applied homogeneous loads in an open system. Ph.D. thesis, California Institute of Technology, Pasadena, Calif.
Development of multiaxial cubical test device with pore water pressure monitoring facilities
  • S Sture
Sture, S. 1979. Development of multiaxial cubical test device with pore water pressure monitoring facilities. Department of Civil Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Va. Report No. VPI-E-79.18.
Cubical devices: versatibility and constraints Advanced triaxial testing of soil and rock. STP 977
  • J R F Arthur
Arthur, J.R.F. 1988. Cubical devices: versatibility and constraints. In Advanced triaxial testing of soil and rock. STP 977. Edited by R.T. Donaghe, R.C. Chaney, and M.L. Silver. American Society for Testing and Materials (ASTM), Philadephia, Pa. pp. 743–765. doi:10.1520/STP29112S.
Effects of cross-anisotropy on three-dimensional behaviour of sand.I: Stress-strain behaviour and shear banding
  • A V Abelev
  • P V Lade
Abelev, A.V., and Lade, P.V. 2003. Effects of cross-anisotropy on three-dimensional behaviour of sand.I: Stress-strain behaviour and shear banding. Journal of Engineering Mechanics, 129(2): 160-166. doi:10.1061/(ASCE)0733-9399(2003)129:2(160).
Available from www.gcts
  • Gcts
GCTS. 2007. CATS software [computer program]. Geotechnical consulting and testing systems (GCTS), Tempe, Ariz. Available from www.gcts.com [accessed 11 December 2009].
Three-dimensional behaviour of sand with anisotropic fabric
  • H Ochiai
  • P V Lade
Ochiai, H., and Lade, P.V. 1983. Three-dimensional behaviour of sand with anisotropic fabric. Journal of Geotechnical Engineering, 109(10): 1313-1328. doi:10.1061/(ASCE)0733-9410(1983) 109:10(1313).
Effects of silt on threedimensional stress-strain behaviour of loose sand
  • S Shapiro
  • J A Yamamuro
Shapiro, S., and Yamamuro, J.A. 2003. Effects of silt on threedimensional stress-strain behaviour of loose sand. Journal of Geotechnical and Geoenvironmental Engineering, 129(1): 1-11. doi:10.1061/(ASCE)1090-0241(2003)129:1(1).