finite element studies of ambuklao and caliraya dam
DESCRIPTION
Published in the Philippine Engineering Journal 1986,TRANSCRIPT
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
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
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
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
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
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