Finite Element Analysis of Warragamba Dam
Objective:
Warragamba Dam is located some 65km to the west of Sydney, Australia. It is the largest concrete gravity dam in the country and its storage provides 70% of the total water supply for Sydney (population of nearly four million). The dam, which is owned by Sydney Water, is to be upgraded for both dam safety and flood mitigation purposes. Back in 1994-5, the option to raise the concrete dam by 23m was proposed and MSC Australia was involved with the 3D finite element modelling and analysis (FEA) of this project. Although this dam raising option was not to proceed by direction of the New South Wales (NSW) government, the other option of constructing an auxiliary spillway has been given the go ahead recently. MSC was also involved in the analysis of the auxiliary spillway excavation study. The dam raising FE analysis will be described in detail while some aspects of the auxiliary spillway excavation simulation will be highlighted.
Summary
Finite Element Modelling
The geometric modelling and mesh discretisation of Warragamba Dam were carried out using the Patran modelling software. A general purpose FE solver, was used for the numerical computation. It has the following analysis capabilities for dam safety assessment: stress/deformation, construction simulation, nonlinear dynamics, seepage, ground/structure interaction, consolidation, heat transfer, creep, normal mode, nonlinear material models, response spectrum, time history, buckling, fluid/structure interaction and fracture mechanics.
Geometry Creation
The topography covering about half a kilometre upstream and downstream of the dam was digitised from a contour plan. The geometry of the dam/rock foundation interface (i.e. the excavation boundaries) was taken from a series of drawings showing a number of cross-sections along the dam. From these digitised points, contour lines were created using a number of curve fitting routines. And from these lines, smooth surfaces were generated. Finally the solid model of foundation and dam was generated from these surfaces. The foundation solid consists of five geological units. The orientation of each unit's interface was interpolated within the area bounded by drill-hole information and extrapolated beyond.
Mesh Creation & Boundary Conditions
A high mesh density within the dam and its immediate surrounds was generated and the mesh transition in the three directions could be achieved. Over 30,000 elements were employed in the mesh. In addition to the 3D solid elements, other elements were also used to represent various aspects of the dam.
The base of the model, which was about 200m below the dam, was fixed in all direction. The vertical boundaries of the model were on roller supports.
Loadings
The loads included in the analysis were:
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Gravity loads due to self-weight of the rock foundation and the concrete
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The hydrostatic pressure on the dam
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Post-tensioning loads in the cables (for the 5m interim raising in the late 1980s)
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Pore water pressure within dam and foundation (carried out by an equivalent thermal analysis)
Joints in the Dam
Six vertical twist joints were used during the construction of the dam in order to allow cantilever action to develop, and to reduce shear-twist action. They were only grouted when the whole dam was completed and the storage water was about three-quarters of the full storage level. Therefore, it was important to model these twist joints in the 3D model. A 2D plane strain FEA would not be able to model the true behaviour of the dam.
Material Properties
The site consists of six units of geological materials and they are:
Unit 1: Bulgo Sandstone - modelled as an isotropic elastic material
Unit 2: Bald Hill Claystone - modelled as an anisotropic elastic material
Unit 3: Coarse grained Sandstone & Conglomerate - modelled as an isotropic elastic material
Unit 4: Hawkesbury Sandstone (fine grained sideritic) - modelled as an isotropic elastic material
Unit 5: Hawkesbury Sandstone (fine to coarse grained) - modelled as an isotropic elastic material
Unit6: Grey shale bands - not modelled in analysis
The thin horizontal shale bands, which exhibit nonlinear shear behaviour, are located within the sandstone units. After a number of sensitivity studies using both interface elements and 3D elements to model these shear bands, it was found that these shear layers in the dam abutments were very unlikely to fail and their influence on the behaviour of the dam was not significant. Therefore they were not modelled in the analysis.
Geostatic Stress Simulation
An initial stress state was assumed prior to dam construction. These stresses were then redistributed during the first step of the analysis. The horizontal stresses and the orientation of the principal stress would be influenced by the topography of the FE model.
Analysis Steps
The simulation of the dam construction and various loading stages were carried out in a number of analysis steps. They are listed as follows:
Original dam construction:
1 Establish geostatic stress state in foundation
2 Add first lift of concrete elements to RL53
3 Apply water load (RL53) to the dam
4 Add second lift of concrete elements to the dam's full height
5 Apply three-quarters of Full Storage Level (FSL) of water pressure
6 Grout all vertical twist joints and apply additional water pressure to RL107.6
7 Apply FSL of water (RL116.7)
8 Transient pore water flow in the dam and foundation
9 Foundation softening
10 Creep simulation
Recent dam raising (interim works):
11 Raise dam crest by 5.1m by adding concrete elements. Install post-tensioned cables and apply post-tensioning loads
12 Study effect of the original design super flood (RL125)
13 Study effect of the existing design flood (RL130.4)
23m dam raising proposal:
1 Repeat steps 1 to 11 above
2 Add new concrete elements to the downstream face and crest in three stages
3 Extend existing post-tensioned cables and reapply post-tensioning loads
4 Increase water load to simulate flooding (RL153)
Dynamic analyses of the raised dam:
1 Eigenvalues and eigenvectors extraction
2 Operating basis earthquake (OBE) of 1 in 500 years with storage (conservatively) at the Probable Maximum Flood (PMF) level using an acceleration response spectrum solution
3 Initial Maximum Design Earthquake (MDE) of 1 in 10,000 years with storage at FSL using a transient dynamic solution
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