Keywords: cavity expansion, finite boundary, non-associated flow rule, general soil.

A theoretical analysis, based on the cylindrical cavity expansion theory, is developed to analyze the pressure-expansion relationship of a cavity surrounded by a soil matrix. This study investigates the expansive behaviour of a cavity with a confined boundary prevailing at a finite distance from the cavity. The approach developed provides an analytical method for the interpretation of a cone penetration test when the test is performed at a restricted boundary site. Estimation of the load-settlement behaviour for a granular column in-group formation also can be accomplished using the approach developed.

Cavity expansion theories have been applied to estimate the bearing capacity of a granular column and to interpret cone penetration test results by many authors [1,2,3,4,5,6]. Previous research emphasized the behaviour of a cavity surrounded by soil with an infinite boundary [7,8,9,10]. When the cavities are closely spaced in a group formation, the surrounding soil and the neighbouring cavities impede lateral cavity expansion. Analytical solutions for the expansive behaviour for a cavity surrounded by clay or sand are developed in this paper. Both soils are modelled as an elastic-perfectly plastic material. The Tresca yield criterion is adopted for clay so that the volume remains unchanged as the soil becomes plastic. The Mohr-Coulomb yield criterion with a non-associated flow rule is used to represent the plastic behaviour of the sand. The axial or vertical stress is assumed to be the intermediate stress and plane strain conditions in the axial direction are assumed.

Analytical results reveal that (1) cavity pressure-radial strain relationship remains the same for a certain ratio between the spacing of cavities and the radius of cavity. (2) The degree of pressure increment increases with an increase of the soil modulus, however, the trend in the pressure increment diminishes for the higher ratios between the cavity spacing and the cavity radius. (3) The degree of pressure increment decreases with an increase of the initial in-situ soil pressure.

1

Gibson, R.E. and Anderson, M.A., "In-situ Measurement of Soil Properties with the Pressure meter", Civil Engineering and Public Works Review, 56(685), 615-618, 1961.

2

Hughes, J.M.O., Wroth, C.P. and Windle, D., "Pressuremeter Tests in Sands", Geotechnique, 27(4), 455-477, 1977.

3

Houlsby, G.T. and Withers, N.J., "Analysis of the Cone Pressuremeter Test in Clay", Geotechnique, 38(4), 575-587, 1988.

4

Yu, H.S., "Cavity Expansion Theory and its Application to the Analysis of Pressuremeters", Ph.D. thesis, University of Oxford, UK, 1990.

5

Bolton, M.D. and Whittle, R.W., "A Non-Linear Elastic/Perfectly Plastic Analysis for Plane Strain Undrained Expression Tests", Geotechnique, 49(1), 133-141, 1999.

6

Chang, M.F., The, C.I. and Cao, L.F., "Undrained Cavity Expansion in Modified Cam Clay II: Application to the Interpretation of the Piezocone Test", Geotechnique, 51(4), 335-350, 2001. doi:10.1680/geot.51.4.335.39390

7

Vesic, A.S., "Expansion of Cavity in Infinite Soil Mass", ASCE, 98(3), 265-290, 1972.

8

Carter, J.P., Booker, J.R. and Yeung, S.K., "Cavity Expansion in Cohesive Frictional Soils", Geotechnique, 36(3), 349-358, 1986.

9

Yu, H.S. and Houlsby, G.T., "Finite Cavity Expansion in Dilatant Soils: Loading Analysis", Geotechnique, 41(2), 173-183, 1991.

10

Collins, I.F. and Yu, H.S., "Undrained Cavity Expansions in Critical State Soils", International Journal for Numerical and Analytical Methods in Geomechanics, 20(7), 489-516, 1996. doi:10.1002/(SICI)1096-9853(199607)20:7<l489::AID-NAG829>3.0.CO;2-V

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