AJSTD Vol. 25 Issue 2 pp. 469-479 (2008)

PRINCIPAL STRESSES IN NON-LINEAR ANALYSIS OF

BAKUN CONCRETE FACED ROCKFILL DAM

Mohd Hilton Ahmad

Structural and Material Engineering Dept, Faculty of Civil and Environmental

Engineering, Universiti Tun Huseein Onn Malaysia (UTHM),

86400 Parit Raja, Batu Pahat, Johor, Malaysia

Jamaloddin Noorzaie, Fayda Al Qbadi

Civil Engineering Department, Faculty of Engineering, Universiti Putra Malaysia

(UPM), 43400 UPM Serdang, Selangor, Malaysia

Received 14 January 2008

ABSTRACT

With rapid population growth and accelerating economic development, much of the world’s

WATER which requires urgent attention to ensure sustainable use. Nowadays, Concrete Faced

Rockfill Dam (CFRD) is preferred among dam consultant due to its advantages. They are

designed to withstand all applied loads; namely gravity load due to its massive weight and

hydrostatic load due to water thrust from the reservoir. Bakun CFRD, which ranks as the second

highest CFRD in the world when completed, is analyzed to its safety due to both loads

mentioned earlier by using Finite Element Method. 2-D plane strain finite element analysis of

non-linear Duncan-Chang hyperbolic Model which formulated by Duncan and Chang is used to

study the structural response of the dam in respect to the deformation and stresses of Main dam

of Bakun’s CFRD project. Dead-Birth-Ghost element technique was used to simulate sequences

of construction of the dam as well as during reservoir fillings. The comparison of rigid and

flexible foundation on the behaviour of the dam was discussed. The maximum and minimum

principal stresses are the maximum and minimum possible values of the normal stresses. The

maximum principal stress controls brittle fracture. In the finite element modeling the concrete

slab on the upstream was represented through six-noded element, while the interface

characteristic between dam body and concrete slab was modeled using interface element. The

maximum settlement and stresses of the cross section was founded and the distribution of them

were discussed and tabulated in form of contours.

Keyword: CFRD dams, non-linear, finite element analysis, water fillings

1. INTRODUCTION

Malaysia, which comprises Peninsular Malaysia, Sabah and Sarawak, is located between

latitudes 1° and 7° North and longitudes 100° and 119° East which covers a total land area of

over 330,000 km2. With rapid population growth and accelerating economic development, much

Corresponding author e-mail: hilton@kuittho.edu.my

Mohd Hilton Ahmad, et al Principal stresses in non-linear analysis...

470

of the natural resources are being depleted at an unsustainable rate. One of these resources is

WATER which requires urgent attention to ensure sustainable use.

In this paper, Bakun Dam which is the second biggest Concrete Faced Concrete Dam (CFRD) in

the world when completed behind Shuibuya Dam in China is analyzed to its safety by using

finite element method. Dam structure often store huge quantity of water at great potential energy

and if in the case of failure does pose an imminent threat to population and property

downstream. There are a few factors need to be taken care of when designing a dam, i.e. safety,

economy, efficiency and appearance. Safety and economy are factors that contradict to each

other; however, we may design an economical dam without sacrificing the safety of the dam.

Dams are designed to withstand all applied loads, e.g. gravity load, hydrostatic, hydrodynamic

pressures etc. The biggest loads on dam are the gravity load due to its massive self weight and

also earthquake loads. The accuracy of the estimation of dam safety under static and earthquake

(dynamic) and the design work require a good understanding of structural response of dam

under both cases. As far as the design aspect concerns, static load and dynamic load are

contradicts as in static we need to design the stiffest structure, however, in dynamic it is

required to design the structure most flexible. Therefore, the engineers should be aware of both

criteria and fulfills to its optimum dam design.

Since dams are considered to be as mega projects, and infrastructures for any nation, hence,

many international organization (International and National Commission on Large Dams

(ICOLDS)), are involved in the documentation data of the concrete faced rockfill dam which

was designed and constructed. After the evaluation of their implementations and operations, the

legislation and guidelines on dam safety are issued, accordingly, to be followed by the owner of

dams, consultants and construction dam industries. CFRD is being recognized as one of the best

choices among the dam consultants and engineers for its advantages.

2. PREVIOUS FINDINGS

There are methods available for prediction of deformations during construction, but they are

limited in number. Development of these methods has probably been curtailed by the

availability of finite element methods in the last 30 to 40 years, their relative ease of use to

model embankment construction and improvements in constitutive relationships to model the

material compressibility and deformation behaviour. In addition, the complexity of stress and

deformation behaviour during construction, particularly for zoned embankments, makes

assessment by simple empirical methods difficult.

Poulos et al (1972) developed charts for estimation of stresses and vertical and horizontal

deformations during construction based on elastic solution for a homogeneous embankment on a

rigid foundation. The methods provide a quick and simple means of estimating deformations.

ICOLD (1993) derived a general equation for the vertical strain of rockfill in terms of vertical

stress, rockfill modulus and creep strain parameters based on the assumption of a linear

relationship between stress and strain of coarse rockfill and non-linear relationship between

strain and time. Derivation are given (refer ICOLD 1993) for the settlement at a specific

elevation and period of time start of construction, settlement at end of construction and

settlement post construction.

Most of the earliest CFRD researchers introduced one-shot loadings in their analysis. From the

analysis of one-shot loading, we found that maximum vertical displacement occurs at the crest

of the dam. This is much contrary as vertical displacement should occur at the foundation level

due to phenomena called “overburden”. Noorzaei et al. (1999), developed finite element

program that it can simulate the sequence of construction of the earthen and rockfill dam, which

is done by the real and ghost technique that complete body of the dam has been discretized and

AJSTD Vol. 25 Issue 2

471

the stages of construction has been represented by real and ghost elements. The result obtained

are most simulate to the actual conditions.

Xu (2000), used three dimensional non-linear finite element method developed computer

software called SDAP3D in the analysis of stress and deformation properties of Wuluwati

CFRD, in China with 138 m. Height and 365 m lengths, with upstream slopes 1:1.6 and

downstream slopes 1:1.5 the program uses Duncan et al (1980), nonlinear elastic model. This

software dealt with the interaction between the concrete slab and the rockfill materials.

Maximum principal stresses occurred in the bottom of the dam body at the end of sequence of

construction and the value of major principal stress is 1.8 MPa, while the minor one is 0.6 MPa

After the impounding the maximum principal stress increased to 2.0 MPa and the minor

principal stress to 0.8 MPa.

Xingzheng et al. (2002), use 3-D finite element analysis to evaluate stresses and deformation of

Yutiao CFRD during construction and reservoir filling stage. During construction, Yutiao

CFRD shows its maximum major principal stresses of 1.78 MPa which occurs at the bottom of

the dam while for the case after reservoir fillings, it gave its maximum value of 1.87 MPa. On

the other hand, maximum minor principal stresses shows its value of 0.74 MPa occurs at the

bottom of the dam during the construction and 0.72 MPa after the reservoir fillings.

Chen et al. (2000) was used a nonlinear elastic developed hyperbolic (Duncan, 1984), E-B

model to analyze Shuibuya (233 m) concrete face rockfill. The maximum horizontal

deformation of the dam is 0.20 m towards the upstream at the end of construction while it is

0.67 m at the end of reservoir filling and its movement towards the downstream. The maximum

vertical deformation occurred at the 2/3 dam height with value 1.67m. at end of construction and

a.77 m at the end of reservoir filling. The maximum principle major and minor stresses is 3.18

MPa and 1.02 MPa, respectively, at the end of construction, and, 3.52 MPa and 1.27 MPa at the

end of reservoir filling. Gao et al. (2001), in this analysis a nonlinear constitutive law of

uncoupled K-G model was used in the calculation of high CFRD. In this case, the stress path is

very complicated since the filling process of the dam is divided into several stages during

construction. The basic formula of the model and the incremental regression method for

obtaining the parameters are introduced. He reported that at the end of reservoir filling, major

and minor principal stresses of Shuibuya Dam is 4.07 MPa and 1.33 MPa respectively.

Realistic simulation of the stress-strain characteristics of the soil (which is non-linear) is the

principal factor governing the accuracy of finite element analysis of embankments. As studied

by Boughton, he showed that the linear analysis of a rockfill dam, using a conventional finite

element program and constant values of elastic properties for the rockfill, gave areas of tensile

stress in the rockfill, independent of the value of elastic modulus employed. As the rockfill

cannot sustain tensions, this is clearly not applicable. Subsequent analysis, simulating nonlinear

behaviour of rockfill, resulted in elimination of the impossible tensile stress (Duncan, 1972).

The hyperbolic model is one of the simpler models that can simulate the non-linear and stress-

level characteristics of rockfill. The most widely used is Duncan-Chang hyperbolic model

3. BAKUN HYDROELECTRIC DAM

The Bakun Hydroelectric Power Dam will be 205 metres high with an approximate crest length

of 748.85 metres and fill volume of approximately 17,000,000m3. Concrete Face Rockfill Dam

features is essentially a slab of concrete placed against rockfill on the upstream slope face as

“watertightness” that extends from the dam crest to the plinth. A 7.5m high “L” type concrete

parapet wall at the upstream of the crest to serve as access road with a dam slope of 1V:1.4H at

the upstream and 1V:1.3H at the downstream. The dam can be divided into different zones as

shown in Figure 1 below (Sarawak Hidro, 2003)

Mohd Hilton Ahmad, et al Principal stresses in non-linear analysis...

472

Fig. 1: Different zones in Bakun Dam.

Table 1: Different zones for Main Bakun Dam.

Zone Designations

Concrete

slab

Have a variable thickness reduced with the height, based on formula

0.3+0.003H.

Zone 1A

& 1B

Both zones as supporting zones for the upstream, over the lower deck of

perimeter joint.

Zone 2A A well compacted of processed fine filter zone (processed fresh Greywacke).

This zone also has a special cushion material with well graded.

Zone 2B Has cushion material with well graded and selected from fresh greywacke, with a

maximum size of 100 mm, this zone be immediately behind the face slab.

Zone 3A A transition material placed adjacent to zone 2B with maximum size of 300 mm

and minimum 5 mm.

Zone 3B The upstream zone forming approximately 50 – 60% of the embankment

including the integrated cofferdam. Consist of slightly weathered rock to fresh

greywacke.

Zone 3C A zone within the downstream placed and compacted in layers about 1m thick. It

consists of 70% fresh greywacke with 30% mudstone. Maximum size 1200 mm

to 5mm.

Zone 3D This zone is placed and compacted in layers up to 2 meters thick and dozed to

downstream face of the dam to serve as slope protection, also used within the

valley bottom to serve a high-capacity under drain. It consist of coarse slightly

weathered to fresh greywacke rockfill materials with maximum size 1500 mm.

4. MODELLING OF BAKUN DAM

Finite Element Method (FEM) is based on a theory whereby an original body is viewed as an

assembly of discrete parts/building blocks. This is done using the modeling techniques and

computations aspects, complex region defining a continuum is discretized into simple geometric

shapes called finite element. The elements that compose the object are of finite size and hence

the name of the method (FEM) The smaller the size, the smaller the errors and as a result, the

solution obtained comes closer to the true solution.

A dam section problems problems involving long bodies, whose geometry and loading do not

significantly in the longitudinal direction, are refereed to as the cases of plane strain. Finite

3D

3C

3B

3B

2B

3A

205 m

1A

1B

2A

Concrete

slab

Grout blanket

AJSTD Vol. 25 Issue 2

473

element analysis has been used to study the behaviour of rockfill and to predict strains in

various portions of the rockfill. The results so far obtained are promising and the method would

be used more widely in future.

Bakun CFRD dam is modeled as 2-D structure and then divided into few layers and each layer

is discreted into few elements comprising of nodes depending on types of element. The

geometry of the dam and the material properties in each section of the dam is designed based on

actual data. Each element is discretized accordingly to respective layer and fit the type of

material comprising in respective section of the dam model. For soil-structure interaction

problems, in our case layer between main dam and concrete face were based that there is no slip

between the structures and the soil or that there is no possibility for shear stresses to develop

(interface is perfectly smooth). There are two cases of dam been considered; namely rigid

foundation and flexible foundation as shown in Figure 2.

For the first case, the dam is designed on a fixed base or rigid foundation. The dam is divided

into eight layers, divided into 28 layers, and then each layer discrete into 936 elements gave a

total of 2870 nodes. There are 3 types of isopaametric elements used in this case; namely 8

noded isoparametric element, 6 noded isoparametric element, and interface isoparametric

element. In this case, the boundary condition is fixed at the base of the dam. The latter case, the

model of main dam is same as prior case and adding the foundation at the bottom of the main

dam. The foundation is divided into four layers, and each layer has infinite elements on both

sides. Addition to the 4 layers of foundation gave increment of 170 elements and 508 nodes

gave sum of 1103 elements and 3378 nodes. The dam which divides into 32 layers is assumed to

be fixed at 40m below the foundation level. Addition of infinite element gave total of 4 types of

elements in this case.

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357

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1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144

1145

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1176 381 1177382 1178

3831179 384 1180 385 1181

386 1182 387 1183 388 1184389 1185

390

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392

1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246

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492

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493

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1532 1533 1534 1535 15361537

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525

526 527 528 529

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1949

1950

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1952

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629 631632 633 634

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636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651

1977 1978 1979 1980 1981 1982

652

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653 654

1984

655

1985 1986

656 657

1987

658 659 660 661

1988 1989

662664 665

666 667 668 669 670 671 672 673 674 675 676677

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2027

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695

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185 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 213 214 215 216 217 218 219 220 221

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230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 276 277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

298299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 324 325

326

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330 331 332

333

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337

338

339

340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 388

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391

392

393

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396

397

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405 406

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410 411 412 413 414 415 416417 418 419 420 421 422 423 424 425 426 427 428 429 430 434

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500

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518520

521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 546 547

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149

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67 68 6970 71 72 73 74

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103

104

105

106 107 108 109110 111

151

152 153154 155 156 157 158

159 160 161 162163 164

165 166

177178

179

1046

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1053

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1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1087 1088 1089

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180 181

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185

186 188

189 190 191 192 193 194 195 196 197 198 199 200 201 201 203

215

216 217218

219 220

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140 141

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222

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225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240253 254 255 256

134133132131

257

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260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276

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296 297 298 299 300 301 302

289 290 291 292

303 304 305 306 307 308 309 310 311324

325 326 327

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362

364

365 366367 358 369 370 371 372 373 374 375 376 377 378 379 380 393 394

395

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401 402 403 404 405 406 407 408 409 410 411 412 413 414 427 428429

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Fig. 2: Finite Element Meshes.

Left: Flexible Foundation Right: Rigid Foundation

The stress-strain relationship for most soil materials in nonlinear and for realistic results the

analysis should take into account. In linear material properties case, the finite element analysis

has no problem because properties are constant at each stress level. The non-linearity arises

from the stress dependence of the stress-strain material parameters. So it was seen from

literature review on CFRD dams, that the following stress-strain law has been adopted, namely,

Linear elastic, Nonlinear elastic and Elasto-Plastic. Stress can be classified as shown in Table 3.

The finite element program which was written for linear analysis is modified to incorporate

material non-linearity, sequential construction of the dam for non-linear analysis and

incremental reservoir filling. In the case of geotechnical problems like high Bakun dam, the

non-linearity arises from the stress dependence of the stress-strain material parameters. The

isotropic hyperbolic model which is implemented in this study can directly capture the non-

linear behaviour and pressure-dependency effects and generate the Et at each level of loading,

Mohd Hilton Ahmad, et al Principal stresses in non-linear analysis...

474

which includes constitutive parameters according to E-B parameters such as K, n, Rf, υ, ∆υ, Kb,

Kur, m are listed in Table 4 (Sarawak Hidro Sdn. Bhd.).

Table 3: Type of stresses.

Type of stress Description

Compressive stress By convention, engineers considers as negative.

Tensile stress By convention, engineers considers as positive.

Normal stress, σn Stress directed perpendicular to a given plane.

Shear stress, τn Stress directed parallel to a given plane.

Principal stresses 3 orthogonal stresses are directed perpendicular to principal

planes upon no shear stress exists.

σ1 ≤ σ2 ≤ σ3 where σ1 = maximum compressive stress axis

σ2 = intermediate stress axis

σ3 = minimum compressive stress axis.

Table 4: Parameters for Duncan’s E-B Model.

Material γ K n φ ∆φ° m Rf Kb Kur

Cushion

material

22.8 400 0.35 50.6 7 0.22 0.78 520 800

Transition

material 3A

22.5 780 0.30 52.5 8 0.25 0.77 525 1500

Rockfill 3B 21.3 850 0.30 52.5 10 0.20 0.77 550 1700

Rockfill 3C 20.6 700 0.35 48.0 7 0.10 0.73 300 1500

Rockfill 3D 20.5 760 0.35 52.5 10 0.18 0.76 460 1500

Foundation 19.0 300 0.45 38.0 2 0 0.8 150 600

The Birth, Dead and Ghost element techniques which used by Norzaie has been used in Finite

element program to simulate the sequence of construction of the dam and each layer is loaded

with stage of construction. At reservoir filling stage analysis, At the end of Bakun dam

construction, it is planned to impound water after the completion of dam body, and in the

analysis the reservoir was considered to be filled in a single stage. Water loading applied normal

to the upstream face. Figure 3 illustrate the sequence of loading for both cases with foundation

and without foundation respectively (for first 3 stages).

5. ANALYSIS AND RESULTS

Non-linear analysis is very much computationally intensive than linear analysis. In linear

analysis, superposition is used to calculate the results for combination load cases but in non-

linear analysis, superposition is not valid. The results for a combination load case are obtained

in non-linear analysis by adding together all component load cases and then performing the

analysis for combined loads.

AJSTD Vol. 25 Issue 2

475

Due to the Bakun Dam is consists of 8 different section with different material properties for

each section, the stresses in the upstream half of the dam could not be expected to mirror those

in the downstream half and this is reflected in the contours of calculated stresses. This is

contradicting of symmetrical dam that has the symmetrical zones at the upstream and

downstream side, as only weight of the dam been considered; we can expect the downstream at

the mirror to the downstream side.

Based on theory, the horizontal stress is greater at the lowest location of the dam, or in another

word, near the base of the dam. Horizontal stress is bigger at low elevation because of the fact

that in the case of a dam cross-section of less deeper height, the lateral movement of rockfill at

any point is comparatively restrained on account of the proximity of rigid foundations, whereas

in the case of the deeper dam cross-section, the much greater deeper of flexible rockfill material

below the corresponding point allow more lateral movement of rockfill at that point, resulting in

reduction of horizontal stress in the rockfill at that point. The same mechanism also applies to

flexible foundation case. However, this applies to symmetrical dam. Due to unsymmetrical

section of dam that have different material properties, we can observed that the maximum

horizontal stress not occurs at the middle but a few meters from the upstream.

Ghost

Birth

Stage 1 loaded (d)

Ghost Birth

Dead

Stage 3 loaded (c)

Ghost

Birth

Stage 1 loaded (a)

Birth Ghost

Dead

(Stage 2 loaded (b) Stage 2 loaded (e)

Ghost

Birth

Dead

Stage 3 loaded (f)

Ghost Birth

Dead

Fig. 3: Sequence of Construction of Bakun Dam.

Mohd Hilton Ahmad, et al Principal stresses in non-linear analysis...

476

Major principal stress shows the almost same patterns and shape with the vertical stresses.

However, a major principal contour shows a bit increase in the values compared to vertical

stresses (Figure 4). At the meanwhile, the minor principal stress has the same behaviour with the

horizontal stress as shown in Figure 5. The major principal stress also showed almost same

value compared to horizontal stresses. From the equation above, this may due to the minimal or

no effect of shear stresses.

Fig. 4: Contours of Normal Stress, σy at the end of construction stage with and without

Foundation for non-linear analysis.

Fig. 5: Contours of Normal Stress, σx at the end of construction stage for with and without

Foundation for non-linear analysis.

Fig. 6: Contours of Minimum Principal Stress, Pmin at the end of construction stage with and

without Foundation for non-linear analysis.

Fig. 7: Contours of Maximum Principal Stress, Pmax at the end of construction stage with and

without Foundation for non-linear analysis.

AJSTD Vol. 25 Issue 2

477

In the analysis for reservoir full condition, the major and minor stresses include the stresses at

the end of construction, which were fed as initial condition in the computer. In case of CFRD,

the buoyancy effect is absent and the water load is applied on the upstream sloping face

resulting in considerable increase in both the horizontal and vertical stresses in the upstream

portion of the rockfill embankment section.

By comparison of the contours shape, the minor principal stress at the end of reservoir filling

become flatter as compared to the contours at the end of construction which looks about parallel

to the slope of the upstream and that due to the fact that the orientation of water pressure acting

normal to concrete slab is more or less close to the minor principal stresses, σ3 in the upstream

portion of the Main Rockfill embankment at the time of completion, while the orientation of the

major principal stresses, σ1 in the rockfill are approximately perpendicular to the orientation of

water pressure acting on the concrete slab. During reservoir impoundment, the increase in major

principal stress is larger than the increase in minor principal stresses. This due to the decrease of

deviator stresses (σ1 - σ3) means decrease in stress level and increasing in the tangent modulus,

as the tangent modulus changed to the unloading tangent modulus. There is no tension stresses

along dam occurred so the dam be more stable and no probability of cracking and leakage.

By comparison of major principal stresses at end of construction and end of reservoir filling

which given in Figure 8 and Figure 9 respectively, the maximum value at the foundation level

for end of construction of flexible foundation and rigid foundation is 3200 kN/m2 and 3500

kN/m2 and for end of reservoir filling is 3500 kN/m

2 respectively for both cases. The dam

however, still considered safe as it still under allowable compressive stresses (30000 kN/m2).

Fig. 8: Contours of Minor Principal Stress, Pmin at reservoir operations for with and without

Foundation for non-linear analysis.

Fig. 9: Contours of Major Principal Stress, Pmax at reservoir operations for with and without

Foundation for non-linear analysis.

6. CONCLUDING REMARKS

By using latest version of hyperbolic non-linear elastic model (Duncan-Chang, 1984), two cases

of loading been considered. First case, at the end of construction under self-weights of the dam

(gravity) and at the end of reservoir impoundment (the values, i.e. displacement, strains and

Mohd Hilton Ahmad, et al Principal stresses in non-linear analysis...

478

stresses obtained at end of constructions are stored in the program). Like linear analysis,

displacement and stresses are discussed at specified elevation in specified stages. Contour at the

end of construction and end of reservoir fillings also discussed.

(i) The maximum of the normal horizontal stress x occurred at the foundation level closer to

the heel of the dam for flexible foundation and about 1/3 of the height from heel at the

upstream face for rigid foundation. For y due to “overburden” of the self-weight of the

dam, the maximum stresses takes place at the middle of the base respectively for both

cases. The major and minor principal stresses occurs at the foundation layer (at elevation

0m).

(ii) As normal stresses, σx and σy increases compared to the end of construction, the major and

minor principal stresses increased as well. Comparison to without foundation case, with

foundation has a more significance increase if looks at their contours. Like normal stresses

(σx and σy), minor principal stresses experienced increase along the upstream at the

upstream slope face and major increased at middle of the dam like vertical stresses. For

rigid foundation, minor principal stress has smaller value of maximum horizontal stresses

but no difference between major principal stress and vertical stress.

REFERENCES

1. Bakun Hydraulic Project, Sarawak Hidro (Malaysia) Sdn. Bhd., 2003

2. Charles, J.A. (1976), The Use of one-diensional compression tests and elastic theory in

predicting deformations of rockfill embankments. Canadian Geotechnical Journal, Vol.

13(3), pp. 189-200.

3. Chen, C., Wang, D., and Tan, J. (2000), Emulating Analysis for Shuibuya Concrete Faced

Rockfill Dam. 20th Congress of ICOLD, International Symposium on Concrete Faced,

China.

4. Clough, R.W. and Woodward, R.J. (1967), Analysis of embankment stresses and

deformations. A.S.C.E., Journal of the Soil Mechanics and Foundations Division, Vol. 93

(SM4), pp. 529-549.

5. Varma, C.V.J. (1992), Rockfill Dams – Finite Element Analysis to Determine Stresses and

Deformations in Membrane Type Rockfill Dam. Central Board of Irrigation and Power,

New Delhi.

6. Duncan, J.M. and Chang, C.Y. (1970), Non-linear Analysis of Stress and Strain in Soils.

Journal of the Soil Mechanics and Foundations Division, ASCE, 96 (SM5), pp. 1629-1653.

7. Duncan, J.M., Byrne, P., Wong, K.S., and Marby, P. (1980), Strength Stress-Strain and Bulk

Modulus Parameters for Finite Element Analyses of Stresses and Movements in Soil

Masses, Report No. UCB/GT/80-01. Department of Civil Engineering, University of

California, Berkeley.

8. Duncan, J.M., Seed, W., and Ozawa, Y. (1984), FEADA84: A Computer Program for Finite

Element Analysis of Dams. Department of Civil Engineering, Virginia Polytechnic Institute

and State University, Blackburg.

9. Guidici, S., Herweynen, R. and Quinlan, P. (2000), Hydroelectric Commission experience

in concrete faced rockfill dams-past, present and future. Proceedings of the International

Symposium on Concrete Faced Rockfill Das, Beijing, ICOLD, pp. 29-46.

AJSTD Vol. 25 Issue 2

479

10. Hinton, E. and Owen, D.R.J. (1977), Finite Element Programming. Academies Press,

London.

11. ICOLD (1993), Rock materials for rockfill dams. Bulletin No. 92, International Commission

on Large Dams.

12. Kenneth L.L. and Izzat M.I. (1975), Static stress by Linear and Nonlinear Methods. Journal

of the Geotechnical Division, Vol. 101, pp. 871-887.

13. Marshal, R.J. and Albero, J.A. (1976), Performance of dams built in Mexico. Proceedings of

the 12th International Congress on Large Dams, Mexico City, ICOLD, pp. 791-782.

14. Neville O.B. (1970), Elastic Analysis for Behaviour of Rockfill. Journal of the Soil

Mechanics and Foundation Division, A.S.C.E., Vol. 96, pp. 1715-1733.

15. Noorzaie, J., Golinavaz H., and Pakbas, M.C. (1999), Nonlinear Analysis of Earth and

Rockfill Dams Considering the Sequence of Construction. Journal Computational

Mechanics for the Next Millennium Solid Mechanics and Fluid Mechanics, Vol. 1.

16. Pinto, N.L. de S., Materon, B., and Lago Marquez, P. (1982), Design and performance of

Foz do Areia concrete membrane as related to basalt properties.” 14th ICOLD Congress, 4,

Q55-R51, pp. 873-905.

17. Poulos, H.G., Booker, J.R. and Ring, G.J. 1972. Simplified calculations of embankment

deformations. Soils and Foundations. Soils and Foundations, Tokyo, Vol 12(4), page 1-17.

18. Saboya, F.J., and Bryne, P.M. (193), Parameters for stress and deformation analysis of

rockfill dams. Canadian Geotechnical Journal, Vol. 30, pp. 690-701.

19. Sowers, G.F., Williams, R.C. and Wallace, T.S. (1965), Compressibility of broken rock and

the settlement of rockfills. Proceedings of the 6th International Conference on Soil

Mechanics and Foundation Engineering, Montreal, University of Toronto Press. Vol. 2, pp.

561-565.

20. Singh, B. and Varshney, R.S. (1995), Engineering for Embankment Dams. Balkema, USA.

21. Xu Z. (2000), Three Dimensional Stress and Deformation Analysis of Wuluwati CFRD.

Proceedings of International Symposium on Concrete Faced Rockfill Dams. Beijing, China.

22. Zienkiewicz, O.C. (1979), Finite Element Method. 3rd Edition. Tata McGraw-Hill

Publishing Limited, New Delhi.

23. Zhang B., Wang, J.G. Ruifeng S. (2004), Time dependent deformation in high concrete-face

slab and cushion layer. Computers and Geotechnics Journal, Vol. 31, pp. 559-573.