This paper demonstrates the applicability of

the finite element method in solution of

typical boundary value in geotechshy

engineering

Finite Element Studies of Ambuklao and Caliraya Damsmiddot

by

Ronaldo 1 Borja Ph D

ABSTRACT

In the last two decades the finite element method has experienced tremendous growth in both theoretical

and applications This paper explores the usefulness of this numerical method in the area

of geotechnical incorporating into the complex factors that cannot readily be handled by closedmiddotform procedures such as dynamic behavior material nonhomogeneities plasticity and creep

Subjects of the studies were two hydroelectric dams in the Philippines namely Am-

studies were performed of Ambuklao Dam to its

induced by the earthquake of April 1985 A creep analysis of Caliraya

buklao and

Dam was also carried out the conventional incremental plasticity and a recently constitutive model to predict the dams time-dependent deformation behavior in the next 40 years

INTRODUCTION

are often faced with a of complex engineering problems for which no stanmiddot dard sol are available Particularly in the area of ical the of difmiddot ficulty of problems normally encountered can be enormous considering that a number of complex factors such as material nonlinearities and non homogeneities may be nvolved

In the past solutions of so-called nonstandard engineering problems were done either on a purely empirical basis or via simplifying assumptions aimed at reducing the problem to one where a standard solution is available Oftentimes the results obtained from any of these approaches were either highly inaccurate or unrealistic

With the advent of high-speed computers and exceptional growth in the development of numemiddot rical are now able to incorporate as many details as are necessary into the solution Among the existing numerical the finite element method seems to have gained the most favorable acceptance because of its reliable accuracy as well as its versatility when

to different classes of problems

This paper demonstrates the computational lity of the finite element method in solving I boundary value problems in the area of geotechnical neering of the studies are

bull Paper presented at the 1985 Philippine Institute of Civil Verde Country Club Pasig Metro Manila November 28middot29 and at

National Convention held at the Valle

sponsored by the Philippine Society of Geology in cooperation with the Society of the Philippines and the Philippine Institute of Mining Metal and Geol Engineers MetromiddotManila Chapter held at the Silahis International Hotel Manila December 17 1985 paper printed with permission of the Nationlll Power Corporation of the Phil ippines

Assistant Professor of Civil University of the Philippines Diliman Quezon City

56

The dam serves a drainage area of about

Am-

basic material zones represented by the central clay core and outer the dam and reveals two

shells with layers of filter

at

to seismic excitation and

the Ambuklao and Caliraya Hydroelectric Dams on a

conditions The behavior of the

long-term sustained loadings are investigated

HOW AMBUKLAO DAM SWAYS AS THE GROUND

Am Dam is a

bu Hydroelectric Project owned

of Luzon The dam has a crest height

Iy metamorphic rocks and diorite

materials in between On April 24 1985 a strong earthquake shookmiddotthe

taken to ensure its safe a numerical

response to ground shaking was

a remedial under-

the dams dynamic

The study was confined to the determination of the dams fundamental periods of vibration

and mode shapes as no time history of ground was to a complete analysis

possible

o 50

SCALE IN METERS

HIGH WATER EL 7520 m

SLOPE CHANGE SLOPE CHANGE

E

GROUT CURTAIN

L Through the Am buklao Dam

For dynamic brium a body in motion the governing finite element-based matrix equashytion at time station can be written as follows

+ (1 )

57

where M C and K are the consistent global mass damping and stiffness matrices respectively dn is the global vector of nodal accelerations d is the global vector of nodal velocities dn is the global

n vector of displacements and f1 is the vector of consistent nodal forces for the applied surface tractions and body forces (including the inertia term - Mil due to seismic excitation) grouped

together If the forcing functions on the right hand side of (1) afe given explicitly the displacement

velocity and acceleration profiles can be determined by temporal discretization (eg Newmark integration schemel or by modal superposition For a complete treatment of the subject the reader

is referred to Owen and Hinton (1980)

Let the displacement velocity and acceleration vectors be of the form

d ae iwt (2a)

d iwawt (2b)

d == _w 2aiwt (2c)

where w is the angular frequency associated with mode shape a i = 1=1 and t is time The eigenshy

value problem for an undamped finite element system requires the determination of the non-trivial

solutions to the homogeneous equations

J (3)( - w-M + K)a == 0

by setting the determinant of the coefficient matrix

(4)

In general equation (4) will result in ncq roots or vibration modes corresponding to the total numshy

ber of free nodal degrees of freedom for a given finite element mesh

Assuming that 11 admits the factorization

(5)

in which L is either upper triangular or diagonal equation (3) can be reducedto the standard form

( S - Iw-)b == 0 (6)

where S L-1 KmiddotL-T is a real symmetri~ matrix b == La and I is the identity matrix The same

roots of (4) can be obtained by setting

IS - Iwl[ = 0 (7)

solving for the eigenvalues w and evaluating the eigenvectors bi of the matrix S The backshysubstitution process 3 i == L-1 b leads to the original eigenvectors or mode shapes of equation (3)i

If M is a diagonal the factorization step indicated in (5) is rendered trivial since L == LTas L

also becomes diagonal Consequently

L= 1M (8)

which impiies that Li =fiJj where Li and Mi are the ith diagonal elements of Land M respectively

58

The dam serves a drainage area of about

Am-

basic material zones represented by the central clay core and outer the dam and reveals two

shells with layers of filter

at

to seismic excitation and

the Ambuklao and Caliraya Hydroelectric Dams on a

conditions The behavior of the

long-term sustained loadings are investigated

HOW AMBUKLAO DAM SWAYS AS THE GROUND

Am Dam is a

bu Hydroelectric Project owned

of Luzon The dam has a crest height

Iy metamorphic rocks and diorite

materials in between On April 24 1985 a strong earthquake shookmiddotthe

taken to ensure its safe a numerical

response to ground shaking was

a remedial under-

the dams dynamic

The study was confined to the determination of the dams fundamental periods of vibration

and mode shapes as no time history of ground was to a complete analysis

possible

o 50

SCALE IN METERS

HIGH WATER EL 7520 m

SLOPE CHANGE SLOPE CHANGE

E

GROUT CURTAIN

L Through the Am buklao Dam

For dynamic brium a body in motion the governing finite element-based matrix equashytion at time station can be written as follows

+ (1 )

57

where M C and K are the consistent global mass damping and stiffness matrices respectively dn is the global vector of nodal accelerations d is the global vector of nodal velocities dn is the global

n vector of displacements and f1 is the vector of consistent nodal forces for the applied surface tractions and body forces (including the inertia term - Mil due to seismic excitation) grouped

together If the forcing functions on the right hand side of (1) afe given explicitly the displacement

velocity and acceleration profiles can be determined by temporal discretization (eg Newmark integration schemel or by modal superposition For a complete treatment of the subject the reader

is referred to Owen and Hinton (1980)

Let the displacement velocity and acceleration vectors be of the form

d ae iwt (2a)

d iwawt (2b)

d == _w 2aiwt (2c)

where w is the angular frequency associated with mode shape a i = 1=1 and t is time The eigenshy

value problem for an undamped finite element system requires the determination of the non-trivial

solutions to the homogeneous equations

J (3)( - w-M + K)a == 0

by setting the determinant of the coefficient matrix

(4)

In general equation (4) will result in ncq roots or vibration modes corresponding to the total numshy

ber of free nodal degrees of freedom for a given finite element mesh

Assuming that 11 admits the factorization

(5)

in which L is either upper triangular or diagonal equation (3) can be reducedto the standard form

( S - Iw-)b == 0 (6)

where S L-1 KmiddotL-T is a real symmetri~ matrix b == La and I is the identity matrix The same

roots of (4) can be obtained by setting

IS - Iwl[ = 0 (7)

solving for the eigenvalues w and evaluating the eigenvectors bi of the matrix S The backshysubstitution process 3 i == L-1 b leads to the original eigenvectors or mode shapes of equation (3)i

If M is a diagonal the factorization step indicated in (5) is rendered trivial since L == LTas L

also becomes diagonal Consequently

L= 1M (8)

which impiies that Li =fiJj where Li and Mi are the ith diagonal elements of Land M respectively

58

where M C and K are the consistent global mass damping and stiffness matrices respectively dn is the global vector of nodal accelerations d is the global vector of nodal velocities dn is the global

n vector of displacements and f1 is the vector of consistent nodal forces for the applied surface tractions and body forces (including the inertia term - Mil due to seismic excitation) grouped

together If the forcing functions on the right hand side of (1) afe given explicitly the displacement

velocity and acceleration profiles can be determined by temporal discretization (eg Newmark integration schemel or by modal superposition For a complete treatment of the subject the reader

is referred to Owen and Hinton (1980)

Let the displacement velocity and acceleration vectors be of the form

d ae iwt (2a)

d iwawt (2b)

d == _w 2aiwt (2c)

where w is the angular frequency associated with mode shape a i = 1=1 and t is time The eigenshy

value problem for an undamped finite element system requires the determination of the non-trivial

solutions to the homogeneous equations

J (3)( - w-M + K)a == 0

by setting the determinant of the coefficient matrix

(4)

In general equation (4) will result in ncq roots or vibration modes corresponding to the total numshy

ber of free nodal degrees of freedom for a given finite element mesh

Assuming that 11 admits the factorization

(5)

in which L is either upper triangular or diagonal equation (3) can be reducedto the standard form

( S - Iw-)b == 0 (6)

where S L-1 KmiddotL-T is a real symmetri~ matrix b == La and I is the identity matrix The same

roots of (4) can be obtained by setting

IS - Iwl[ = 0 (7)

solving for the eigenvalues w and evaluating the eigenvectors bi of the matrix S The backshysubstitution process 3 i == L-1 b leads to the original eigenvectors or mode shapes of equation (3)i

If M is a diagonal the factorization step indicated in (5) is rendered trivial since L == LTas L

also becomes diagonal Consequently

L= 1M (8)

which impiies that Li =fiJj where Li and Mi are the ith diagonal elements of Land M respectively

58

Matrix diagonaiization of M can be achieved by lumping masses at the nodes Consider the following finite element expression for M written on the element level (consult Owen and Hinton 1980)

(9 )

where m~b is a ty submatrix of me associated with element nodes a and b Na and Nb are the nodal function m is mass density and n e is the element domain It can be seen that if the numerical integration of (9) is performed at the element nodes me diagonalizes since

== I when a = b

0 otherwise (10)

where I nd 0 are identity and null matrices

Numerical Solution

The computer program used in the is a multipurpose finite element program called SPIN 20 A module of this program performs the matrix operations outlined in the preshyced ing secti on for and eigenvector determ inati on The consistent mass and stiffness matrices are com and assembled internally for linear elastic or materials obeying the associative flow rule Element can be any of the standard four- or nineshynoded quadrilateral elements

The finite element mesh used for the dam problem is shown in Figure 2 Ignoring some minor material and geometric irregularities indicated in Figure 1 the cross section of the dam was assumed to be symmetric about its centerline

The mesh consists of 48 nodes and 35 4-noded quadrilateral nodes were assumed campi fixed at the leaving a total number of 2x (48 6) 84 deshygrees of freedom or vibration modes

Numerical is facilitated by a standard 2x2 Gauss quadrature rule on each element The material constants for each element were evaluated at the element centroid for the elements were lumped at the nodes via selective numerical discussed in the preceding section

solver of the iterative-type was used for evaluating the vibration and mode mass matrix factorizationback substitution steps of the preceding section were em

Material

The thirty five elements of the mesh shown in 2 were divided into two material groups the inner core and the outer rock fill materials Material properties each

group were estimated from the following 1 Core Estimates of the soils index bility and were

based on la test resu I ts on test pits dug at the clay core

section of the dam

Table 1 summarizes the average values of compressibil parameters used in the These values obtained from five-one dimensional consolidation tests exhibit a consistently stiff behavior characteristic of a well-com middle clay core material

59

o ~O I 150 2 250 350 400 450

HORI L ES J

1 finite Mesh for Ambuklao Dam

Triaxial compression tests were also performed for shear strength determination with coheshysion C and friction () adopted as strength indicators The average values of C and (j) are tabulated in 2 for various types of namely unconsol undrained Ul conshysolidated undrained (CU) and consolidated (CD) Also shown in Table 2 are the strength properties obtained from saturated consolidated-drained direct shear tests

The clays behavior was modelled using the Cam Clay theory by Roscoe and Burland (1 This model assumes an stress-sLrain behavior in which the yield surfaces are a family of ellipsoids centered about the hydrostatic axis Although the clay core material may have been preconsolidated to a certain degree due to aging the inertia loads were assumed enough to yielding An elasto-plastic stressmiddot strain matrix of the form by Borja and Kavazanjian (1 was used in stiffness matrix formation

2 Rock Fill Rock-fill materials were assumed to be isotropic and linearly elastic with the following material constants

ratio v 030 Youngs modulus E kp

where p is the mean normal stress and k is a constant (Lambe and Whitman 1969)

Ta b Ie Ambuklao Dam Central Core

Compressibility

Index 00271 Swelli Cam Clay Index X o 0012

2 Virgin Compression Index 0153 plusmn~ ~ 0018 Clay Index A 043C 0066 plusmn 0008~c

3 Void Ratio at p 1 tonsqm on the consolidation line 070~ ~ ~ ~

Table 2 Am buklao Dam Clay

Parameters

Friction Cohesion InitialType of Test

Angl e (j deg tonssqm modulus

A Triaxial 1 UU 2 CU 3 CD

21 24 29

64 38

variable 128 103

8 40 12 variable

6]

above for E necessitates an estimate of the stress distribution within the dam due to gravity loads A iminary statical analysis was performed to obtain these self weight-induced stresses for use as input in the eigenvalue

The constant k was determined from a calibration study based on a recorded horizontal moveshyment 4 of a bench mark in the middle of the dams crest when the reservoir was gradually filled to spillway crest 740 the wet season of 1 to early 1 (Fucik Edbrooke 1958) From this study the constant k was estimated to be about

Results

Shown in 3 are the mode shapes defining first five Mode 1 has a fundamental period of 3

3a) mode not seem to result in significant seconds and appears to be a

change are y distortional

Mode 2 has a fundamental of 252 seconds (Figure Oscillations are Iy vershytical resu in significant volume The components of displacements are symshymetric about the centerline causing lateral expansion to develop at the crest during the time instant shown in Figure At another time instant not shown the top zone of the dam may also contract du oscillation as the nodal d are reversed

M 3 through 5 appear to be higher vertical and sidesway modes (Figure d e) Mode 4 is a higher level mode having a period of 177 seconds (Figure

two vertical mode shapes 3b and d are worthy of note The deformed shown are clearly In lities the inner

clay core and the outer rock-fill materials the more com inner material apparently tending to pull the less compressible rock-fill to a state of larger deformation

MODE I

(a ) (b)

0 (c ) (d)

MODE PERIOD SEC 323

2 252 3 183 4 I 77 5 145

(e)

Figure 3 Ambuklao The Five Modes Vibration

62

DAM PREDICTION OF CREEP AND CYCLIC MOVEMENTS

Background

The Cal Hydroelectric Dam of Lumban Laguna is part of the Kalayaan Power Plant Sysshytem the National Power Corporation of the Phi

The 45 meter-high dam sits on a volcanic bedrock primarily of agglomerate and basalt with its main dike spanning about 300 meters across the Caliraya River Constructed of rolled earth fill clay to silty composition the dam wasmiddot about forty years ago and has since served as a water impounder until the of the in 1982

As part of an on-going project study to assess the dams present a finite element deformation anal ysis was conducted The results presented in this paper cover the prediction of dam movements due to the reservoir drawdownfilling as well as creep deformations expected to develop in the next forty years

e numerical algorithm oyed in the is based on an creep-inclusive rate constitutive of the form (summation implied on repeated subscripts)

bull I (11)- O If

where 0ij is the Cauchy stress tensor Ekl is the small strain tensor Cijkl is the material t n tensor and the overdots denote a material time differentiation The quantity o ISIJ

the stress relaxation rate due to creep which is converted into element pseudo-forces via

(1

where B is the strain-displacement matrix and is the element For a discussion of the development of (11) the is referred to Borja and Kavazanjian (1985)

300

~

z ~ 280

0 f shylt gt w J 260 W

(

o 20 40 60

HORIZONTAL

80 100

COORDINATES M

120 140 160

4 Finite Mesh for Caliraya Dam

63

at Sta 0+380

240

Numerical Solution

The finite element program used in the analysis is a module of SPIN 20 which performs the time integration of (11) by the conventional incremental theory of plasticity

The finite element mesh for the dam is shown in Figure 4 for cross section at Sta 0+380 The mesh consists of 87 nodes of which 20 are fixed and 73 isoparametric 4-noded quadrilateral eleshyments resulting in a total number of 2x (87-20) = 134 unknown degrees of freedom The numerical integration rules employed are as discussed in Section 2 Material properties used are as summarized in Tables 3 and 4

Initial stresses are required as input data to enable complete definition of initial states of stress and their positions relative to the corresponding yield surfaces Initial stresses are due to both the dams self weight and hydrostatic pressure acting normal to the upstream face of the dam as the reservoir was filled to design capacity

Table 3 Caliraya Earth FillDam

Compressibility amp Creep Parameters

1 SwellingRecompression Index Cam Clay Index X 043 Cr

Cr 00250 00109

2 Virgin Compression Index Cam Clay Index -shy 043 Cc

Cc 02500 01090

3 Secondary Compression Index Natural Log Index lj 043 Ca

C a 00067 00029

4 Average Void Ratio at p = 1 tonsqm on the isotropic consolidation line 155

Tab Ie 4

Caliraya Earth Fill Dam Strength Parameters

Type of Test Friction Angle dJ deg

Cohesion C tonssqm

1 UU 25 4 9

2 CU 15 10 6

3 CD 18 62

To obtain the self weight-induced stresses an elastostatic analysis was performed using an average soil unit weight of 1 76 tonssqm (standard deviation 016 tonsqm from lab test reshySUlts) Superimposing the additional stresses due to hydrostatic pressure as the reservoir was filled to Elev 288 the total principal stresses and their directions are as depicted in Figure 5

64

1

Discussion of Results

movement due to creep Under sustained initial stresses resulting from gravity and loads finite element was a Ilowed to creep according to the secondary compression

equation A com definition of all the com of creep strain was by employing normality rule on the same elli yield surfaces as in the ti plasticity model

Figure 6 illustrates the d ent due to creep to develop over the next forty year A maximum crest settlement of about 10 centimeters can be seen from this e

A time history of movement due to creep of a at the center of the dams crest is also plotted in Figure 6 As a on the correctness of the above the soil was assumed to have aged tv 40 years from the time that the dam was completed Over the next

40 years the settlement duemiddot secondary compression of a dam 45 meters high is estimated to

6t yCex ( 1 +- ) x 450 meterOy 109101 + e tv

00067 400 10 ( 1 + ) x 450

1 + 10 400

0050 meter

With movements due to shearing distortion still to be included the above check verifies the premiddot dicted settlement of 010 meter obtained from the computer analysis

2 Cyclic movements due to drawdown and filling High and low water elevation of 289 m and 286 m vely were recorded for Lake during the period ry 1983 to

1984 Choosing Elev 288 m as a reference elevation predicted displacement profiles due to reservoir

drawdown and fil are as plotted in Fig 7 results of 7 were obtained from elastic with elastic constants derived from the Cam Clay As permanent strains are to become reasonably small after several a stable hysteresis loop was

assumed It can be seen from Fig 7 that a maximum displacement of about 1 cm is likely to occur in the

neighborhood of nodes 19 and 21 as the water elevation fluctuates from Elev 286 to Elev 289 This movement is considered small to cause serious cracking in the dams u concrete provided that the drawdownfilling rates are slow

I

t I

1shy

J

+ + + +

DAM STRESS SCALE SCALE

TONSM2

METERS

Figure 5 Dam Total and Directions

65

E n l-Z w I III U laquo l Il It)

i5 Il w w a u l

05

19650 0 laquo 10

DAM DISPLACEMENTS SCALE SCALE

I I I t--I---i o 5 10 15 METERS 0 01 02 METER

100 1000 TIME AFTER DAMS COMPLETION YRS

Figure 6 Caliraya Dam I_U-LIU Creep Displacement ProfIle

I

FILLING TO l EL289--=_1REFERENCE

PROFILE

~-~

I

DISPLACEMENTS DAM SCALE SCALE

--+--1 o 001 002 METER o 5 10 15 METERS

Figure 7 Caliraya Dam Cyclic Movement Due to Reservoir Drawdown Filling

CONCLUDING REMARKS

This paper demonstrates the litymiddot of the finite element method in the solution of

typical boundary value problems in geotechnical engineering

Although the results in this paper were establ ished a priori and remain subject to

verification by actual field instrumentation it was demonstrated that the above numerical method

can be useful in accounting for complex factors such as material nonlinearities and nonmiddot

ies into the solution

ACKNOWLEDGMENT

The author wishes to thank Salvador F Reyes of the Department of Civil Engineering Un of the Phil for his helpful comments and suggestions Funding for these studies was provided by the National Power of the Phil on a joint AmbuklaoCaliraya remedial project research

REFERENCES 1 BORJA R1 and KAVAZANJIAN E JR (1 A constitutive model for the stress-strainshy

time behavior of wet No3

2 FUCIK EM and EDBROOK RF (1958) Ambuklao rock-fill dam and Journal of the Soil Mechanics and Foundation Division vol 84 No pp 1864-1

to 1864-22

3 LAMBE TW and WH ITMAN RV (19691 Soil Mechanics Wiley New York

4 OWEN D R J and HINTON E (19801 Finite Elements in Plasticity Theory and Pi Press Limited UK

5 ROSCOE KH and BURLAND JB (1 On the generalized stress-strain behavior of wet clays Engineering Plasticity Cambridge pp

67

o ~O I 150 2 250 350 400 450

HORI L ES J

1 finite Mesh for Ambuklao Dam

Triaxial compression tests were also performed for shear strength determination with coheshysion C and friction () adopted as strength indicators The average values of C and (j) are tabulated in 2 for various types of namely unconsol undrained Ul conshysolidated undrained (CU) and consolidated (CD) Also shown in Table 2 are the strength properties obtained from saturated consolidated-drained direct shear tests

The clays behavior was modelled using the Cam Clay theory by Roscoe and Burland (1 This model assumes an stress-sLrain behavior in which the yield surfaces are a family of ellipsoids centered about the hydrostatic axis Although the clay core material may have been preconsolidated to a certain degree due to aging the inertia loads were assumed enough to yielding An elasto-plastic stressmiddot strain matrix of the form by Borja and Kavazanjian (1 was used in stiffness matrix formation

2 Rock Fill Rock-fill materials were assumed to be isotropic and linearly elastic with the following material constants

ratio v 030 Youngs modulus E kp

where p is the mean normal stress and k is a constant (Lambe and Whitman 1969)

Ta b Ie Ambuklao Dam Central Core

Compressibility

Index 00271 Swelli Cam Clay Index X o 0012

2 Virgin Compression Index 0153 plusmn~ ~ 0018 Clay Index A 043C 0066 plusmn 0008~c

3 Void Ratio at p 1 tonsqm on the consolidation line 070~ ~ ~ ~

Table 2 Am buklao Dam Clay

Parameters

Friction Cohesion InitialType of Test

Angl e (j deg tonssqm modulus

A Triaxial 1 UU 2 CU 3 CD

21 24 29

64 38

variable 128 103

8 40 12 variable

6]

above for E necessitates an estimate of the stress distribution within the dam due to gravity loads A iminary statical analysis was performed to obtain these self weight-induced stresses for use as input in the eigenvalue

The constant k was determined from a calibration study based on a recorded horizontal moveshyment 4 of a bench mark in the middle of the dams crest when the reservoir was gradually filled to spillway crest 740 the wet season of 1 to early 1 (Fucik Edbrooke 1958) From this study the constant k was estimated to be about

Results

Shown in 3 are the mode shapes defining first five Mode 1 has a fundamental period of 3

3a) mode not seem to result in significant seconds and appears to be a

change are y distortional

Mode 2 has a fundamental of 252 seconds (Figure Oscillations are Iy vershytical resu in significant volume The components of displacements are symshymetric about the centerline causing lateral expansion to develop at the crest during the time instant shown in Figure At another time instant not shown the top zone of the dam may also contract du oscillation as the nodal d are reversed

M 3 through 5 appear to be higher vertical and sidesway modes (Figure d e) Mode 4 is a higher level mode having a period of 177 seconds (Figure

two vertical mode shapes 3b and d are worthy of note The deformed shown are clearly In lities the inner

clay core and the outer rock-fill materials the more com inner material apparently tending to pull the less compressible rock-fill to a state of larger deformation

MODE I

(a ) (b)

0 (c ) (d)

MODE PERIOD SEC 323

2 252 3 183 4 I 77 5 145

(e)

Figure 3 Ambuklao The Five Modes Vibration

62

DAM PREDICTION OF CREEP AND CYCLIC MOVEMENTS

Background

The Cal Hydroelectric Dam of Lumban Laguna is part of the Kalayaan Power Plant Sysshytem the National Power Corporation of the Phi

The 45 meter-high dam sits on a volcanic bedrock primarily of agglomerate and basalt with its main dike spanning about 300 meters across the Caliraya River Constructed of rolled earth fill clay to silty composition the dam wasmiddot about forty years ago and has since served as a water impounder until the of the in 1982

As part of an on-going project study to assess the dams present a finite element deformation anal ysis was conducted The results presented in this paper cover the prediction of dam movements due to the reservoir drawdownfilling as well as creep deformations expected to develop in the next forty years

e numerical algorithm oyed in the is based on an creep-inclusive rate constitutive of the form (summation implied on repeated subscripts)

bull I (11)- O If

where 0ij is the Cauchy stress tensor Ekl is the small strain tensor Cijkl is the material t n tensor and the overdots denote a material time differentiation The quantity o ISIJ

the stress relaxation rate due to creep which is converted into element pseudo-forces via

(1

where B is the strain-displacement matrix and is the element For a discussion of the development of (11) the is referred to Borja and Kavazanjian (1985)

300

~

z ~ 280

0 f shylt gt w J 260 W

(

o 20 40 60

HORIZONTAL

80 100

COORDINATES M

120 140 160

4 Finite Mesh for Caliraya Dam

63

at Sta 0+380

240

Numerical Solution

The finite element program used in the analysis is a module of SPIN 20 which performs the time integration of (11) by the conventional incremental theory of plasticity

The finite element mesh for the dam is shown in Figure 4 for cross section at Sta 0+380 The mesh consists of 87 nodes of which 20 are fixed and 73 isoparametric 4-noded quadrilateral eleshyments resulting in a total number of 2x (87-20) = 134 unknown degrees of freedom The numerical integration rules employed are as discussed in Section 2 Material properties used are as summarized in Tables 3 and 4

Initial stresses are required as input data to enable complete definition of initial states of stress and their positions relative to the corresponding yield surfaces Initial stresses are due to both the dams self weight and hydrostatic pressure acting normal to the upstream face of the dam as the reservoir was filled to design capacity

Table 3 Caliraya Earth FillDam

Compressibility amp Creep Parameters

1 SwellingRecompression Index Cam Clay Index X 043 Cr

Cr 00250 00109

2 Virgin Compression Index Cam Clay Index -shy 043 Cc

Cc 02500 01090

3 Secondary Compression Index Natural Log Index lj 043 Ca

C a 00067 00029

4 Average Void Ratio at p = 1 tonsqm on the isotropic consolidation line 155

Tab Ie 4

Caliraya Earth Fill Dam Strength Parameters

Type of Test Friction Angle dJ deg

Cohesion C tonssqm

1 UU 25 4 9

2 CU 15 10 6

3 CD 18 62

To obtain the self weight-induced stresses an elastostatic analysis was performed using an average soil unit weight of 1 76 tonssqm (standard deviation 016 tonsqm from lab test reshySUlts) Superimposing the additional stresses due to hydrostatic pressure as the reservoir was filled to Elev 288 the total principal stresses and their directions are as depicted in Figure 5

64

1

Discussion of Results

movement due to creep Under sustained initial stresses resulting from gravity and loads finite element was a Ilowed to creep according to the secondary compression

equation A com definition of all the com of creep strain was by employing normality rule on the same elli yield surfaces as in the ti plasticity model

Figure 6 illustrates the d ent due to creep to develop over the next forty year A maximum crest settlement of about 10 centimeters can be seen from this e

A time history of movement due to creep of a at the center of the dams crest is also plotted in Figure 6 As a on the correctness of the above the soil was assumed to have aged tv 40 years from the time that the dam was completed Over the next

40 years the settlement duemiddot secondary compression of a dam 45 meters high is estimated to

6t yCex ( 1 +- ) x 450 meterOy 109101 + e tv

00067 400 10 ( 1 + ) x 450

1 + 10 400

0050 meter

With movements due to shearing distortion still to be included the above check verifies the premiddot dicted settlement of 010 meter obtained from the computer analysis

2 Cyclic movements due to drawdown and filling High and low water elevation of 289 m and 286 m vely were recorded for Lake during the period ry 1983 to

1984 Choosing Elev 288 m as a reference elevation predicted displacement profiles due to reservoir

drawdown and fil are as plotted in Fig 7 results of 7 were obtained from elastic with elastic constants derived from the Cam Clay As permanent strains are to become reasonably small after several a stable hysteresis loop was

assumed It can be seen from Fig 7 that a maximum displacement of about 1 cm is likely to occur in the

neighborhood of nodes 19 and 21 as the water elevation fluctuates from Elev 286 to Elev 289 This movement is considered small to cause serious cracking in the dams u concrete provided that the drawdownfilling rates are slow

I

t I

1shy

J

+ + + +

DAM STRESS SCALE SCALE

TONSM2

METERS

Figure 5 Dam Total and Directions

65

E n l-Z w I III U laquo l Il It)

i5 Il w w a u l

05

19650 0 laquo 10

DAM DISPLACEMENTS SCALE SCALE

I I I t--I---i o 5 10 15 METERS 0 01 02 METER

100 1000 TIME AFTER DAMS COMPLETION YRS

Figure 6 Caliraya Dam I_U-LIU Creep Displacement ProfIle

I

FILLING TO l EL289--=_1REFERENCE

PROFILE

~-~

I

DISPLACEMENTS DAM SCALE SCALE

--+--1 o 001 002 METER o 5 10 15 METERS

Figure 7 Caliraya Dam Cyclic Movement Due to Reservoir Drawdown Filling

CONCLUDING REMARKS

This paper demonstrates the litymiddot of the finite element method in the solution of

typical boundary value problems in geotechnical engineering

Although the results in this paper were establ ished a priori and remain subject to

verification by actual field instrumentation it was demonstrated that the above numerical method

can be useful in accounting for complex factors such as material nonlinearities and nonmiddot

ies into the solution

ACKNOWLEDGMENT

The author wishes to thank Salvador F Reyes of the Department of Civil Engineering Un of the Phil for his helpful comments and suggestions Funding for these studies was provided by the National Power of the Phil on a joint AmbuklaoCaliraya remedial project research

REFERENCES 1 BORJA R1 and KAVAZANJIAN E JR (1 A constitutive model for the stress-strainshy

time behavior of wet No3

2 FUCIK EM and EDBROOK RF (1958) Ambuklao rock-fill dam and Journal of the Soil Mechanics and Foundation Division vol 84 No pp 1864-1

to 1864-22

3 LAMBE TW and WH ITMAN RV (19691 Soil Mechanics Wiley New York

4 OWEN D R J and HINTON E (19801 Finite Elements in Plasticity Theory and Pi Press Limited UK

5 ROSCOE KH and BURLAND JB (1 On the generalized stress-strain behavior of wet clays Engineering Plasticity Cambridge pp

67

Triaxial compression tests were also performed for shear strength determination with coheshysion C and friction () adopted as strength indicators The average values of C and (j) are tabulated in 2 for various types of namely unconsol undrained Ul conshysolidated undrained (CU) and consolidated (CD) Also shown in Table 2 are the strength properties obtained from saturated consolidated-drained direct shear tests

The clays behavior was modelled using the Cam Clay theory by Roscoe and Burland (1 This model assumes an stress-sLrain behavior in which the yield surfaces are a family of ellipsoids centered about the hydrostatic axis Although the clay core material may have been preconsolidated to a certain degree due to aging the inertia loads were assumed enough to yielding An elasto-plastic stressmiddot strain matrix of the form by Borja and Kavazanjian (1 was used in stiffness matrix formation

2 Rock Fill Rock-fill materials were assumed to be isotropic and linearly elastic with the following material constants

ratio v 030 Youngs modulus E kp

where p is the mean normal stress and k is a constant (Lambe and Whitman 1969)

Ta b Ie Ambuklao Dam Central Core

Compressibility

Index 00271 Swelli Cam Clay Index X o 0012

2 Virgin Compression Index 0153 plusmn~ ~ 0018 Clay Index A 043C 0066 plusmn 0008~c

3 Void Ratio at p 1 tonsqm on the consolidation line 070~ ~ ~ ~

Table 2 Am buklao Dam Clay

Parameters

Friction Cohesion InitialType of Test

Angl e (j deg tonssqm modulus

A Triaxial 1 UU 2 CU 3 CD

21 24 29

64 38

variable 128 103

8 40 12 variable

6]

above for E necessitates an estimate of the stress distribution within the dam due to gravity loads A iminary statical analysis was performed to obtain these self weight-induced stresses for use as input in the eigenvalue

The constant k was determined from a calibration study based on a recorded horizontal moveshyment 4 of a bench mark in the middle of the dams crest when the reservoir was gradually filled to spillway crest 740 the wet season of 1 to early 1 (Fucik Edbrooke 1958) From this study the constant k was estimated to be about

Results

Shown in 3 are the mode shapes defining first five Mode 1 has a fundamental period of 3

3a) mode not seem to result in significant seconds and appears to be a

change are y distortional

Mode 2 has a fundamental of 252 seconds (Figure Oscillations are Iy vershytical resu in significant volume The components of displacements are symshymetric about the centerline causing lateral expansion to develop at the crest during the time instant shown in Figure At another time instant not shown the top zone of the dam may also contract du oscillation as the nodal d are reversed

M 3 through 5 appear to be higher vertical and sidesway modes (Figure d e) Mode 4 is a higher level mode having a period of 177 seconds (Figure

two vertical mode shapes 3b and d are worthy of note The deformed shown are clearly In lities the inner

clay core and the outer rock-fill materials the more com inner material apparently tending to pull the less compressible rock-fill to a state of larger deformation

MODE I

(a ) (b)

0 (c ) (d)

MODE PERIOD SEC 323

2 252 3 183 4 I 77 5 145

(e)

Figure 3 Ambuklao The Five Modes Vibration

62

DAM PREDICTION OF CREEP AND CYCLIC MOVEMENTS

Background

The Cal Hydroelectric Dam of Lumban Laguna is part of the Kalayaan Power Plant Sysshytem the National Power Corporation of the Phi

The 45 meter-high dam sits on a volcanic bedrock primarily of agglomerate and basalt with its main dike spanning about 300 meters across the Caliraya River Constructed of rolled earth fill clay to silty composition the dam wasmiddot about forty years ago and has since served as a water impounder until the of the in 1982

As part of an on-going project study to assess the dams present a finite element deformation anal ysis was conducted The results presented in this paper cover the prediction of dam movements due to the reservoir drawdownfilling as well as creep deformations expected to develop in the next forty years

e numerical algorithm oyed in the is based on an creep-inclusive rate constitutive of the form (summation implied on repeated subscripts)

bull I (11)- O If

where 0ij is the Cauchy stress tensor Ekl is the small strain tensor Cijkl is the material t n tensor and the overdots denote a material time differentiation The quantity o ISIJ

the stress relaxation rate due to creep which is converted into element pseudo-forces via

(1

where B is the strain-displacement matrix and is the element For a discussion of the development of (11) the is referred to Borja and Kavazanjian (1985)

300

~

z ~ 280

0 f shylt gt w J 260 W

(

o 20 40 60

HORIZONTAL

80 100

COORDINATES M

120 140 160

4 Finite Mesh for Caliraya Dam

63

at Sta 0+380

240

Numerical Solution

The finite element program used in the analysis is a module of SPIN 20 which performs the time integration of (11) by the conventional incremental theory of plasticity

The finite element mesh for the dam is shown in Figure 4 for cross section at Sta 0+380 The mesh consists of 87 nodes of which 20 are fixed and 73 isoparametric 4-noded quadrilateral eleshyments resulting in a total number of 2x (87-20) = 134 unknown degrees of freedom The numerical integration rules employed are as discussed in Section 2 Material properties used are as summarized in Tables 3 and 4

Initial stresses are required as input data to enable complete definition of initial states of stress and their positions relative to the corresponding yield surfaces Initial stresses are due to both the dams self weight and hydrostatic pressure acting normal to the upstream face of the dam as the reservoir was filled to design capacity

Table 3 Caliraya Earth FillDam

Compressibility amp Creep Parameters

1 SwellingRecompression Index Cam Clay Index X 043 Cr

Cr 00250 00109

2 Virgin Compression Index Cam Clay Index -shy 043 Cc

Cc 02500 01090

3 Secondary Compression Index Natural Log Index lj 043 Ca

C a 00067 00029

4 Average Void Ratio at p = 1 tonsqm on the isotropic consolidation line 155

Tab Ie 4

Caliraya Earth Fill Dam Strength Parameters

Type of Test Friction Angle dJ deg

Cohesion C tonssqm

1 UU 25 4 9

2 CU 15 10 6

3 CD 18 62

To obtain the self weight-induced stresses an elastostatic analysis was performed using an average soil unit weight of 1 76 tonssqm (standard deviation 016 tonsqm from lab test reshySUlts) Superimposing the additional stresses due to hydrostatic pressure as the reservoir was filled to Elev 288 the total principal stresses and their directions are as depicted in Figure 5

64

1

Discussion of Results

movement due to creep Under sustained initial stresses resulting from gravity and loads finite element was a Ilowed to creep according to the secondary compression

equation A com definition of all the com of creep strain was by employing normality rule on the same elli yield surfaces as in the ti plasticity model

Figure 6 illustrates the d ent due to creep to develop over the next forty year A maximum crest settlement of about 10 centimeters can be seen from this e

A time history of movement due to creep of a at the center of the dams crest is also plotted in Figure 6 As a on the correctness of the above the soil was assumed to have aged tv 40 years from the time that the dam was completed Over the next

40 years the settlement duemiddot secondary compression of a dam 45 meters high is estimated to

6t yCex ( 1 +- ) x 450 meterOy 109101 + e tv

00067 400 10 ( 1 + ) x 450

1 + 10 400

0050 meter

With movements due to shearing distortion still to be included the above check verifies the premiddot dicted settlement of 010 meter obtained from the computer analysis

2 Cyclic movements due to drawdown and filling High and low water elevation of 289 m and 286 m vely were recorded for Lake during the period ry 1983 to

1984 Choosing Elev 288 m as a reference elevation predicted displacement profiles due to reservoir

drawdown and fil are as plotted in Fig 7 results of 7 were obtained from elastic with elastic constants derived from the Cam Clay As permanent strains are to become reasonably small after several a stable hysteresis loop was

assumed It can be seen from Fig 7 that a maximum displacement of about 1 cm is likely to occur in the

neighborhood of nodes 19 and 21 as the water elevation fluctuates from Elev 286 to Elev 289 This movement is considered small to cause serious cracking in the dams u concrete provided that the drawdownfilling rates are slow

I

t I

1shy

J

+ + + +

DAM STRESS SCALE SCALE

TONSM2

METERS

Figure 5 Dam Total and Directions

65

E n l-Z w I III U laquo l Il It)

i5 Il w w a u l

05

19650 0 laquo 10

DAM DISPLACEMENTS SCALE SCALE

I I I t--I---i o 5 10 15 METERS 0 01 02 METER

100 1000 TIME AFTER DAMS COMPLETION YRS

Figure 6 Caliraya Dam I_U-LIU Creep Displacement ProfIle

I

FILLING TO l EL289--=_1REFERENCE

PROFILE

~-~

I

DISPLACEMENTS DAM SCALE SCALE

--+--1 o 001 002 METER o 5 10 15 METERS

Figure 7 Caliraya Dam Cyclic Movement Due to Reservoir Drawdown Filling

CONCLUDING REMARKS

This paper demonstrates the litymiddot of the finite element method in the solution of

typical boundary value problems in geotechnical engineering

Although the results in this paper were establ ished a priori and remain subject to

verification by actual field instrumentation it was demonstrated that the above numerical method

can be useful in accounting for complex factors such as material nonlinearities and nonmiddot

ies into the solution

ACKNOWLEDGMENT

The author wishes to thank Salvador F Reyes of the Department of Civil Engineering Un of the Phil for his helpful comments and suggestions Funding for these studies was provided by the National Power of the Phil on a joint AmbuklaoCaliraya remedial project research

REFERENCES 1 BORJA R1 and KAVAZANJIAN E JR (1 A constitutive model for the stress-strainshy

time behavior of wet No3

2 FUCIK EM and EDBROOK RF (1958) Ambuklao rock-fill dam and Journal of the Soil Mechanics and Foundation Division vol 84 No pp 1864-1

to 1864-22

3 LAMBE TW and WH ITMAN RV (19691 Soil Mechanics Wiley New York

4 OWEN D R J and HINTON E (19801 Finite Elements in Plasticity Theory and Pi Press Limited UK

5 ROSCOE KH and BURLAND JB (1 On the generalized stress-strain behavior of wet clays Engineering Plasticity Cambridge pp

67

above for E necessitates an estimate of the stress distribution within the dam due to gravity loads A iminary statical analysis was performed to obtain these self weight-induced stresses for use as input in the eigenvalue

The constant k was determined from a calibration study based on a recorded horizontal moveshyment 4 of a bench mark in the middle of the dams crest when the reservoir was gradually filled to spillway crest 740 the wet season of 1 to early 1 (Fucik Edbrooke 1958) From this study the constant k was estimated to be about

Results

Shown in 3 are the mode shapes defining first five Mode 1 has a fundamental period of 3

3a) mode not seem to result in significant seconds and appears to be a

change are y distortional

Mode 2 has a fundamental of 252 seconds (Figure Oscillations are Iy vershytical resu in significant volume The components of displacements are symshymetric about the centerline causing lateral expansion to develop at the crest during the time instant shown in Figure At another time instant not shown the top zone of the dam may also contract du oscillation as the nodal d are reversed

M 3 through 5 appear to be higher vertical and sidesway modes (Figure d e) Mode 4 is a higher level mode having a period of 177 seconds (Figure

two vertical mode shapes 3b and d are worthy of note The deformed shown are clearly In lities the inner

clay core and the outer rock-fill materials the more com inner material apparently tending to pull the less compressible rock-fill to a state of larger deformation

MODE I

(a ) (b)

0 (c ) (d)

MODE PERIOD SEC 323

2 252 3 183 4 I 77 5 145

(e)

Figure 3 Ambuklao The Five Modes Vibration

62

DAM PREDICTION OF CREEP AND CYCLIC MOVEMENTS

Background

The Cal Hydroelectric Dam of Lumban Laguna is part of the Kalayaan Power Plant Sysshytem the National Power Corporation of the Phi

The 45 meter-high dam sits on a volcanic bedrock primarily of agglomerate and basalt with its main dike spanning about 300 meters across the Caliraya River Constructed of rolled earth fill clay to silty composition the dam wasmiddot about forty years ago and has since served as a water impounder until the of the in 1982

As part of an on-going project study to assess the dams present a finite element deformation anal ysis was conducted The results presented in this paper cover the prediction of dam movements due to the reservoir drawdownfilling as well as creep deformations expected to develop in the next forty years

e numerical algorithm oyed in the is based on an creep-inclusive rate constitutive of the form (summation implied on repeated subscripts)

bull I (11)- O If

where 0ij is the Cauchy stress tensor Ekl is the small strain tensor Cijkl is the material t n tensor and the overdots denote a material time differentiation The quantity o ISIJ

the stress relaxation rate due to creep which is converted into element pseudo-forces via

(1

where B is the strain-displacement matrix and is the element For a discussion of the development of (11) the is referred to Borja and Kavazanjian (1985)

300

~

z ~ 280

0 f shylt gt w J 260 W

(

o 20 40 60

HORIZONTAL

80 100

COORDINATES M

120 140 160

4 Finite Mesh for Caliraya Dam

63

at Sta 0+380

240

Numerical Solution

The finite element program used in the analysis is a module of SPIN 20 which performs the time integration of (11) by the conventional incremental theory of plasticity

The finite element mesh for the dam is shown in Figure 4 for cross section at Sta 0+380 The mesh consists of 87 nodes of which 20 are fixed and 73 isoparametric 4-noded quadrilateral eleshyments resulting in a total number of 2x (87-20) = 134 unknown degrees of freedom The numerical integration rules employed are as discussed in Section 2 Material properties used are as summarized in Tables 3 and 4

Initial stresses are required as input data to enable complete definition of initial states of stress and their positions relative to the corresponding yield surfaces Initial stresses are due to both the dams self weight and hydrostatic pressure acting normal to the upstream face of the dam as the reservoir was filled to design capacity

Table 3 Caliraya Earth FillDam

Compressibility amp Creep Parameters

1 SwellingRecompression Index Cam Clay Index X 043 Cr

Cr 00250 00109

2 Virgin Compression Index Cam Clay Index -shy 043 Cc

Cc 02500 01090

3 Secondary Compression Index Natural Log Index lj 043 Ca

C a 00067 00029

4 Average Void Ratio at p = 1 tonsqm on the isotropic consolidation line 155

Tab Ie 4

Caliraya Earth Fill Dam Strength Parameters

Type of Test Friction Angle dJ deg

Cohesion C tonssqm

1 UU 25 4 9

2 CU 15 10 6

3 CD 18 62

To obtain the self weight-induced stresses an elastostatic analysis was performed using an average soil unit weight of 1 76 tonssqm (standard deviation 016 tonsqm from lab test reshySUlts) Superimposing the additional stresses due to hydrostatic pressure as the reservoir was filled to Elev 288 the total principal stresses and their directions are as depicted in Figure 5

64

1

Discussion of Results

movement due to creep Under sustained initial stresses resulting from gravity and loads finite element was a Ilowed to creep according to the secondary compression

equation A com definition of all the com of creep strain was by employing normality rule on the same elli yield surfaces as in the ti plasticity model

Figure 6 illustrates the d ent due to creep to develop over the next forty year A maximum crest settlement of about 10 centimeters can be seen from this e

A time history of movement due to creep of a at the center of the dams crest is also plotted in Figure 6 As a on the correctness of the above the soil was assumed to have aged tv 40 years from the time that the dam was completed Over the next

40 years the settlement duemiddot secondary compression of a dam 45 meters high is estimated to

6t yCex ( 1 +- ) x 450 meterOy 109101 + e tv

00067 400 10 ( 1 + ) x 450

1 + 10 400

0050 meter

With movements due to shearing distortion still to be included the above check verifies the premiddot dicted settlement of 010 meter obtained from the computer analysis

2 Cyclic movements due to drawdown and filling High and low water elevation of 289 m and 286 m vely were recorded for Lake during the period ry 1983 to

1984 Choosing Elev 288 m as a reference elevation predicted displacement profiles due to reservoir

drawdown and fil are as plotted in Fig 7 results of 7 were obtained from elastic with elastic constants derived from the Cam Clay As permanent strains are to become reasonably small after several a stable hysteresis loop was

assumed It can be seen from Fig 7 that a maximum displacement of about 1 cm is likely to occur in the

neighborhood of nodes 19 and 21 as the water elevation fluctuates from Elev 286 to Elev 289 This movement is considered small to cause serious cracking in the dams u concrete provided that the drawdownfilling rates are slow

I

t I

1shy

J

+ + + +

DAM STRESS SCALE SCALE

TONSM2

METERS

Figure 5 Dam Total and Directions

65

E n l-Z w I III U laquo l Il It)

i5 Il w w a u l

05

19650 0 laquo 10

DAM DISPLACEMENTS SCALE SCALE

I I I t--I---i o 5 10 15 METERS 0 01 02 METER

100 1000 TIME AFTER DAMS COMPLETION YRS

Figure 6 Caliraya Dam I_U-LIU Creep Displacement ProfIle

I

FILLING TO l EL289--=_1REFERENCE

PROFILE

~-~

I

DISPLACEMENTS DAM SCALE SCALE

--+--1 o 001 002 METER o 5 10 15 METERS

Figure 7 Caliraya Dam Cyclic Movement Due to Reservoir Drawdown Filling

CONCLUDING REMARKS

This paper demonstrates the litymiddot of the finite element method in the solution of

typical boundary value problems in geotechnical engineering

Although the results in this paper were establ ished a priori and remain subject to

verification by actual field instrumentation it was demonstrated that the above numerical method

can be useful in accounting for complex factors such as material nonlinearities and nonmiddot

ies into the solution

ACKNOWLEDGMENT

The author wishes to thank Salvador F Reyes of the Department of Civil Engineering Un of the Phil for his helpful comments and suggestions Funding for these studies was provided by the National Power of the Phil on a joint AmbuklaoCaliraya remedial project research

REFERENCES 1 BORJA R1 and KAVAZANJIAN E JR (1 A constitutive model for the stress-strainshy

time behavior of wet No3

2 FUCIK EM and EDBROOK RF (1958) Ambuklao rock-fill dam and Journal of the Soil Mechanics and Foundation Division vol 84 No pp 1864-1

to 1864-22

3 LAMBE TW and WH ITMAN RV (19691 Soil Mechanics Wiley New York

4 OWEN D R J and HINTON E (19801 Finite Elements in Plasticity Theory and Pi Press Limited UK

5 ROSCOE KH and BURLAND JB (1 On the generalized stress-strain behavior of wet clays Engineering Plasticity Cambridge pp

67

DAM PREDICTION OF CREEP AND CYCLIC MOVEMENTS

Background

The Cal Hydroelectric Dam of Lumban Laguna is part of the Kalayaan Power Plant Sysshytem the National Power Corporation of the Phi

The 45 meter-high dam sits on a volcanic bedrock primarily of agglomerate and basalt with its main dike spanning about 300 meters across the Caliraya River Constructed of rolled earth fill clay to silty composition the dam wasmiddot about forty years ago and has since served as a water impounder until the of the in 1982

As part of an on-going project study to assess the dams present a finite element deformation anal ysis was conducted The results presented in this paper cover the prediction of dam movements due to the reservoir drawdownfilling as well as creep deformations expected to develop in the next forty years

e numerical algorithm oyed in the is based on an creep-inclusive rate constitutive of the form (summation implied on repeated subscripts)

bull I (11)- O If

where 0ij is the Cauchy stress tensor Ekl is the small strain tensor Cijkl is the material t n tensor and the overdots denote a material time differentiation The quantity o ISIJ

the stress relaxation rate due to creep which is converted into element pseudo-forces via

(1

where B is the strain-displacement matrix and is the element For a discussion of the development of (11) the is referred to Borja and Kavazanjian (1985)

300

~

z ~ 280

0 f shylt gt w J 260 W

(

o 20 40 60

HORIZONTAL

80 100

COORDINATES M

120 140 160

4 Finite Mesh for Caliraya Dam

63

at Sta 0+380

240

Numerical Solution

The finite element program used in the analysis is a module of SPIN 20 which performs the time integration of (11) by the conventional incremental theory of plasticity

The finite element mesh for the dam is shown in Figure 4 for cross section at Sta 0+380 The mesh consists of 87 nodes of which 20 are fixed and 73 isoparametric 4-noded quadrilateral eleshyments resulting in a total number of 2x (87-20) = 134 unknown degrees of freedom The numerical integration rules employed are as discussed in Section 2 Material properties used are as summarized in Tables 3 and 4

Initial stresses are required as input data to enable complete definition of initial states of stress and their positions relative to the corresponding yield surfaces Initial stresses are due to both the dams self weight and hydrostatic pressure acting normal to the upstream face of the dam as the reservoir was filled to design capacity

Table 3 Caliraya Earth FillDam

Compressibility amp Creep Parameters

1 SwellingRecompression Index Cam Clay Index X 043 Cr

Cr 00250 00109

2 Virgin Compression Index Cam Clay Index -shy 043 Cc

Cc 02500 01090

3 Secondary Compression Index Natural Log Index lj 043 Ca

C a 00067 00029

4 Average Void Ratio at p = 1 tonsqm on the isotropic consolidation line 155

Tab Ie 4

Caliraya Earth Fill Dam Strength Parameters

Type of Test Friction Angle dJ deg

Cohesion C tonssqm

1 UU 25 4 9

2 CU 15 10 6

3 CD 18 62

To obtain the self weight-induced stresses an elastostatic analysis was performed using an average soil unit weight of 1 76 tonssqm (standard deviation 016 tonsqm from lab test reshySUlts) Superimposing the additional stresses due to hydrostatic pressure as the reservoir was filled to Elev 288 the total principal stresses and their directions are as depicted in Figure 5

64

1

Discussion of Results

movement due to creep Under sustained initial stresses resulting from gravity and loads finite element was a Ilowed to creep according to the secondary compression

equation A com definition of all the com of creep strain was by employing normality rule on the same elli yield surfaces as in the ti plasticity model

Figure 6 illustrates the d ent due to creep to develop over the next forty year A maximum crest settlement of about 10 centimeters can be seen from this e

A time history of movement due to creep of a at the center of the dams crest is also plotted in Figure 6 As a on the correctness of the above the soil was assumed to have aged tv 40 years from the time that the dam was completed Over the next

40 years the settlement duemiddot secondary compression of a dam 45 meters high is estimated to

6t yCex ( 1 +- ) x 450 meterOy 109101 + e tv

00067 400 10 ( 1 + ) x 450

1 + 10 400

0050 meter

With movements due to shearing distortion still to be included the above check verifies the premiddot dicted settlement of 010 meter obtained from the computer analysis

2 Cyclic movements due to drawdown and filling High and low water elevation of 289 m and 286 m vely were recorded for Lake during the period ry 1983 to

1984 Choosing Elev 288 m as a reference elevation predicted displacement profiles due to reservoir

drawdown and fil are as plotted in Fig 7 results of 7 were obtained from elastic with elastic constants derived from the Cam Clay As permanent strains are to become reasonably small after several a stable hysteresis loop was

assumed It can be seen from Fig 7 that a maximum displacement of about 1 cm is likely to occur in the

neighborhood of nodes 19 and 21 as the water elevation fluctuates from Elev 286 to Elev 289 This movement is considered small to cause serious cracking in the dams u concrete provided that the drawdownfilling rates are slow

I

t I

1shy

J

+ + + +

DAM STRESS SCALE SCALE

TONSM2

METERS

Figure 5 Dam Total and Directions

65

E n l-Z w I III U laquo l Il It)

i5 Il w w a u l

05

19650 0 laquo 10

DAM DISPLACEMENTS SCALE SCALE

I I I t--I---i o 5 10 15 METERS 0 01 02 METER

100 1000 TIME AFTER DAMS COMPLETION YRS

Figure 6 Caliraya Dam I_U-LIU Creep Displacement ProfIle

I

FILLING TO l EL289--=_1REFERENCE

PROFILE

~-~

I

DISPLACEMENTS DAM SCALE SCALE

--+--1 o 001 002 METER o 5 10 15 METERS

Figure 7 Caliraya Dam Cyclic Movement Due to Reservoir Drawdown Filling

CONCLUDING REMARKS

This paper demonstrates the litymiddot of the finite element method in the solution of

typical boundary value problems in geotechnical engineering

Although the results in this paper were establ ished a priori and remain subject to

verification by actual field instrumentation it was demonstrated that the above numerical method

can be useful in accounting for complex factors such as material nonlinearities and nonmiddot

ies into the solution

ACKNOWLEDGMENT

The author wishes to thank Salvador F Reyes of the Department of Civil Engineering Un of the Phil for his helpful comments and suggestions Funding for these studies was provided by the National Power of the Phil on a joint AmbuklaoCaliraya remedial project research

REFERENCES 1 BORJA R1 and KAVAZANJIAN E JR (1 A constitutive model for the stress-strainshy

time behavior of wet No3

2 FUCIK EM and EDBROOK RF (1958) Ambuklao rock-fill dam and Journal of the Soil Mechanics and Foundation Division vol 84 No pp 1864-1

to 1864-22

3 LAMBE TW and WH ITMAN RV (19691 Soil Mechanics Wiley New York

4 OWEN D R J and HINTON E (19801 Finite Elements in Plasticity Theory and Pi Press Limited UK

5 ROSCOE KH and BURLAND JB (1 On the generalized stress-strain behavior of wet clays Engineering Plasticity Cambridge pp

67

Numerical Solution

The finite element program used in the analysis is a module of SPIN 20 which performs the time integration of (11) by the conventional incremental theory of plasticity

The finite element mesh for the dam is shown in Figure 4 for cross section at Sta 0+380 The mesh consists of 87 nodes of which 20 are fixed and 73 isoparametric 4-noded quadrilateral eleshyments resulting in a total number of 2x (87-20) = 134 unknown degrees of freedom The numerical integration rules employed are as discussed in Section 2 Material properties used are as summarized in Tables 3 and 4

Initial stresses are required as input data to enable complete definition of initial states of stress and their positions relative to the corresponding yield surfaces Initial stresses are due to both the dams self weight and hydrostatic pressure acting normal to the upstream face of the dam as the reservoir was filled to design capacity

Table 3 Caliraya Earth FillDam

Compressibility amp Creep Parameters

1 SwellingRecompression Index Cam Clay Index X 043 Cr

Cr 00250 00109

2 Virgin Compression Index Cam Clay Index -shy 043 Cc

Cc 02500 01090

3 Secondary Compression Index Natural Log Index lj 043 Ca

C a 00067 00029

4 Average Void Ratio at p = 1 tonsqm on the isotropic consolidation line 155

Tab Ie 4

Caliraya Earth Fill Dam Strength Parameters

Type of Test Friction Angle dJ deg

Cohesion C tonssqm

1 UU 25 4 9

2 CU 15 10 6

3 CD 18 62

To obtain the self weight-induced stresses an elastostatic analysis was performed using an average soil unit weight of 1 76 tonssqm (standard deviation 016 tonsqm from lab test reshySUlts) Superimposing the additional stresses due to hydrostatic pressure as the reservoir was filled to Elev 288 the total principal stresses and their directions are as depicted in Figure 5

64

1

Discussion of Results

movement due to creep Under sustained initial stresses resulting from gravity and loads finite element was a Ilowed to creep according to the secondary compression

equation A com definition of all the com of creep strain was by employing normality rule on the same elli yield surfaces as in the ti plasticity model

Figure 6 illustrates the d ent due to creep to develop over the next forty year A maximum crest settlement of about 10 centimeters can be seen from this e

A time history of movement due to creep of a at the center of the dams crest is also plotted in Figure 6 As a on the correctness of the above the soil was assumed to have aged tv 40 years from the time that the dam was completed Over the next

40 years the settlement duemiddot secondary compression of a dam 45 meters high is estimated to

6t yCex ( 1 +- ) x 450 meterOy 109101 + e tv

00067 400 10 ( 1 + ) x 450

1 + 10 400

0050 meter

With movements due to shearing distortion still to be included the above check verifies the premiddot dicted settlement of 010 meter obtained from the computer analysis

2 Cyclic movements due to drawdown and filling High and low water elevation of 289 m and 286 m vely were recorded for Lake during the period ry 1983 to

1984 Choosing Elev 288 m as a reference elevation predicted displacement profiles due to reservoir

drawdown and fil are as plotted in Fig 7 results of 7 were obtained from elastic with elastic constants derived from the Cam Clay As permanent strains are to become reasonably small after several a stable hysteresis loop was

assumed It can be seen from Fig 7 that a maximum displacement of about 1 cm is likely to occur in the

neighborhood of nodes 19 and 21 as the water elevation fluctuates from Elev 286 to Elev 289 This movement is considered small to cause serious cracking in the dams u concrete provided that the drawdownfilling rates are slow

I

t I

1shy

J

+ + + +

DAM STRESS SCALE SCALE

TONSM2

METERS

Figure 5 Dam Total and Directions

65

E n l-Z w I III U laquo l Il It)

i5 Il w w a u l

05

19650 0 laquo 10

DAM DISPLACEMENTS SCALE SCALE

I I I t--I---i o 5 10 15 METERS 0 01 02 METER

100 1000 TIME AFTER DAMS COMPLETION YRS

Figure 6 Caliraya Dam I_U-LIU Creep Displacement ProfIle

I

FILLING TO l EL289--=_1REFERENCE

PROFILE

~-~

I

DISPLACEMENTS DAM SCALE SCALE

--+--1 o 001 002 METER o 5 10 15 METERS

Figure 7 Caliraya Dam Cyclic Movement Due to Reservoir Drawdown Filling

CONCLUDING REMARKS

This paper demonstrates the litymiddot of the finite element method in the solution of

typical boundary value problems in geotechnical engineering

Although the results in this paper were establ ished a priori and remain subject to

verification by actual field instrumentation it was demonstrated that the above numerical method

can be useful in accounting for complex factors such as material nonlinearities and nonmiddot

ies into the solution

ACKNOWLEDGMENT

The author wishes to thank Salvador F Reyes of the Department of Civil Engineering Un of the Phil for his helpful comments and suggestions Funding for these studies was provided by the National Power of the Phil on a joint AmbuklaoCaliraya remedial project research

REFERENCES 1 BORJA R1 and KAVAZANJIAN E JR (1 A constitutive model for the stress-strainshy

time behavior of wet No3

2 FUCIK EM and EDBROOK RF (1958) Ambuklao rock-fill dam and Journal of the Soil Mechanics and Foundation Division vol 84 No pp 1864-1

to 1864-22

3 LAMBE TW and WH ITMAN RV (19691 Soil Mechanics Wiley New York

4 OWEN D R J and HINTON E (19801 Finite Elements in Plasticity Theory and Pi Press Limited UK

5 ROSCOE KH and BURLAND JB (1 On the generalized stress-strain behavior of wet clays Engineering Plasticity Cambridge pp

67

1

Discussion of Results

movement due to creep Under sustained initial stresses resulting from gravity and loads finite element was a Ilowed to creep according to the secondary compression

equation A com definition of all the com of creep strain was by employing normality rule on the same elli yield surfaces as in the ti plasticity model

Figure 6 illustrates the d ent due to creep to develop over the next forty year A maximum crest settlement of about 10 centimeters can be seen from this e

A time history of movement due to creep of a at the center of the dams crest is also plotted in Figure 6 As a on the correctness of the above the soil was assumed to have aged tv 40 years from the time that the dam was completed Over the next

40 years the settlement duemiddot secondary compression of a dam 45 meters high is estimated to

6t yCex ( 1 +- ) x 450 meterOy 109101 + e tv

00067 400 10 ( 1 + ) x 450

1 + 10 400

0050 meter

With movements due to shearing distortion still to be included the above check verifies the premiddot dicted settlement of 010 meter obtained from the computer analysis

2 Cyclic movements due to drawdown and filling High and low water elevation of 289 m and 286 m vely were recorded for Lake during the period ry 1983 to

1984 Choosing Elev 288 m as a reference elevation predicted displacement profiles due to reservoir

drawdown and fil are as plotted in Fig 7 results of 7 were obtained from elastic with elastic constants derived from the Cam Clay As permanent strains are to become reasonably small after several a stable hysteresis loop was

assumed It can be seen from Fig 7 that a maximum displacement of about 1 cm is likely to occur in the

neighborhood of nodes 19 and 21 as the water elevation fluctuates from Elev 286 to Elev 289 This movement is considered small to cause serious cracking in the dams u concrete provided that the drawdownfilling rates are slow

I

t I

1shy

J

+ + + +

DAM STRESS SCALE SCALE

TONSM2

METERS

Figure 5 Dam Total and Directions

65

E n l-Z w I III U laquo l Il It)

i5 Il w w a u l

05

19650 0 laquo 10

DAM DISPLACEMENTS SCALE SCALE

I I I t--I---i o 5 10 15 METERS 0 01 02 METER

100 1000 TIME AFTER DAMS COMPLETION YRS

Figure 6 Caliraya Dam I_U-LIU Creep Displacement ProfIle

I

FILLING TO l EL289--=_1REFERENCE

PROFILE

~-~

I

DISPLACEMENTS DAM SCALE SCALE

--+--1 o 001 002 METER o 5 10 15 METERS

Figure 7 Caliraya Dam Cyclic Movement Due to Reservoir Drawdown Filling

CONCLUDING REMARKS

This paper demonstrates the litymiddot of the finite element method in the solution of

typical boundary value problems in geotechnical engineering

Although the results in this paper were establ ished a priori and remain subject to

verification by actual field instrumentation it was demonstrated that the above numerical method

can be useful in accounting for complex factors such as material nonlinearities and nonmiddot

ies into the solution

ACKNOWLEDGMENT

The author wishes to thank Salvador F Reyes of the Department of Civil Engineering Un of the Phil for his helpful comments and suggestions Funding for these studies was provided by the National Power of the Phil on a joint AmbuklaoCaliraya remedial project research

REFERENCES 1 BORJA R1 and KAVAZANJIAN E JR (1 A constitutive model for the stress-strainshy

time behavior of wet No3

2 FUCIK EM and EDBROOK RF (1958) Ambuklao rock-fill dam and Journal of the Soil Mechanics and Foundation Division vol 84 No pp 1864-1

to 1864-22

3 LAMBE TW and WH ITMAN RV (19691 Soil Mechanics Wiley New York

4 OWEN D R J and HINTON E (19801 Finite Elements in Plasticity Theory and Pi Press Limited UK

5 ROSCOE KH and BURLAND JB (1 On the generalized stress-strain behavior of wet clays Engineering Plasticity Cambridge pp

67

E n l-Z w I III U laquo l Il It)

i5 Il w w a u l

05

19650 0 laquo 10

DAM DISPLACEMENTS SCALE SCALE

I I I t--I---i o 5 10 15 METERS 0 01 02 METER

100 1000 TIME AFTER DAMS COMPLETION YRS

Figure 6 Caliraya Dam I_U-LIU Creep Displacement ProfIle

I

FILLING TO l EL289--=_1REFERENCE

PROFILE

~-~

I

DISPLACEMENTS DAM SCALE SCALE

--+--1 o 001 002 METER o 5 10 15 METERS

Figure 7 Caliraya Dam Cyclic Movement Due to Reservoir Drawdown Filling

CONCLUDING REMARKS

This paper demonstrates the litymiddot of the finite element method in the solution of

typical boundary value problems in geotechnical engineering

Although the results in this paper were establ ished a priori and remain subject to

verification by actual field instrumentation it was demonstrated that the above numerical method

can be useful in accounting for complex factors such as material nonlinearities and nonmiddot

ies into the solution

ACKNOWLEDGMENT

The author wishes to thank Salvador F Reyes of the Department of Civil Engineering Un of the Phil for his helpful comments and suggestions Funding for these studies was provided by the National Power of the Phil on a joint AmbuklaoCaliraya remedial project research

REFERENCES 1 BORJA R1 and KAVAZANJIAN E JR (1 A constitutive model for the stress-strainshy

time behavior of wet No3

2 FUCIK EM and EDBROOK RF (1958) Ambuklao rock-fill dam and Journal of the Soil Mechanics and Foundation Division vol 84 No pp 1864-1

to 1864-22

3 LAMBE TW and WH ITMAN RV (19691 Soil Mechanics Wiley New York

4 OWEN D R J and HINTON E (19801 Finite Elements in Plasticity Theory and Pi Press Limited UK

5 ROSCOE KH and BURLAND JB (1 On the generalized stress-strain behavior of wet clays Engineering Plasticity Cambridge pp

67

ACKNOWLEDGMENT

The author wishes to thank Salvador F Reyes of the Department of Civil Engineering Un of the Phil for his helpful comments and suggestions Funding for these studies was provided by the National Power of the Phil on a joint AmbuklaoCaliraya remedial project research

REFERENCES 1 BORJA R1 and KAVAZANJIAN E JR (1 A constitutive model for the stress-strainshy

time behavior of wet No3

2 FUCIK EM and EDBROOK RF (1958) Ambuklao rock-fill dam and Journal of the Soil Mechanics and Foundation Division vol 84 No pp 1864-1

to 1864-22

3 LAMBE TW and WH ITMAN RV (19691 Soil Mechanics Wiley New York

4 OWEN D R J and HINTON E (19801 Finite Elements in Plasticity Theory and Pi Press Limited UK

5 ROSCOE KH and BURLAND JB (1 On the generalized stress-strain behavior of wet clays Engineering Plasticity Cambridge pp

67