The induced anisotropy of Leighton Buzzard sand

The induced anisotropy of Leighton Buzzard sand under generalised stress conditions was investigated using a new, automated hollow cylinder apparatus. Identical test specimens of sand were isotropically consolidated followed by anisotropic consolidation, involving different magnitudes of the three principal stresses and rotation of the major principal stress. Details of the stress paths followed are presented. The induced anisotropy of the test specimens was analysed by exploring the relationships between the deviator strain and the principal and volumetric strains. Analysis of the experimental data indicated that a predominately linear relationship exists between the deviator strain and the principal and volumetric strains for all principal stress combinations and rotation of the major principal stress. The magnitude of the intermediate principal stress was found to have a profound influence on the strain responses. When the intermediate and minor principal stresses were maintained equal, the magnitudes of all strain components were found to be proportional to the rotation of the major principal stress. However, the latter relationship disappeared and the magnitudes of the resultant strains were smaller once the intermediate principal stress increased relative to the minor principal stress. Introduction The deformational response of a soil to applied load depends on the magnitude and orientation of the principal stresses. Many laboratory test apparatus are limited in the range of stress states that can be applied to a soil sample. For example, the triaxial apparatus can only subject a test-specimen to axi-symmetric loading conditions. Only the hollow cylinder apparatus (HCA) and some new designs of the directional shear cell allow reliable investigation of the effects of anisotropy. Both apparatus allow independent combinations of the three principal stresses and rotation of the major-to-minor principal stress axis. The particulate nature of soil leads to anisotropic strength and stiffness characteristics. Anisotropic behaviour can be divided into two categories (Hoque & Tatsuoka, 1998): 1. Inherent anisotropy due to the development of an anisotropic macro or micro fabric after the deposition of particulates through air or water or when compacted. 2. Induced anisotropy developed in a soil due to the application of anisotropic stress changes. This study investigates the induced anisotropy of Leighton Buzzard sand using a HCA. The effects of rotation of the major-to-minor principal stress axis and relative change in the Patrick J Naughton & Brendan C O’Kelly Page 3 magnitude of the intermediate principal stress on the deformational response of the samples are investigated. Overview of hollow cylinder apparatus The HCA used in the present study was developed at University College Dublin, Ireland (O’Kelly, 2000; Naughton, 2002). The test apparatus subjects a 100mm outer diameter x 71mm inner diameter x 200mm high hollow cylindrical test-specimen to an inner pressure (pi), an outer pressure (po), an axial load (W), and a torque (T), Figure 1a. The test apparatus is close-loop controlled allowing precise regulation of the applied loads and pressures. Figure 1b presents the resultant normal and principal stresses induced in an element of the testspecimen wall. The deformational response of the test-specimen is shown in Figure 1c. The deformational response of the test-specimen is recorded using both internal and external instrumentation. The internal instrumentation is connected directly or is in close proximity to the test-specimen walls and measures the actual deformation occurring over a central gauge length of the test-specimen. Two proximity transducers measure the inner and outer displacements of the test-specimen walls (ui and uo, respectively) at sample mid height, while two modified double-axis Imperial College-type inclinometers record the axial normal (w) and circumferential shear ( ) deformations over the middle third of the test-specimen. A single-axis inclinometer is also used to record the circumferential shear deformation. Figure 1. (a) System of pressures, axial and torsional loads applied to the testspecimen. (b) Resultant normal and principal stresses acting on an element of the test-specimen wall. (c) Deformational response of the test-specimen. The external instrumentation determines the axial normal and circumferential shear deformations from the movement of the loading mechanisms which apply the axial load and the torque to the test-specimen. Displacements of the inner and outer test-specimen walls are determined from measured volume changes of the test-specimen itself and the inner bore cavity. (a) (b) (c) Patrick J Naughton & Brendan C O’Kelly Page 4 The automated test apparatus is capable of regulating the induced stresses in the test-specimen to 0.5 kPa during sample loading under either drained or undrained test conditions. The deformational response of the test-specimen is recorded using the internal and external instrumentation to a resolution of 5.3x10 -5 strain and 6.3x10 -5 strain, or better, respectively. A more detailed description of the HCA is given in O’Kelly & Naughton (2003). The control programmes automatically compensate for membrane penetration effects using a sample specific non-destructive method developed by Sivathayalan & Vaid (1998) and for membrane restraint effects using corrections developed by Tatsuoka et al. (1986). Investigation of anisotropy This study examined the induced anisotropy of Leighton Buzzard sand. Identical testspecimens were anisotropically consolidated by increasing the effective major-to-minor principal stress ratio, R’; reorientation of the major-to-minor principal stress axes, ; and changing the magnitude of the intermediate principal stress relative to the magnitude of the major and minor principal stresses. The relative magnitude of the intermediate principal stress was quantified in terms of the intermediate principal stress parameter, b. The b parameter has a range between 0 and 1. With b = 0, the intermediate and minor principal stresses are equal, while b = 1 results in the intermediate and major principal stress being equal. Properties of the sand Fine-to-medium, white Leighton Buzzard sand was examined in the present study. Some physical properties of the sand are summarised in Table 1. Table 1. Properties of the Leighton Buzzard sand examined in this study. Property Coefficient of uniformity Coefficient of curvature Specific gravity Maximum void ratio Minimum void ratio Value 1.32 0.96 2.64 0.77 0.50 Sample preparation method Hollow cylindrical test-specimens were formed using a wet-pluviation technique developed by O’Kelly (2000). Test-specimens are formed between inner and outer moulds using waterpluviation. Tapping the sides of the moulds causes the test-specimen to compact. Saturated test-specimens in very loose to loose states were formed in a single layer by depositing saturated sand through water. Pluviation has the added benefit that it replicates the sedimentation process and hence the fabric of many natural sand deposits. The preparation method provides a convenient means of studying the anisotropy of sand in the laboratory. Good repeatability of the initial properties of the test-specimens was achieved using this preparation technique (Naughton & O’Kelly, 2003). Stress paths followed After sample setup, the test-specimens were isotropically consolidated from an effective stress of 50 kPa at the end of saturation, to an effective stress of 100 kPa. This was to ensure all testspecimens were normally consolidated before anisotropic consolidation. The anisotropic stress paths consisted of increasing R’ from R’ = 1.0 to R’ = 1.5, while rotating , accompanied by either maintaining b = 0 or increasing b from b = 0 to b = 0.5. Tests were designated as Ybbaa, where bb denotes the final magnitude of the b parameter with the decimal point removed and aa the magnitude of rotation at the end of anisotropic consolidation. In total, eight tests were conducted. The test-specimens had a target initial Patrick J Naughton & Brendan C O’Kelly Page 5 relative density of 75 %. The initial properties of the test-specimens, immediately after sample setup, are summarised in Table 2. Table 2. Initial properties of the sand samples immediately after sample setup. Test Mass of dry sand in testspecimen (g) Actual relative density (%) Height of testspecimen (mm) Inner radius of testspecimen (mm) Outer radius of testspecimen (mm) Y000