The differential equation by Terzaghi and Fr?hlich, better known as Terzaghi’s one-dimensional consolidation equation, simulates the visco-elastic behaviour of soils depending on the loads applied as it happens, for ...The differential equation by Terzaghi and Fr?hlich, better known as Terzaghi’s one-dimensional consolidation equation, simulates the visco-elastic behaviour of soils depending on the loads applied as it happens, for example, when foundations are laid and start carrying the weight of the structure. Its application is traditionally based on Taylor’s solution that approximates experimental results by introducing non-dimensional variables that, however, contradict the actual behaviour of soils. The proposal of this research is an exact solution consisting in a non-linear equation that can be considered correct as it meets both mathematical and experimental requirements. The solution proposed is extended to include differential equations relating to two/three dimensional consolidation by adopting a transversally isotropic model more consistent with the inner structure of soils.展开更多
The examination of wave motions is traditionally based on the differential equation of D’Alambert, the solution of which describes the motion along a single dimension, while its bidimensional extension takes on the c...The examination of wave motions is traditionally based on the differential equation of D’Alambert, the solution of which describes the motion along a single dimension, while its bidimensional extension takes on the concept of plane waves. Considering these elements and/or limits, the research is divided into two parts: in the first are written the differential equations relating on the conditions two/three-dimensional for which the exact solutions are found;in the second the concepts are extended to the analysis of the propagation of wave motions in porous media both artificial and natural. In the end the work is completed by a series of tests, which show the high reliability of the physical-mathematical models proposed.展开更多
文摘The differential equation by Terzaghi and Fr?hlich, better known as Terzaghi’s one-dimensional consolidation equation, simulates the visco-elastic behaviour of soils depending on the loads applied as it happens, for example, when foundations are laid and start carrying the weight of the structure. Its application is traditionally based on Taylor’s solution that approximates experimental results by introducing non-dimensional variables that, however, contradict the actual behaviour of soils. The proposal of this research is an exact solution consisting in a non-linear equation that can be considered correct as it meets both mathematical and experimental requirements. The solution proposed is extended to include differential equations relating to two/three dimensional consolidation by adopting a transversally isotropic model more consistent with the inner structure of soils.
文摘The examination of wave motions is traditionally based on the differential equation of D’Alambert, the solution of which describes the motion along a single dimension, while its bidimensional extension takes on the concept of plane waves. Considering these elements and/or limits, the research is divided into two parts: in the first are written the differential equations relating on the conditions two/three-dimensional for which the exact solutions are found;in the second the concepts are extended to the analysis of the propagation of wave motions in porous media both artificial and natural. In the end the work is completed by a series of tests, which show the high reliability of the physical-mathematical models proposed.
