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Theoretical Analysis of Fluid Inclusions for In Situ Soil Stress and Deformation Measurements

^a Swiss Federal Research Station for Agroecology and Agriculture (FAL), Reckenholzstrasse 191, CH-8046 Zurich, Switzerland
^b University of Connecticut, Dep. of Civil and Environmental Engineering, 261 Glenbrook Road, Storrs, CT 06269-2037
^c Laboratory of Soil & Environmental Physics (LASEP), School of Architectural, Civil and Environmental Engineering (ENAC) Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

View larger version (27K): [in a new window]   Fig. 1. Basic principal of (a) a pressuremeter to determine pressure-deformation relations of soil and rock in situ (after Mair and Wood, 1987) and (b) a Bolling probe to measure stress in soil under vehicle traffic (after Bolling, 1987).

View larger version (37K): [in a new window]   Fig. 2. Typical pressure profiles under the wheels of (a) a compact wheel loader (Volvo L30B ZS) and (b) steel track of an excavator (Liebherr 942) measured with Bolling-probes (Bolling, 1987) by Berli et al. (unpublished data, 2000).

View larger version (19K): [in a new window]   Fig. 3. (a) Initially circular cylindrical fluid inclusion within a soil matrix subjected to remotely applied stresses 11 and 22, (b) inclusion pressure pI equal to the matrix stress normal to (c) the inclusion surface 1.

View larger version (67K): [in a new window]   Fig. 4. Finite-element mesh (refined zone) used to calculate deformation and pressure of a cylindrical, initially circular liquid inclusion (plane strain situation) within a linear elastic membrane embedded in elasto-plastic material undergoing remote stress 11, 22.

View larger version (28K): [in a new window]   Fig. 5. (a) Pressure pi and (b) relative volume, V/V0, of an initially circular inclusion within linear elastic material subjected to isotropic remote stress 11 = 22 for different products of fluid compressibility, , and matrix bulk modulus, K, for Poisson's ratio = 0.3.

View larger version (26K): [in a new window]   Fig. 6. (a) Pressure pi and (b) aspect ratio of an initially circular inclusion within linear elastic material subjected to anisotropic remote stress |11| |22| (with (11 + 22)/2 = 100 kPa) for different products of fluid compressibility, , and matrix bulk modulus, K.

View larger version (33K): [in a new window]   Fig. 7. Non-dimensional inclusion pressure –2pi/(11 + 22) as a function of fluid compressibility and matrix bulk modulus K for Poisson's ratio = 0.3.

View larger version (25K): [in a new window]   Fig. 8. (a) Pressure pi and (b)relative volume, V/V0, of an initially circular inclusion within linear elastic material of Poisson's ratio subjected to remote stress 11 = 22 with fluid compressibility = 10–5 kPa–1 and matrix bulk modulus K = 103 kPa.

View larger version (24K): [in a new window]   Fig. 9. (a) Pressure pi and (b) aspect ratio of an initially circular inclusion within linear elastic material of Poisson's ratio under anisotropic remote stress |11| |22| (with (11 + 22)/2 = 100 kPa) with fluid compressibility = 10–5 kPa–1 and matrix bulk modulus K = 103 kPa.

View larger version (36K): [in a new window]   Fig. 10. Inclusion pressure within linear elastic perfectly-plastic material (Poisson's ratio = 0.3) for different yield stresses 0 under isotropic remote stress 11 = 22 with fluid compressibility = 10–5 kPa–1 and matrix bulk modulus K = 103 kPa.

View larger version (25K): [in a new window]   Fig. 11. Pressure pi (a) and aspect ratio (b) of an initially circular inclusion within linear elastic perfectly-plastic material (Poisson's ratio = 0.3) for different yield stress 0 subjected to anisotropic remote stress |11| |22| (with (11 + 22)/2 = 100 kPa) with fluid compressibility = 10–5 kPa–1 and matrix bulk modulus K = 103 kPa.

View larger version (21K): [in a new window]   Fig. 12. (a) Inclusion pressure pi and (b) aspect ratio within linear elastic material under isotropic (11 = 22 = 0 to 100 kPa) and anisotropic (11 = 100 kPa, 22 = 0...100 kPa) remote stress with fluid compressibility = 5 x 10–7 kPa–1 (water), soil bulk modulus K = 104 kPa and Poisson's ratio = 0.3 for different membrane stiffness (KMe, = 0.49).

View larger version (36K): [in a new window]   Fig. 13. Measured and calculated pressure in a Bolling probe (Bolling, 1987) as a function of surface load and probe depth for constant contact area.

View larger version (31K): [in a new window]   Fig. 14. Measured probe pressures for different field and laboratory experiments (Bolling, 1987) compared to predicted upper and lower limits for the probe pressure based on Eq. [26] and [29].

View larger version (57K): [in a new window]   Fig. 15. Cylindrical silicon rubber membrane (front) and assembled Bolling probe tip (back) (probe design: Institute of Terrestrial Ecology – ETH Zurich).

View larger version (34K): [in a new window]   Fig. 16. (a) Cylindrical rubber membrane (length l, inner radius r, membrane thickness t) undergoing an internal pressure p resulting in circumferential and axial stresses, zz. Radial stresses were neglected due to the small membrane thickness.

View larger version (18K): [in a new window]   Fig. 17. (a) Young's modulus and (b) Poisson's ratio of the silicon rubber membrane used for the Bolling probe (Bolling, 1987).