Dynamic Elasto-Visco-Plastic Material Model for Modelling of Light Weight Deflectometer Test: a uniaxial preliminary study

A uniaxial material model comprising elastic (resilient), viscous (damping), plastic (permanent) and inertia forces is derived in this thesis. The behaviour of the model is studied and the capability of the model to replicate the behaviour of soils subjected to a Light Weight Deflectometer (LWD) test is investigated.

Based on literature review, material equations originating in impact engineering are used as the governing equations of the proposed model instead of traditional road/railway geotechnic material equations, e.g. a stress dependent resilient modulus, because the impact engineering equations are suitable for dynamic phenomena with high velocities and are capable of modelling seating. Because of the novelty of the model, only uniaxial case is considered in this research. The predominantly uniaxial nature of an LWD test is conveniently used during the simplification. To have the numerical solution of the proposed model fully under control, the solution is obtained via own-built \MATLAB code. Central difference numerical method is used during the solution for the linearization of the problem in the time domain and a uniaxial case of closest point projection method is used to drive the evolution of plastic state variables. No experiment was performed during this research. Instead, the model is calibrated using published and digitized LWD deflection data.

The thesis shows that it is possible to create and solve a model comprising dynamic elasto-visco-plastic behaviour. It also shows that the model is capable of producing results of promising quality. The investigation of the behaviour of the model shows that all its parts, i.e. stiffness, inertia, damping and permanent forces, significantly contribute to the response of the model, which finding is in contradiction with the contemporary accepted assumptions about the LWD behaviour. Main findings are: (i) the model is very load sensitive, thus, to utilize the full potential of the model, the time-load data measured for the whole time interval of an LWD test needs to be uploaded into the model; (ii) for the same reason, the model need to be calibrated on the whole time-deflection data; (iii) the power stiffness governing equation is more suitable for modelling of LWD testing than the more widely used stress dependent resilient modulus approach, because it enables to model the phenomenon of seating and (iv) Armstrong-Frederic hardening rule, used in this thesis, is the simplest non-linear plastic governing rule, which is capable to deliver a non-zero increment of permanent deflection under cyclic loading. However, the rule is not entirely suitable for stress/force driven tests and some problems with the uniqueness of plastic material constant identification are encountered during the investigation.

The findings of this thesis support the notion that the dynamic nature of LWD test should be acknowledged and that the current LWD testing procedure should be used with caution. Main recommendations are: (i) time-deflection and time-load data should be measured for a minimum of \mbox{30 ms} but recommended \mbox{50-60 ms} and the data should be recorded as inextricable part of an LWD test; (ii) the deflection of a soil surface under an LWD plate should be measured preferably to the deflection of an LWD plate itself; (iii) further research should be aimed on improving the governing equations of the permanent part of the model, with Armstrong-Frederic hardening rule possibly being replaced by multiple plasticity surface models and (iv) special attention should be paid if the results of LWD testing are directly compared to the results of a different Quality Assurance/Quality Control method.

The author of this thesis acknowledges that to follow the aforementioned recommendations will require additional research aimed at the construction of LWD devices, especially at: (i) eliminating the systematic error between LWD surface and LWD plate measurements; (ii) minimizing the error of internal numerical integration, which decreases the reliability of measured data after approximately 15 ms of measurement and (iii) including load measurements into more than just few types of LWD devices.

In summary, this thesis presents a dynamic elasto-visco-plastic model, which, for as far as the author of the thesis was able to review, is first of its kind in the context of LWD modelling. Only uniaxial representation of the problem is studied in this thesis in order to avoid the usage of a commercial final element method software, thus to have the numerical solution of the novel model fully under control. Though only uniaxial, results of this study provide useful insight into LWD mechanics and points out possible problems for future research.