Prediction of Time-Dependent Long-Term Performance of Embankments On Soft Compressible Soils

Significant Achievements, Anticipated Outcomes and Future Work

A numerical model has been developed to predict the multiple characteristics of long term embankment behaviour such as vertical settlements/heaves, lateral deformations, pore water pressures and reinforcement strains at any location under different loading conditions, considering the time dependent creep behaviour of the foundation soil. The long term performance of the Lenegham embankment constructed recently near New Castle, NSW was analysed using this model and compared with the observed field performance. The predicted performance has been found to agree well with the observed performance verifying the validity of the model. It should be noted that the model had to be modified several times during its development to suit the particular soft soil characteristics and to improve the predictions. The analysis had to be carried out several times for achieving the goal of developing this model. A journal article is being prepared to publish the details of the numerical model and its verification against field performance of a full-scale real embankment.

There is considerable uncertainty concerning the selection of parameters for the foundation soft soil and other components and therefore a detailed parametric study is planned for the future. Multiple analyses for the variation of important parameters on the long term performance of the geosynthetic stabilised embankment is to be investigated in a systematic manner. This study will also enable us to develop design guidelines easily usable by practicing engineers that covers a wide range of values of important parameters that are relevant for different types of soils.

Computational Techniques Used

This research involves the use of the finite element method (FEM) in which the foundation soil, embankment fill, geosynthetic reinforcement and prefabricated vertical drains (PVDs) are represented by different types of continuum elements with appropriate material models. The entire structure is discretised into small elements, called the finite element mesh, and the interaction between different components are modelled with appropriate interface elements. The nodes of the finite element mesh are numbered consecutively with integers from 1 to the total number of nodes in the finite element mesh. Each node will have a specified number of degrees of freedom depending on the element to which it is connected and its constitutive model. Similarly, the elements are numbered in another sequence from 1 to the total number of elements. Each element will have different stiffness depending on its geometry, material characteristic, constitutive model, etc.

In an analysis, the size of the problem is defined first by the total number of nodal points, total number of all types of elements, the number of different material sets, the special dimensions of the problem, the maximum number of nodes per element, the maximum number of integration points in any of the elements and the maximum number of history variables to be stored at each integration point. This enables the determination of the maximum storage required for the variables until completion of the analysis. Then the entire finite element mesh is read (i.e., the geometry of each element and how it is connected to the other elements) and the data stored. The material model set number of each element is also input and this data appropriately stored.

The stiffness of each element is calculated in accordance to the constitutive model of the material and the global stiffness of the entire problem assembled. The global stiffness matrix could be of several millions in size depending the size of the problem, material characteristics, numbering of the nodes, etc. In effect, this gives a system of linear equations in terms of the nodal variables and in AFENA these equations are solved using a "skyline" solution technique. The system of equations for the particular problem is non-symmetric and an appropriate solution method is used.

Program AFENA adopts a macro instruction language. As such, it could be used to construct specific algorithms, i.e. AFENA is a variable algorithm program. One can create his/her own solution algorithm by specifying, in the appropriate order, a set of macro instructions selected from a list of possibilities. Each macro command acts as a signal to the program to carry out a predetermined sequence of computations, e.g.,

• EXCA – read from the data following the macro instructions the numbers of the elements to be removed from the present mesh
• TIME – advance the time by the most current value input on DT macro data record (i.e., TIME = TIME + DT)
• UCON – Compute the non-symmetric tangent stiffness matrix and the load vector for consolidation analysis
• SOLV – Solve the current set of linear equations and update the nodal variables

In the analysis of the embankment, the initial stresses are calculated first and the embankment numerically constructed in small increments of embankment fill added. Since the material characteristics are non-linear as well as stress and time dependent, tiny increments and time steps are used. For each increment and/or time step, the element stiffness matrix is calculated and the global stiffness matrix assembled and solved. This enables the updating of appropriate material characteristics and geometry for the subsequent increment. Internal checks are provided for verification of convergence of the solution and verification of accuracy and equilibrium.

For modelling the foundation soil, the constitutive creep model proposed by Kutter and Sathialingam (1992), based on Perzyna’s viscoplastic theory (1963) is implemented in this program as a different material type. In this formulation, a radial mapping rule was used to represent the stress states of soil similar to that adopted in the bounding surface formulation of Dafalias and Herrmann (1982). In contrast to Perzyna’s viscoplastic theory, viscoplastic strains are allowed to occur for all stress states, regardless of the position of the stress point in relation to the yield surface. The detailed description of this model can be found in Kutter and Sathialingam (1992).

It is also worth noting that the finite element solution procedure proposed by Carter et al. (1979) for the large deformation consolidation analysis with Jaumann’s definition of stress rate has also been implemented in AFENA. The large deformation formulation facilitates to update the nodal coordinates at the end of each load increments. Provision has been made to update the length of the geotextile–reinforcement elements and to change the orientation of the slip plane of the reinforcement-soil interface elements for each increment.

Publications, Awards and External Funding

External Funding and Awards

None.

Publications

1. Manivannan, G., Gnanendran, C.T. and Lo, S-C.R. (2003). Elasto-viscoplastic analysis of embankments on soft soils. Proceedings of the 12th Asian Regional Conference on Soil Mechanics and Geotechnical Engineering held in Singapore, 4 - 8 Aug. 2003. World Scientific Publishing Co., Singapore. ISBN 981-238-559-2 (set).
2. Gnanendran, C.T., Lo, S-C.R. and Manivannan, G. (2004). Nonlinear finite element modelling of triaxial extension effect of marine clay. The eNZ of the Earth - Proceedings of the 9th ANZ Geomechanics Conference, Auckland, NZ - Feb 8-11, 2004. NZ Geotechnical Society Inc. and the Australian Geomechanics Society. Editors: G. Farquhar, P. Kelsey, J. Marsh and D. Fellows. ISBN: 0-86869-123-2. Vol. 2, pp. 619-625.