A fully coupled, effective stress based elasto-plastic model is presented for a rigorous analysis of flow and deformation in variably saturated porous media subjected to monotonic and cyclic loading. The governing equations are derived based on the effective stress concept, equations of equilibrium, and conservation equations of mass and momentum using a systematic macroscopic approach. Both elastic and elasto-plastic constitutive equations are developed. All model coefficients are identified in terms of measurable parameters. The governing equations presented are general in nature, embodying all previously presented formulations in the field. A unified bounding surface plasticity model is developed to describe the stress-strain behaviour of variably saturated soils subjected to monotonic and cyclic loading. The model is formulated incrementally within the critical state framework using the effective stress approach. The model takes into account the effects of both plastic volumetric strain and matric suction on the hardening of the bounding surface. Cyclic behaviour is captured through a new mapping rule in which the point of stress reversal is taken as the centre of projection. The effect of particle crushing at high stresses is considered through a three-segmented critical state and isotropic compression lines. A non-associative flow rule is employed to generalise application of the model to all soils. Solution to the governing equations is obtained numerically using the finite element approach, with the finite difference method employed for the time integration of the rate equations. The elasto-plastic constitutive equations are integrated explicitly using Euler???s forward and the modified Euler integration schemes. Yield surface correction schemes are adopted to improve accuracy of the solution. Essential elements of the proposed model are validated by comparing numerical predictions with experimental data from the literature for fully and partially saturated soils subjected to monotonic and cyclic loadings in drained, undrained, isotropic and deviatoric conditions. The results demonstrate capability of the coupled model to predict essential characteristics of variably saturated soils subjected to monotonic and cyclic loadings in a unified manner.

A fully coupled, effective stress based elasto-plastic model is presented for a rigorous analysis of flow and deformation in variably saturated porous media subjected to monotonic and cyclic loading. The governing equations are derived based on the effective stress concept, equations of equilibrium, and conservation equations of mass and momentum using a systematic macroscopic approach. Both elastic and elasto-plastic constitutive equations are developed. All model coefficients are identified in terms of measurable parameters. The governing equations presented are general in nature, embodying all previously presented formulations in the field. A unified bounding surface plasticity model is developed to describe the stress-strain behaviour of variably saturated soils subjected to monotonic and cyclic loading. The model is formulated incrementally within the critical state framework using the effective stress approach. The model takes into account the effects of both plastic volumetric strain and matric suction on the hardening of the bounding surface. Cyclic behaviour is captured through a new mapping rule in which the point of stress reversal is taken as the centre of projection. The effect of particle crushing at high stresses is considered through a three-segmented critical state and isotropic compression lines. A non-associative flow rule is employed to generalise application of the model to all soils. Solution to the governing equations is obtained numerically using the finite element approach, with the finite difference method employed for the time integration of the rate equations. The elasto-plastic constitutive equations are integrated explicitly using Euler???s forward and the modified Euler integration schemes. Yield surface correction schemes are adopted to improve accuracy of the solution. Essential elements of the proposed model are validated by comparing numerical predictions with experimental data from the literature for fully and partially saturated soils subjected to monotonic and cyclic loadings in drained, undrained, isotropic and deviatoric conditions. The results demonstrate capability of the coupled model to predict essential characteristics of variably saturated soils subjected to monotonic and cyclic loadings in a unified manner.

Canegro is a leading sugarcane crop simulation model and has been used extensively in agronomic research and management. The model has been under development since the late 1980s at the South African Sugarcane Research Institute (SASRI). The Decision Support System for Agrotechnology Transfer (DSSAT) is a software package containing models for a wide range of field crops, and utilities for processing, storing and analysing model inputs and outputs. Canegro was included as part of version 3.1 of DSSAT in the mid-1990s. The SASRI Canegro model was subsequently developed further, but these changes were never integrated, nor incorporated, into DSSAT. DSSAT has also developed substantially, and as of version 4 adopted a modular Cropping System Model (CSM) structure, providing numerous scientific and practical advantages over previous non-modular versions. The DSSAT-Canegro v.3 model was not modified to use this modular structure. Following recognition of the advantages offered by DSSAT and its modular CSM, a project was initiated to incorporate the Canegro model into the DSSAT CSM. The project entailed: (i) restructuring and integrating the current Canegro plant growth and development code into the DSSAT v4 CSM modular framework, making use of its generic modules for management, soil, weather and the energy balance; (ii) verification of DSSAT CSM Canegro model results against the current SASRI version of Canegro to ensure that the new model produced similar results to the original model, for a set of simulated situations; and (iii) evaluation of the new DSSAT CSM Canegro model against experimental datasets. The new DSSAT v4 CSM Canegro model has been verified to behave identically to the SASRI Canegro model when the water balance is not modelled and growth can occur at climatic potential rates. When the water balance is simulated but where the crop is not stressed, near identical output is produced by both models. Under water-stressed conditions, some discrepancies appear between the two models, due to differences in the calculation of reference evaporation, soil surface evaporation and runoff. Validation of the new model against data from 16 experimental crops produced root mean squared errors of 6.62 t ha-1 for stalk dry mass and 3.59 t ha-1 for sucrose mass – very similar to published values for Canegro. This project has yielded a functional, well-documented, maintainable and user-friendly version of the Canegro model, which is available for universal use via the official release of the DSSAT v4.5. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.