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# Finite Element Analysis of Seepage and Stresses in a Concrete Gravity Dam (Essay Sample)

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Finite Element Analysis of Seepage and Stresses in a Concrete Gravity Dam
The dam's design takes into account anisotropic permeable soil layers, impermeable rock, and various material properties. This report presents a finite element analysis of seepage flow and stresses in a concrete gravity dam with sheet piling. The analysis is carried out using the seepageflow2D program, addressing the impact of sheet piling on total flow and uplifting pressure distributions. source..

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Finite Element Analysis of Seepage and Stresses in a Concrete Gravity Dam
Table of Contents TOC \f \o "1-9" \hAbstract31. Introduction42. Seepage Analysis (Question 1)5(a) Model Creation5(b) Mesh and Seepage Flow Vector Field5(c) Total Predicted Flow5(d) Uplifting Pressure Distribution6(e) Analysis without Sheet Piling73. Stresses Analysis (Question 2)9(a) Contour Plot of Major Principal Stress (S1)9(b) Location of Maximum Major Principal Stress9(c) Safety Factor Against Tensile Failure9(d) Distribution of Vertical Direct Stresses (SY)9(e) Distribution of Vertical Effective Stress on Soil9(f) Accuracy of Results9(g) Mesh Representation104. Conclusions115. References126. Appendices: The Finite Element Input file for Seepage Analysis (Question 1)13
Table of Figures
TOC \c "Figure" \h Figure 1: Mesh and Seepage Flow Vector Field6
Figure 2: Total Predicted Flow7
Figure 3: Uplifting Pressure Distribution8
Figure 4: Analysis without Sheet Piling8
Figure 5: Stresses Analysis, the finite elements’ edges9
Figure 6: Contour Plot of Major Principal Stress (S1)10
Figure 7: Safety Factor Against Tensile Failure11
Figure 8: Distribution of Vertical Direct Stresses (SY)12
Figure 9: Distribution of Vertical Effective Stress on Soil13
Figure 10: Mesh Representation14
Abstract
The dam's design takes into account anisotropic permeable soil layers, impermeable rock, and various material properties. This report presents a finite element analysis of seepage flow and stresses in a concrete gravity dam with sheet piling. The analysis is carried out using the seepageflow2D program, addressing the impact of sheet piling on total flow and uplifting pressure distributions.
1. Introduction
When assessing the design of a concrete gravity dam, finite element analyses are essential, particularly when taking into account elements like the characteristics of structural materials, impermeable rock, and anisotropic permeable soil. The use of the seepageflow2D tool to evaluate seepage flow and dam stresses is covered in this study.
A thorough structural analysis has been motivated by the early design of a concrete gravity dam with sheet piling, situated against an anisotropic permeable soil and impermeable rock layers. Finite Element Analysis (Finite Element Analysis) is used in this work to examine two important factors: seepage flow beneath the dam and stresses in the concrete construction. An extensive analysis was made possible by the concrete's material qualities and the soil layers' anisotropic permeability coefficients. Through the use of the seepageflow2D tool, we may analyze seepage flow in order to comprehend possible flow patterns, measure the distribution of uplift pressure at the base of the dam, and determine how sheet piling affects the behavior of the system.
The study goes beyond seepage analysis and uses the LUSAS software for Finite Element Modeling to analyze stress. In this section, we will examine how the main stresses within the dam are distributed, pinpoint the essential stress locations, and assess the safety against tensile concrete collapse. The assessment of the effective vertical stress on the soil and the vertical direct stresses along the dam's base are also included in the study. This research addresses both structural and hydraulic factors, providing a comprehensive analysis of the proposed dam design's structural integrity. The results are intended to offer insightful information for improving the design and making sure it can withstand a range of loading scenarios.
2. Seepage Analysis (Question 1)
“””
* Step 1
An uplift force acting at the base of the gravity dam (without drainage gallery)
Uplift force (U)= × yw × (H+ h)
An uplift force acting at the base of the gravity dam (with drainage gallery)
Uplift force (UDG) = Yw × h + 3 × Yw × (H − h) = 1 × (H+2h)
Where,
b = base width of the dam
Yw = unit weight of water kN/m³
H = depth of water stored in a dam
h = depth of tail water
* Step 2
Yw = 10 kN/m3, Yconc = 24 kN/m3
H = 65 m, h = 5 m
An uplift force of the dam having drainage gallery
Uplift force (UDG) = ¼w × h + {} × yw × (H − h) = ¼ × (H + 2h) = 10 × (65+ 5) = 250 k N
* Step 3
The total uplift pressure acting at the base of dam = Area of pressure diagram
.. Total uplift pressure
= 250 × 10+ 40 × 50 + 1 + 200 × 40 + × 400 × 10
= 2500+ 2000+ 4000 + 2000
= 10500 kN/m²
* Answer
Answer
= 10500 kN/m²
“””
(a) Model Creation
The creation of the model involved the declaration of the inputfilename variable and finally invoking the seepageflow2D() function by parsing in the inputfilename value so as to read the input finite element file. This in turn enabled the utility of the graphical interface of seepageflow2D, the dam's geometry, including points, lines, surfaces, and lines with prescribed total head, was defined as shown in the qn1_dam_simulation.m file code below.
% qn1_dam_simulation.m
inputfilename = 'Finite Element Analysis_file.txt';
seepageflow2D(inputfilename)
The Finite Element Analysis_file.txt input Finite Element file that was parsed into the is also shown below, showing 10 tri-nodal elements connected along 16 nodes with the total head prescribed at the two nodes at the bottom-most of the dam on the upstream side, that is, at the nodes 10 and 11
TITLE = Qn1FiniteElementAanalysis_Assignment
ELEMENTS=10
1 1 2 7 50 50
2 2 3 8 50 50
3 3 4 9 50 50
4 4 5 10 50 50
5 5 6 11 50 50
6 6 7 12 50 50
7 7 8 13 50 50
8 8 9 14 50 50
9 9 10 15 50 50
10 10 1 16 50 50
NODE_COORDINATES=16
1 0.0 0.0
2 0.0 20.0
3 20.0 20.0
4 40.0 20.0
5 50.0 20.0
6 80.0 60.0
7 80.0 70.0
8 90.0 70.0
9 90.0 50.0
10 100.0 20.0
11 100.0 0.0
12 90.0 0.0
13 80.0 0.0
14 70.0 0.0
15 60.0 0.0
16 50.0 0.0
NODES_WITH_PRESCRIBED_TOTAL_HEAD=2
10 100.0
11 100.0
UNIT_WEIGHT_OF_FLUID=10000
YOUNGS_MODULUS=30000
POISSON_RATIO=0.25
CONCRETE_DENSITY=2400
TENSILE_STRENGTH=2.5
NUMBER_OF_NODE_SETS_FOR_FLOW_CALCULATION = 1
NODE_SET_NUMBER = 1
NUMBER_OF_NODES = 2
2 1
NODES_FOR_PORE_PRESSURE_PRINTING = 1
1
As shown above, all the required input parameters were set in as in their respective SI units, that is, the unit weight of water = 10kN/m^3, the youngs modulus of concrete as 30MPa, poisson ratio as 0.25, the concrete self-weight of 2400kg/m^3. Other finite element parameters include the number of node sets for flow calculation, which was set as 1 considering only the bottom-most node at coordinate (100.0, 0.0) at the upstream side, the node set number also as 1, and finally the same bottom-most node for the pore pressure printing.
(b) Mesh and Seepage Flow Vector Field
A graphical output from seepageflow2D in the figure 1 below illustrates the mesh and seepage flow vector field under the dam, providing insights into the computational model. The seepage flow is observed to be prominent along the finite element edges which appear as equipotential lines colored red in the equipotential lines subplot in the figure 1 below, where the maximum seepage flow is observed to be maximum at the bottom-most part of the upstream side of the dam
-635635-6354741545Figure 1: Mesh and Seepage Flow Vector FieldFigure 1: Mesh and Seepage Flow Vector Field
(c) Total Predicted Flow
The total predicted flow under the dam along its entire length was computed, offering an understanding of the seepage characteristics as shown in the figure 2 below. The total predicted flow is also observed to be prominent along the finite element edges which appear as total head lines colored red in the total head subplot in the figure 2 below, where the maximum total predicted flow is also observed to be maximum at the bottom-most part of the upstream side of the dam.
center63504170045Figure 2: Total Predicted FlowFigure 2: Total Predicted Flow
(d) Uplifting Pressure Distribution
As shown in the figure 3 below, a graph generated using MATLAB, displays the uplifting pressure distribution at the dam's base. This graph provides insights into the potential areas of concern regarding uplift pressures where the uplifting pressure distribution is observed to be such that the uplifting pressure is prominent along the finite element edges which appear as the pore pressure lines colored gray in the ‘pore pressure, u’ subplot in the figure 3 below, where the maximum uplifting pressure is observed to be maximum at the bottom-most part of the upstream side of the dam.
center63504224020Figure 3: Uplifting Pressure DistributionFigure 3: Uplifting Pressure Distribution
(e) Analysis without Sheet Piling
To evaluate the impact of sheet piling, the analysis was repeated without sheet piling by setting the parameter value NODE_SET_NUMBER = 1 as in the input finite element file so as to make a prismatic finite element model of the dam, rather than a sheet-piled model and corresponding total flow and uplifting pressure distributions were compared with the initial analysis as shown in the figure below. The was however, observed decrease in the enhancement of the dam's performance by increasing uplifting pressures and thus increasing the seepage flows as shown in the figure 4 below. This thus contributed to the reduced stability and safety of the dam by taking out the sheet piles.
03623310Figure 4: Analysis without Sheet PilingFigure 4: Analysis without Sheet Piling064770
3. Stresses Analysis (Question 2)
“””
To create a model of a concrete dam in LUSAS, you can follow these steps:
Begin by creating a new model in LUSAS and defining the model units. For example, if you want to use meters as the unit of length, you can set the model units to "m".
Create the geometry of the dam. You can do this by drawing the shape of the dam using the appropriate tools in LUSAS. Make sure to include the waterline level and the ground level in your geometry.
Once the geometry is created, you can divide the dam into finite elements by meshing the model. You can use ...

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