Cavity expansion analysis with applications to cone penetration test and root-soil interaction - Zhuang, Peizhi (2017)
As one of the most versatile and reliable in-situ devices, cone penetrometers have been extensively used in soil exploration (e.g. soil classification, soil profiling, back-calculation of soil properties etc.) both experimentally and theoretically over the past 80 years. To improve its site accessibility, reduce the required sample size with minimal boundary effects, or model soil penetration by plant roots or earthworms, cone penetrometers with various sizes are often employed both in the field and laboratory. Consequently, size-dependent performance may appear, and this is one of the subjects of this research. A series of cone penetration tests with three sized cone penetrometer (12mm, 6mm, 3mm) on the Leighton Buzzard sand with two fractions (E and C) was performed at the 1g condition. Evident size effects were observed both in the cone tip resistance and shaft friction. To account for the observed size-dependent behaviour, theoretical methods based on the cavity expansion theory were developed in addition to the available experimental findings. Firstly, a size-dependent quasi-static cavity expansion solution was developed by improving the conventional cavity expansion theory incorporating with a strain gradient theory of plasticity. A stiffer response is modelled for a smaller cylindrical/ spherical cavity with this solution. Based on the analogy of cone penetration and quasi-static cavity expansion, the developed size-dependent expansion solution for spherical cavities was employed to quantify the size effect in the cone tip resistance, and fair good agreements were achieved between the theoretical prediction and experimental results. Subsequently, the scale effect observed in shaft friction resistance was explained in terms of the interface frictional strength and mobilised lateral soil stress. The size-dependent interface frictional strength was discussed based on the available experimental data of other researchers, and an improved solution based on the elastic cylindrical cavity expansion solution was derived to quantify the size dependency of the mobilised lateral stress on the shaft. In the light of above discussions, dominating factors influencing the size-dependent behaviours in the cone penetration test are summarised. The other objective of the present research was to model the mechanical interaction between a growing root tip and the surrounding soil. Two elastic solutions for computing the stress and displacement fields around a displacement-controlled ellipse were developed based on the complex variable theory of elasticity and Fourier series method. By assuming the axial cross section of a root tip as a half-ellipse, the two-dimensional soil response to a short-term growing root tip was discussed with the derived elastic solutions. Benefits of radial swelling of the root tip to its axial penetration were summarised, and an approximate analytical method to estimate the soil resistance mobilised by a short-term root growth was suggested and employed in the present root tip-soil interaction analyses. In addition, influences of the additional shear stress in the process of static and quasi-static cavity expansion were analysed with an elastic-perfectly-plastic model. For Tresca materials, a non-equal initial stress field was considered in the static stress solution, and a quasi-static expansion solution was then derived for a cavity deforming in a hydrostatic stress field considering the material compressibility. The static stress solution is capable of calculating the stress redistribution around a circular rotating probe, and the large-strain quasi-static solution may be useful in theoretical predictions of the tip resistance of a rotating penetrometer (or pile) which has been often utilised in needle cone penetration tests for modelling the root tip elongation. Then the introduced methods in above solutions were applied to the static stress analysis of a circular cavity surrounded by the Mohr-Coulomb material under a non-equal stress field. Based on the conformal mapping function proposed by Detournay and Fairhurst (1987), both a loading and unloading analysis were carried out with the derived analytical solution. It can provide a simple method to predict the plastic failure zone and calculate the stress redistribution around a circular excavation (e.g. tunnel, pipeline) either under loading or unloading.