Seismic Analysis of Concrete Gravity Dam

(Using ABAQUS)

COURSE PROJECT REPORT

(of CE-620)

By

RAYJADA SATWIK PANKAJKUMAR (184044002)

PRAJAPATI RAVINDRA SITARAM MANJU (183040051)

MOHD FAISAL ANSARI (183040043)

Under the guidance of

Prof. Yogesh M. Desai

Department of Civil Engineering

Centre for Computational Engineering & Science (CCES)

Indian Institute of Technology Bombay

April-2019

i

Acceptance Certificate

Department of Civil Engineering

Indian Institute of Technology Bombay

This is to certify that project report entitled “Seismic Analysis of Concrete Gravity Dam (Using

Abaqus)” is submitted by Rayjada Satwik Pankajkumar. (Roll No. 184044002), Prajapati Ravindra

Sitaram Manju (183040051) and Mohd Faisal Ansari (183040043) in the partial fulfilment of the

requirement for the course Finite Element Methods (CE620).

Prof. Yogesh M. Desai

(Course Instructor)

Date:

ii

Acknowledgement

We are submitting this report with a deep sense of fulfilment and boundless joy. At this stage,

we would like to express our sincere gratitude towards all individuals who helped us directly or

indirectly to complete this work.

First we would like to express our deep sense of gratitude towards our course instructor Prof.

Yogesh M. Desai, Professor, Civil Engineering Department IIT Bombay for their valuable

guidance, support and encouragement. We would like to thank all teaching assistants (TAs) for

their resourceful help.

We would like to thank Civil Engineering Department, IIT Bombay and Centre for

Computational Engineering & Science (CCES) for providing advanced facilities during our work.

Rayjada Satwik Pankajkumar

Prajapati Ravindra Sitaram Manju

Mohd Faisal Ansari

Date: 30/04/2019

iii

Contents

Acceptance Certificate ................................................................................................................................... i

Acknowledgement ........................................................................................................................................ ii

Contents ....................................................................................................................................................... iii

Table of Figures ........................................................................................................................................... iv

List of Tables ................................................................................................................................................ v

Abstract ........................................................................................................................................................ vi

1 Introduction ........................................................................................................................................... 1

2 Problem Formulation and Analysis ....................................................................................................... 2

2.1 Overview ....................................................................................................................................... 2

Verification of plain strain formulation using linear elastic concrete model ............................................ 3

2.1.1 Introduction to ABAQUS ..................................................................................................... 3

2.1.2 2D plain strain analysis ......................................................................................................... 4

2.1.3 3D analysis .......................................................................................................................... 10

2.1.4 Comparison of results obtained from 2D plain strain and 3D analysis ............................... 11

2.2 Dam analysis under seismic load using concrete damage plasticity model ................................ 12

2.2.1 Definition of material properties (Concrete Damage plasticity) ......................................... 12

2.2.2 Definition of analysis steps ................................................................................................. 13

2.2.3 Definition of earthquake load and application .................................................................... 14

2.2.4 Results and convergence study ........................................................................................... 16

3 Conclusion .......................................................................................................................................... 18

4 References ........................................................................................................................................... 19

iv

Table of Figures

Figure 1 Schematic Diagram of Koyna dam ................................................................................................. 2

Figure 2 Abaqus Window ............................................................................................................................. 3

Figure 3 Abaqus User Interface .................................................................................................................... 4

Figure 4 Generation of Part ........................................................................................................................... 4

Figure 5 Assigning Material property ........................................................................................................... 5

Figure 6 Defining and Assigning Material property ..................................................................................... 6

Figure 7 Assembly Generation ..................................................................................................................... 6

Figure 8 Defining Analysis Step ................................................................................................................... 7

Figure 9 Assigning Boundary Condition ...................................................................................................... 7

Figure 10 Assigning Gravity Load................................................................................................................ 8

Figure 11 Applying Hydrostatic Load .......................................................................................................... 8

Figure 12 FEM Model of Dam ..................................................................................................................... 9

Figure 13 Selecting output data .................................................................................................................... 9

Figure 14 Creation of Job for analysis ........................................................................................................ 10

Figure 15 Result Visualization .................................................................................................................... 10

Figure 16 3D Analysis ................................................................................................................................ 11

Figure 17 Tensile behavior of concrete ....................................................................................................... 12

Figure 18 Assigning material behavior properties ...................................................................................... 13

Figure 19 Type of analysis .......................................................................................................................... 13

Figure 20 Increment size for convergence .................................................................................................. 14

Figure 21 Koyna earthquake ground motion (Wang, Zhang, Wang, & Yu, 2014) ..................................... 14

Figure 22 Assigning amplitude data ........................................................................................................... 15

Figure 23 Assigning boundary condition .................................................................................................... 16

Figure 24 Convergence of Mises stress ...................................................................................................... 16

Figure 25 Results for mesh size 2m and 5m ............................................................................................... 17

v

List of Tables

Table 1 Comparison of results obtained from 2D plain strain and 3D analysis .......................................... 11

Table 2 Convergence study ......................................................................................................................... 16

vi

Abstract

Dam is critical structure used for purposes such as hydroelectric power generation, irrigation etc. Collapse

of dam under the action of earthquake endanger the life of the people living in the downstream of the dam.

In India, most of the dams have been constructed between the periods of 1971 to 1989 and as a result may

not have incorporated the design aspects related to earthquake and behavior of non-homogenous materials.

In general, dam is analyzed assuming plain strain behavior. To validate this assumption, 3D analysis of

dam is necessary. To demonstrate above mention effects, analysis of concrete gravity dam is presented

using finite element software ABAQUS. As Koyna dam located at Koyna (Maharashtra) region experienced

moderate damage during earthquake occurred in 1967, this dam is selected for this study. This study

provides foundation of seismic analysis using stepwise approach. Hence, preliminary analysis is

demonstrated without considering effects such as hydrodynamic pressure on the dam and soil structure

interaction etc. Convergence study and validation of plain strain formulation make this study a beginner’s

guide for seismic analysis of gravity dam incorporating advanced concrete damage model

1

1 Introduction

Dam is used to raise the level of water and thus forms a reservoir which in turn is used for water supply,

hydroelectric power generation, irrigation etc. In fact, large dam construction has been the main form of

investment in irrigation undertaken by the Indian government. Hence, it should remain stable and functional

even after catastrophic events such as an earthquake. However, in India most of the dams have been

constructed between the period of 1971 to 1989 and as a result may not have incorporated the design aspects

related to earthquake and behavior of non-homogenous materials such as concrete and earth which are now

available therefore it becomes utterly important to analyze the behavior of these dams under displacement

type of loading and predict its reliability (Chopra & Chakrabharti, 1973).

Development in the field of Finite Element Analysis and construction material technology has made it

simpler to achieve the above mentioned objective wherein one can impose a predicted future displacement

loading on the dam and with the help of an almost reliable material behavior asses its performance. In

addition, material model should incorporate non-linear behavior of the concrete due to change in

microstructural behavior and damage to the concrete. Hence, concrete damaged plasticity model developed

in the past are used for this study (Chopra & Chakrabharti, 1973; Houqun, 2014; Yazdani & Schreyer,

1990) (Houqun, 2014).

In general, dam is analyzed assuming plain strain behavior. To validate this assumption, 3D analysis of

dam is necessary.

To demonstrate above mention effect, analysis of concrete gravity dam is presented using finite element

software ABAQUS (Dassault Systèmes Simulia Corp., 2014). Koyna region (Maharashtra) was subjected

to an earthquake of magnitude 6.5 in the year 1967. Koyna dam located in this region experienced moderate

damage during devastating earthquake. Hence, Koyna dam (Maharashtra) is selected for this study to assess

the true behavior under am earthquake incorporating non-linearity in the material (concrete) arising as a

result of damage. The results of analysis are used to locate the critical locations where stresses gets accrued

with the help of which amount of repair work and its reliability can be assessed.

2

2 Problem Formulation and Analysis

2.1 Overview

This study aims to verify of plain stain formulation by analyzing a typical plain strain problem of

concrete gravity dam and comparing results with 3D analysis. Further, this study formulates methodology

to perform seismic analysis (time history analysis) of gravity dam without considering hydrodynamic

effects and soil-structure interaction. In addition, advanced material models of concrete (concrete damage

plasticity model) is also incorporated it simulate as built condition for the assessment of damage. Hence,

this study is classified into two parts as follows

a) Verification of plain strain formulation using linear elastic concrete model

b) Seismic analysis of gravity dam using concrete damage plasticity model without

considering hydrodynamic effects and soil-structure interaction.

Data for Dam located at Koyna, Maharashtra, India is used for this study as shown in Figure 1. As, Koyna

dam experienced moderate damage during 6.5 magnitude earthquake in 1967. ABAQUS finite element

software is used for analysis.

Figure 1 Schematic Diagram of Koyna dam

91

.75 m

66

.5 m

14.8 m

70 m

Length = 807 m

3

Verification of plain strain formulation using linear elastic concrete model

For verification of plain strain formulation, 2D plain strain model is created in ABAQUS

using linear elastic concrete material model and stress results are compared with 3D analysis for

which model is created in similar manner. This section provides details of 2D plain strain model

and only comparison of results are provided for 3D models.

2.1.1 Introduction to ABAQUS

ABAQUS provides platform for solving problems of various domains classified as i)

Standard/explicit Model ii) Computational Fluid Dynamics Models iii) Electromagnetic model. In general,

domain of structural engineering deals with solid mechanics and fluid statics related problem. Hence,

Standard explicit model database is to be used for this study. This database deals with High-speed dynamic

analysis, complex contact problems, highly nonlinear quasi-static problems, materials with degradation and

failure along with simple solid mechanics and structural analysis problem incorporating thermal and heat

transfer effects (ABAQUS, 2014).

Select with Standard/Explicit Model

Figure 2 Abaqus Window

ABAQUS follows linear approach for creation of model starting from creation of parts to analysis. Each

action is divided in separate section as shown in Figure 3. Additional inputs can be provided from model

wizard located at the left side of the screen.

4

Figure 3 Abaqus User Interface

2.1.2 2D plain strain analysis

This section provides details of 2D plain strain analysis concrete gravity dam.

2.1.2.1 Creation of geometry (Part)

Geometry is defined in the “Part” section of the ABAQUS. For 2D analysis “2D planner

Deformable Shell” type is selected.

Part > Create Part > Create Isolated Point > Create Lines Connected

Figure 4 Generation of Part

5

2.1.2.2 Definition of material and section properties (Property)

Material and section properties are defined in the “Property” section of the ABAQUS. Linear elastic

material with following properties is selected for this study.

Density = 2643 kg/m3

Modulus of Elasticity = 31027 MPa

Poisson’s ration = 0.2

Property > Create Material > General > Density

> Mechanical > Elasticity > Elastic

Figure 5 Assigning Material property

Section properties can be defined as shown in the figure and previously defined property is assigned to

the geometry as per following steps.

Property > Create Section > Material

Property > Assign Section > Select Geometry> Select Section

6

Figure 6 Defining and Assigning Material property

2.1.2.3 Generation of assembly

All individual created parts are assembled in the “assembly” section. As only one part is created (dam) for

this study, one individual assembly with ne part is defined.

Assembly > Create Instance > Select Independent (Mesh on instance)

Figure 7 Assembly Generation

2.1.2.4 Definition of analysis steps

Analysis step is defined from “Step” section. Static general step is selected with

Step > Create Step (named: static) > Static, General under General

7

Figure 8 Defining Analysis Step

2.1.2.5 Applying load and boundary condition

Base of the dam is assumed to be rigid. No soil-structural interaction is not considered. Boundary condition

is assigned from “Load” section and steps to assign fixed boundary condition as presented below.

Load > Create Boundary Condition > Select edges from geometry > Select Displacement Rotation

Figure 9 Assigning Boundary Condition

8

Dam is subjected to load due to self weight and hydrostatic load. Hydrostatic load is applied as face of dam

face upto 91.75m height.

Go To Load > Create Load > Select Gravity> Select Geometry>Uniform of -9.81 in Component 2

Figure 10 Assigning Gravity Load

For hydrostatic load assignment following steps should be followed.

Go to Load > Create Load > Select Load Type - Pressure> Select geometry > Select Hydrostatic >

Magnitude = 9.81 * height of water level

Figure 11 Applying Hydrostatic Load

9

2.1.2.6 Defining element type and meshing

For 2D plain strain analysis CPE4RT (An A 4-node bilinear plane strain quadrilateral, reduced integration,

hourglass control) element with size 4m is selected.

Figure 12 FEM Model of Dam

2.1.2.7 Selection of required output data

Step > output > Static, General under General

Figure 13 Selecting output data

10

2.1.2.8 Definition of job

Analysis steps are perfomed by creating job from “Job” section. This section perfomes input data check,

analysis and provides results. Erros and messages can be seen from monitor.

Figure 14 Creation of Job for analysis

2.1.2.9 Visualization of results

Results and contours of output properties can be seen from “Results” from the “Job” section. Figure shows.

Data can be extracted from X-Y data section of the “Visualization”.

Figure 15 Result Visualization

2.1.3 3D analysis

3D.Analysis is done by defining 3D part having length of 800m. Reaming steps are same as presented in

the previous section. For 3D analysis C3D8R (An 8-node linear brick, reduced integration, hourglass

control) element is used with same size of the element (8m). Figure shows part details and stress contours.

11

Figure 16 3D Analysis

2.1.4 Comparison of results obtained from 2D plain strain and 3D analysis

In this study, maximum wan mises stress is secondary quantity of interest. Comparison is done of maximum

wan mises stress obtained from 2D plain stress and 3D analysis and presented in the Table 1. Difference of

both results is around 1.5% which validates 2D plain strain assumption.

Table 1 Comparison of results obtained from 2D plain strain and 3D analysis

Maximum wan mises

stress – 2D analysis (Pa)

Maximum wan mises

stress – 3D analysis (Pa)

Difference in the results

(Pa)

Percentage difference

(%)

2608640 2649880 41240 1.5529

12

2.2 Dam analysis under seismic load using concrete damage plasticity model

As discussed, concrete damage plasticity model captures nonlinearity in concrete behavior arising from

microstructural changes that take place in the material. Hence, it is necessary to employ such models to

simulate actual behavior of the material. This section presets steps for seismic analysis of gravity dam using

damage plasticity modelling. Convergence study is also presented at the end.

As shown, 2D plain strain analysis can be successfully done instated of computationally expensive 3D

analysis of dam. ABAQUS has sequences of sections for each step of finite element modelling. In this

section steps that differs from 2D static analysis listed below are presented.

Definition of material properties (Concrete Damage plasticity)

Definition of analysis steps

Definition of earthquake load and application

History output data (Similar to field output from history output. Hence, not presented )

2.2.1 Definition of material properties (Concrete Damage plasticity)

Concrete damaged plasticity model used by in the evaluation of Koyna dam is used for this study. Details

of the same as follows.

Density = 2643 kg/m3

Modulus of Elasticity = 31027 MPa

Poisson’s ration = 0.2

Dilation angle = 36.31o

Compressive initial yield stress= 13.0 MPa

Compressive ultimate stress = 24.1 MPa

Tensile failure stress = 2.9 MPa

Damping with 𝛽 =0.00323

Figure 17 Tensile behavior of concrete

Property > Create Material > General > Density

> Mechanical > Elasticity > Elastic

13

> Mechanical > Plasticity> Concrete Damaged Plasticity

> Mechanical > Damping

Figure 18 Assigning material behavior properties

2.2.2 Definition of analysis steps

In addition to the static general case, “Dynamic, Implicit” step is selected from “Step” section as shown

below.

Step > Create Step (named: static) >” Static, General” under General

Step > Create Step (named: static) >” Dynamics, Implicit” under Dynamics

Figure 19 Type of analysis

Continue> Basic > Time Period (10s)

(To specify period of analysis. Here duration of earthquake is taken as time for analysis-10s)

Incrimination>Max increments (2000 considering)

> Increment size (Initial: 0.02- time interval at which earthquake is recorded; Max:1e-15 for convergence)

14

Figure 20 Increment size for convergence

2.2.3 Definition of earthquake load and application

Koyna region experienced devastating earthquake in . Hence, hence time history of Koyna earthquake is

used for this analysis. Horizontal and vertical ground motions are presented in the figure

Figure 21 Koyna earthquake ground motion (Wang, Zhang, Wang, & Yu, 2014)

2.2.3.1 Definition of Amplitude data

Earthquake time histories for both components of the ground motion are defined in the “Amplitude” section

of model database (Left side of the window).

Amplitude > Tabular data (Name Time History) > Fixed Interval: 0.02 > Paste earthquake data points

15

Figure 22 Assigning amplitude data

2.2.3.2 Application of Boundary condition

Apply defined ground motions as two separate boundary conditions as follows.

Load > Create Boundary Condition> Select Dynamic Step and Displacement/Rotation Type > Continue

> Select A1 for horizontal motion and A2 for vertical motion with factor 9.81

> Select Amplitude defined earlier

16

Figure 23 Assigning boundary condition

2.2.4 Results and convergence study

Seismic analysis procedure presented earlier repeated several time with different sizes of mesh to achieve

converge of Maximum Misses stress. Time history results are compiled using “XY data” from

“visualization” section for this purpose.

Table 2 Convergence study

Approximate mesh size (m) Maximum Mises stress ( Pa)

10

5 25042900

2 25448200

1 25686600

0.5 25864200

0.35 26010000

0.25 26112000

Figure 24 Convergence of Mises stress

17

Figure 25 Results for mesh size 2m and 5m

18

3 Conclusions

For verification of plain strain formulation, 2D plain strain model is created in ABAQUS using

linear elastic concrete material model and stress results are compared with 3D analysis for which

model is created in same manner. Similar results obtained from both the analysis with negligible

error of 1.55%. Further, procedure for time history analysis is also presented. Convergence study

of mises stress shows that size of element plays critical role in convergence. However, effect of

meshing techniques and type of element are not address. In addition, advanced concrete damage

model is also incorporated to simulate real behavior. Thus, this has proven to a beginner’s guide for

seismic analysis of gravity dam incorporating advanced concrete damage models.

19

4 References

ABAQUS. (2014). Abaqus Analysis User’s Manual (v 6.14). Retrieved April 28, 2019, from

https://www.sharcnet.ca/Software/Abaqus/6.14.2/v6.14/books/usb/default.htm?startat=pt01ch03s02

abx11.html

Chopra, A. K., & Chakrabharti, P. (1973). The Koyna Earthquake and the damage to Koyna dam. Bulletin

of the Seismological Society of America, 63(2), 381–397.

Dassault Systèmes Simulia Corp. (2014). Abaqus v. 6.14. Providence, RI: Dassault Systèmes Simulia Corp.

Houqun, C. (2014). Seismic safety of high concrete dams. Eartquake Engineering and Engineering

Vibration, 13, 1–16.

Wang, G., Zhang, S., Wang, C., & Yu, M. (2014). Seismic performance evaluation of dam-reservoir-

foundation systems to near-fault ground motions. Natural Hazards, 72(2), 651–674.

https://doi.org/10.1007/s11069-013-1028-9

Yazdani, S., & Schreyer, H. L. (1990). Combined plasticity and damage mechanics model for plain

concrete. Journal of Engineering Mechanics, 116(7), 1435–1450.