Full paper

DAM ENGINEERING Vol XXIV Issue 1 19

Impact of Near-Fault vs. Far-Field GroundMotions on the Seismic Response of an Arch

Dam with Respect to Foundation Type

M A Hariri-Ardebili(1) and V E Saouma(2)

ABSTRACT

In the present paper, the impact of input ground motion characteristics on the seismic

response of a typical concrete arch dam has been investigated by relying on the foundation

numerical model. For this purpose six ground motions, including near-fault and far-field

recordings, with various characteristics in the acceleration response spectrum, have been

used to analyze the coupled system. Three different options have been introduced for the

dam-foundation interaction: 1) foundation rock is assumed to be rigid; 2) foundation rock is

modelled as a massless medium; and 3) a massed foundation is assumed with the inclusion

of infinite elements at the far-end boundaries. The reservoir medium is assumed to be

compressible, and has been modelled according to the Eulerian approach. It has also been

observed that modelling the foundation as a massed element decreases stresses relative to the

massless model, while use of a rigid foundation model leads to stress concentration at the

dam-foundation interface. In all these foundation types, near-fault ground motions have led

to higher responses than far-field motions, especially for the upper parts of the dam body,

with less scattering of results in far-field ground motion.

Keywords: Dam-foundation interaction, near-fault ground motion, massed foundation,

seismic performance evaluation.

1. INTRODUCTION

Dams are complex infrastructures, and their behaviour depends on various parameters and

parametric combinations. Chopra[1] proposed a set of factors that significantly influence the

3D numerical analysis of arch dams. These factors consist of: the semi-unbounded size of the

reservoir and foundation rock domains; dam-water interaction; wave absorption at the

reservoir boundary; water compressibility; dam-foundation-rock interaction; and spatial

variations in ground motion at the dam-rock interface.

(1)Ph.D. Student, Email: [email protected]; (2)Professor, Email: [email protected]; Department

of Civil, Environmental & Architectural Engineering, University of Colorado at Boulder, Boulder, CO, US.

Saouma paper publish:. 17/12/13 11:34 9

DAM ENGINEERING Vol XXIV Issue 120

In considering the complex nature of materials and loads, as well as their interaction in a

coupled dam-reservoir-foundation system, either all sources of system non-linearities should

be considered, or they should all be neglected in favour of analyzing the system based on a

linear elastic assumption of materials, which entails use of the appropriate toolset in order to

interpret results.

In the present paper a typical double curvature arch dam will be studied for the purpose

of investigating the influence of the foundation numerical model, and its boundary

conditions, on the seismic response of the system when subjected to both near-fault and

far-field ground motions. Various types of foundation models, i.e. rigid, massless and

massed foundations, will be used in the finite element model of a dam-reservoir-foundation

system.

Moreover, a set of site-specific ground motions with a range of characteristics (near-fault

and far-field) will be introduced to determine the effects of seismic input mechanisms on the

safety evaluation of dams. A straightforward methodology will be proposed in an effort to

systematize the seismic assessment of concrete dams.

Lastly, the results will be compared in terms of stresses, displacement and demand-capacity

ratios. In addition the effects of seismic input for arch dams, in terms of ground motion

components, rotation and spatial permutations, will all be examined.

2. LITERATURE REVIEW

Many researchers have investigated past efforts to model both the dam-foundation interaction

and dam-foundation dynamic responses that incorporate various boundary conditions.

Researchers such as Chopra & Chakrabarti[2], Fenves & Chopra[3] and Leger &

Boughoufalah[4], have all studied the importance of the foundation interaction with respect to

the seismic behaviour of dams.

Nuss et al[5], Chopra[1] and Chopra & Nuss[6] all concluded that if only the foundation rock

flexibility is taken into consideration in numerical models, then stresses would be overestimated

for all cases, in comparison with the massed foundation model.

Bayraktar et al[7] analyzed the effect of base-rock characteristics on the stochastic

dynamic response of dam-reservoir-foundation systems subjected to different earthquake

input mechanisms. Lemos & Gomes[8] investigated the failure mechanism of the foundation

in a concrete dam, and demonstrated that if the numerical analysis included the failure of

either the rock joints or the foundation interface, then the inertial behaviour of the rock

should be taken into consideration. Moreover, the boundaries at the top and sides of the

model must be able to simulate energy radiation into the far-field, while the bottom boundary

is assigned as a non-reflecting boundary.

These authors also reported that both the experimental (i.e. shaking table test) and

numerical displacements of a point in the middle of the dam block show good agreement.

Qiumei et al[9] performed seismic analyses on reinforcement concrete gravity dams subjected

M A HARIRI-ARDEBILI AND V E SAOUMA

Saouma paper publish:. 17/12/13 11:34 0


to near-field, pulse-like ground motions using a massless foundation. They found that the

principal stress and displacement of all the specified points with a pulse-like ground

motion were greater than those obtained without using any such motion.

Zhang et al[10] studied two different models: a massless foundation model, and a viscous-

spring boundary input model that incorporates radiation damping. The responses of the 3D

canyon without the dam were first analyzed using a massless truncated foundation along

with a viscous-spring boundary; in a subsequent step, linear and non-linear analyses of the

dam-foundation system were conducted. The authors concluded that stresses, displacements

and contraction joint openings are all significantly reduced for both the linear and non-linear

analyses when using the viscous-spring boundary model.

Bayraktar et al[11] and Akköse et al[12] compared near-fault and far-field ground motion

effects on the non-linear response of dam-reservoir massless foundation systems; they found

a greater seismic demand on stresses and displacements when the dam is subjected to

near-fault ground motion. Saleh & Madabhushi[13] examined the dynamic response of dams

on rigid soil foundations, in addition to the resulting hydrodynamic pressure on the dam

face, according to the dynamic centrifuge modelling technique. They determined that including

a flexible foundation significantly reduces the dynamic response of the dam.

Lebon et al[14] focused on the 3D non-linear rock-dam seismic interaction, by considering

various soil-structure interaction models based on the finite element approach. Saouma et al[15]

investigated the 2D and 3D time-history finite element analysis of rock-structure interactions

by considering lateral energy dissipation, and the interaction between the far-field and actual

numerical model. This approach is quite straightforward, and makes use of the principle of

virtual work for deriving the transferred damping and stiffness matrices.

Chen et al[16] assessed the influence of damping on the seismic response analysis of an arch

dam. They found that the damping ratio greatly influenced the seismic response of an arch

dam when applying a massless foundation model; their work also identified good agreement

between the results of this viscous-spring boundary input model, and the output from the

massless foundation model with a 10% damping ratio.

Hariri-Ardebili & Mirzabozorg[17] targeted the non-linear dynamic analysis of a coupled

system, featuring a reservoir-dam-foundation in 3D space, using the smeared crack

approach. The foundation was assumed to be massed, while infinite elements at the far-end

boundary and viscous boundary conditions were input to model the foundation medium. It

was found that the response of a system with massed foundations, including infinite elements,

is identical to that when the artificial absorbing boundary on the far-end of the foundation

has been modelled using a viscous boundary.

In another vein the seismic performance and safety evaluation of hydraulic structures were

investigated by, among others, Ghanaat[18] and Yamaguchi et al[19]. Ghanaat proposed a

damage estimation methodology for concrete dams that was adopted in guidelines published

by USACE[20], which suggests a systematic method based on linear time-history results in

terms of both local and global performance indices.

IMPACT OF NEAR-FAULT VS. FAR-FIELD GROUND MOTIONS ON THE SEISMIC

RESPONSE OF AN ARCH DAM WITH RESPECT TO FOUNDATION TYPE

Saouma paper publish:. 17/12/13 11:34 Page 21


Hariri-Ardebili & Mirzabozorg[21] studied the seismic performance of concrete arch dams

using real ground motions, as well as Endurance Time Acceleration Functions (ETAFs); they

found ETAFs to be capable of identifying various performance levels with acceptable accuracy.

3. MODELLING THE DAM-RESERVOIR INTERACTION

Modelling the fluid-structure interaction and hydrodynamic pressure on concrete dams was

first attempted by UC Berkeley’s Chopra research team[22-25]. The hydrodynamic pressure

distribution in reservoirs is governed by the pressure wave equation. By assuming that water

is linearly compressible, and neglecting viscosity, the small amplitude irrotational motion of

water is governed by the following 3D wave equation[26]:

(1)

where P is the hydrodynamic pressure, and c0 is the pressure wave velocity in water.

For earthquake excitation, the boundary conditions of reservoir water can be summarized

as follows: at the fluid-structure surface (i.e. dam-reservoir boundary condition), no flow can

cross the interface. This condition is based on the fact that the face of concrete dams is

impermeable. In the following equation, superscript “s” refers to the structure:

(2)

where as is the normal acceleration of the dam body on the upstream face, n is the normal

vector on the dam-reservoir interface towards the outer side of the dam body, and ρw is thereservoir water density.

If no energy is being absorbed on the reservoir bottom, then the same boundary condition

represented in Equation 2 can be used for the foundation-reservoir boundary; however, due

to sediment and energy absorption at the reservoir bottom, the boundary condition can be

rewritten as follows:

(3)

where α is the wave reflection coefficient at the reservoir bottom and sides.In high dams surface waves are negligible, and hydrodynamic pressure on the free surface

is set to zero. For modelling of the far-end truncated boundary a viscous boundary condition

(referred to as the Sommerfeld boundary condition) is employed, in order to completely

absorb the outgoing pressure waves:


n



(4)

4. MODELLING THE DAM-FOUNDATION INTERACTION

As previously mentioned, three types of foundations with different characteristics and boundary

conditions have been examined in the present paper. The rigid foundation model, which

neglects the dam-foundation interaction, as well as both the foundation material stiffness

and mass, is introduced into the overall coupled equation of motion. In the conventional

massless foundation model only flexibility (stiffness) of the foundation finite element model

is taken into account in setting up the coupled system equation. An appropriate volume of

foundation rock must be included in the dam model to account for the effects of foundation

flexibility[27]. Also, the foundation model should extend out to a distance beyond which its

effects on dam deflections and stresses become negligible.

A prismatic foundation mesh constructed on semi-circular planes can typically be

employed[27], along with smaller elements near the dam-foundation contact region where the

largest deformations and stresses occur. In contrast, larger elements are used away from the

dam where interaction with the dam is reduced. According to the standard massless

foundation model, the volume of the foundation rock region extends a distance equal to one

or two dam heights in the upstream, downstream and downward directions. Since wave

propagation is neglected in this model, all nodes on the exterior surfaces of the foundation

mesh are fixed in space, as shown in Figure 1a.

The last type of foundation is massed, and includes appropriate boundary conditions at the

far-end, in order to absorb outgoing waves. The most famous artificial boundary condition at

the far-end boundaries of a foundation medium is known to be the viscous boundary (Figure

1b), which generally uses three orthogonal dampers in all exterior nodes of the foundation

model for energy absorption[28]:

(5)

where tn and ts are the normal and shear tractions respectively; u, v, and w are the normal

and two tangential particle velocities at the boundary, ρf is the foundation mass density, VSand VP are the shear and pressure wave velocities at the foundation medium and, lastly, a1,

a2 and a3 are dimensionless numbers.

It was determined that setting these parameters equal to unity on the far-end boundary of

the foundation led to the highest efficiency in absorbing the outgoing seismic waves[28].

Radiation damping can thus be derived from Equation 5, and applied to the far-end boundary

of the foundation using lumped dashpots, which are added to the global damping matrix of

the structure as follows:



. . .



(6)

where Cni and Cs

i are the damping factors in the normal and tangential directions respectively,

and Ni is the element shape function.


(a) (b)

(c)

Figure 1. a) Standard massless foundation model; b) massed foundation with viscous boundaries;c) massed foundation with infinite elements



This solution is exact if the P and S waves both impinge the artificial boundary at

right angles. These are only approximate solutions for inclined body waves, whose

reflected energy is only a small proportion of the total energy. In many cases, the further

the artificial boundary is chosen from a source that radiates waves, the more the angle of

incidence with respect to the artificial boundary will approach 90º and, hence, the better

the viscous dampers will perform[15].

The other way to prevent wave reflection at the artificial boundary is by introducing infinite

elements at the foundation exterior (Figure 1c). The use of infinite elements, stiffness and

damping pertinent to the semi-infinite medium via the artificial boundary of the structure, has

been incorporated into these analyses. The basic idea behind infinite elements is to allow the

use of elements with special shape functions for the geometry at the far-end truncated boundary.

Two sets of shape functions will therefore be applied: the standard shape function, Ni; and a

growth shape function, Mi, which grows without a bound as the coordinate of the ith node

approaches infinity. The Ni functions are applied to field variables[17], while Mi is applied to the

geometry. These Mi shape functions, and their derivatives, are presented in Table 1 for a

20-node solid element with a face in infinity (Figure 1c). The effect of a semi-infinite medium

via the far-end boundary of the foundation is taken into account once the resultant stiffness

matrices, and their related proportional damping matrices, have been assembled into both the

global stiffness matrix and global damping matrix of the system.

The stiffness matrix of infinite elements is calculated as follows:

(7)

where ξ, η, and ζ constitute the local coordinate system of the infinite elements, [J] is theJacobian matrix, and [B] is the matrix transforming the nodal displacement of the consideredelement into the Gaussian point strains within the element, given as:

(8)

(9)





5. COUPLED MOTION EQUATION SYSTEM

The equations of the dam-foundation (as the structure) and reservoir take the following form:

(10)

where [M], [C] and [K] are the mass, damping and stiffness matrices of the structure (inthe case of a massless foundation, the stiffness matrix includes both dam and foundation

properties, and the mass matrix includes only the dam body, while the massed foundation

model uses both dam and foundation characteristics in [M] and [K] matrices). [G], [C’]and [K’] are matrices representing the mass, damping and stiffness equivalent matricesof the reservoir, respectively. Matrix [Q] is the coupling matrix; {f1} is the vector thatincludes both the body and hydrostatic force; {P} and {U} are the hydrodynamic pressureand displacement vectors, respectively; and {Ug} is the ground acceleration vector. Adetailed definition of all these matrices and vectors is available in published literature by

Mirzabozorg et al[26].


..

Table 1. Growth shape functions, and their derivatives, for one face in infinity



6. NUMERICAL MODEL OF THE COUPLED SYSTEM

The Karaj Dam in Iran was selected as the case study herein, in order to investigate the

effects of foundation modelling on the structural response of arch dams. This dam offers a

symmetric double curvature; its crest is 390m long, and it extends a height of 168m above

the foundation. A general view of Karaj Dam is displayed in Figure 2a. The dam structure

and foundation medium have been modelled using 20-node isoparametric elements. The

radius of the foundation region, which was modelled in a semi-spherical shape, was set at

330m, with the centre of the semi-spherical body located at the middle of the dam body

crest. The reservoir was simulated using 8-node isoparametric fluid elements, extending

roughly twice the height of the dam body in the upstream direction. The finite element

model of the dam-reservoir-foundation system is shown in Figure 2b.

Due to the inherent rate dependence of the mechanical and strength properties of mass

concrete[20], the dynamic properties differ from the static properties as follows: the modulus

of elasticity, Poisson’s ratio, and tensile and compressive strength of mass concrete under

static and dynamic conditions are equal to 26GPa, 32GPa, 0.17, 0.13, 3.66MPa, 5.00MPa,

37.0MPa and 50.0MPa, respectively. In addition, the mass concrete density is 2450kg/m3.

The static and dynamic modulus of deformation of the foundation is set at 16.3GPa, and

the Poisson’s ratio equals 0.15. The pressure wave propagation velocity and density of

water equal 1436m/sec and 1000kg/m3, respectively. The mass and stiffness proportional

damping is applied on the structure, whose damping ratio for the fundamental mode has

been selected to be 5%. For the non-linear failure analysis of concrete dams it is possible to

use the quasi-linear damping mechanism, which may be updated during the seismic analysis

based on the instantaneous stiffness matrix of the dam body.

The Karaj Dam, also known as the Amirkabir Dam, is located 63km northwest of Tehran,

the Iranian capital, and 23km north of the city of Karaj in the Alborz Mountains. The

Alborz seismic zone contains a high density of active faults. Since many of the region’s

earthquakes have not been associated with surface faulting and, moreover, since the

meizoseismal areas of many of these earthquakes are relatively extensive, locating the active

fault becomes a complicated task. The largest faults on the southern edge of the Alborz

range are the North Tehran fault, Mosha fault, North Qazvin fault, and Damghan fault[29].

Figure 3 presents the seismotectonic map of the Central Alborz region, including the Karaj

Dam[30]. As is visible in this figure a contractional fault crosses very close to the dam, and

another crosses at the middle of the reservoir. The largest fault, however, is Mosha to the

north of the dam and reservoir. A preliminary paleoseismological study encompassing the

Mosha fault has indicated a minimal left-lateral component of 2 ± 0.1mm/yr for theHolocene period. Assuming a characteristic coseismic average displacement lying between

0.35m (Mw 6.5, a 1665 event) and 1.2m (Mw 7.1, an 1830 event), by using the moment

magnitudes assigned to these two earthquakes Ritz et al[31] estimated mean maximum

recurrence intervals along this portion of the Mosha fault of 160 and 620 years.






(a)

(b)

Figure 2. a) General view of Karaj Dam; b) finite element model of the dam-reservoir-masslessfoundation system



7. VERIFICATION OF THE INFINITE ELEMENT APPROACH

This section will compare the results of the dam-foundation-reservoir system using conventional

viscous boundary conditions, with those of the infinite elements on the exterior boundaries

of the foundation medium. The coupled system is excited using both real ground motion[17],

and an intensifying step-like acceleration function. Crest displacement in the stream direction

is compared for both cases; as observed in Figure 4, no noticeable differences exist between

the two models. Moreover, the maximum arch and cantilever stresses are nearly identical, as

previously reported by Hariri-Ardebili & Mirzabozorg[17].

It is worth noting that the major limitation of this viscous boundary method is the

frequency dependence of the damping coefficients; consequently, these coefficients can only

be used (or are more appropriately used) in frequency domain analyses, although they are

also often introduced in time domain analyses. Despite the viscous boundary model being

able to eliminate wave reflections, it does not necessarily account for the proper boundary

conditions in a way that simply assumes a linear shear strain variation and, moreover, these

reflections are, in turn, transformed into equivalent nodal forces to be applied in the numerical

model[15]. On the other hand, the infinite element method is completely compatible with the

time domain analysis; more specifically, this approach relies on a revised set of shape

functions to generate the foundation stiffness matrix.



Figure 3. Seismotectonic map of the Central Alborz region, including the Karaj Dam[30]



8. UNDAMPED COUPLED FREQUENCIES

This section will discuss the undamped modal responses of the arch dam-reservoir-foundation

system. The eigenvalue problem for the natural frequencies of an undamped finite element

model that includes fluid-structure interaction effects can be written as follows:

(11)


(a)

(b)

Figure 4. Comparison of the infinite element vs. viscous boundary approaches for: a) a one componentintensifying step-like acceleration function; b) a three component real ground motion



in which M and K are the mass and stiffness matrices, subscripts “s” and “f” refer to the

structure and fluid, respectively, and Sfs is the portion of the fluid domain boundary where

fluid medium motion is directly coupled to the motion of a structure.

On this boundary the fluid and structure have the same displacement normal to the

boundary, while the tangential motions are uncoupled. In this equation, both the stiffness

and mass matrices are asymmetric. Solving this last equation using Lanczos’ formulation, or

any other appropriate method able to solve the asymmetric coupled equation, yields the

undamped coupled frequencies of the dam-reservoir-foundation system.



Figure 5. a) Comparison of the undamped coupled dam modes; b) sample of key dam mode shapes

(a)

(b)



Figure 5 shows the vibration periods for the first 30 modes of the dam-reservoir system,

considering foundation effects. In addition, this figure depicts some of the selected dam

mode shapes on a rigid foundation. As observed in this figure, the massed foundation

model leads to higher periods than the massless foundation, and both models produce

higher values for the period than the rigid foundation model. It can be noted that based on

this figure, the influence of foundation on the period covering the first ten modes (T > 0.15sec)is more significant than the subsequent modes.

9. LOADING OF THE COUPLED SYSTEM

The loads applied to the system are: dam self-weight, hydrostatic pressure at normal water

level, earthquake loading, and resulting hydrodynamic pressure on the upstream face. It is

worth noting that water pressure due to tailwater on the downstream face of the dam has

been neglected. To investigate both the near-fault and far-field ground motion effects on the

seismic safety performance of concrete dams, three ground motions have been selected for

each group. The characteristics of these motions are listed in Table 2, which only shows the

major horizontal components of ground motion applied in the stream direction. The last row

of this table also contains the significant duration of each ground motion (in considering all

component effects), as calculated based on an Arias Intensity on Husid diagram.


Table 2. Characteristics of the near-fault and far-field ground motions



Acceleration and velocity time-histories of all scaled ground motions are depicted in Figure 6;

in addition, Figure 7 shows the horizontal acceleration response spectrum of the Karaj Dam site

(as a target spectrum) with a maximum credible level (MCL) obtained by conducting a hazard

analysis of the dam site. The ground motions have been scaled in order to provide acceptable

consistency to the target spectrum over a range of structural periods, Tmin to Tmax, as defined.

The dam’s small-amplitude fundamental period of vibration is denoted here by T1. Tmax is set

at 2T1, and Tmin should typically be set at 0.2T1. If a substantial response and damage can occur

due to responses in modes with periods shorter than Tmin, then Tmin should be selected sufficiently

small so as to capture this important behavioural pattern[32,33]. It is also worth pointing out that

the selected period range considers all effective modes contributing to the vibrational behaviour of

the dam (i.e. the contributed effective mass equals at least 90% of the total system mass).

For high concrete arch dams, setting the lower bound to 0.1sec is generally appropriate

for the purpose of spectrum matching[21,27]. Based on Figure 4, the value of T1 differs for the

various models. To achieve iso-intensity ground motions in all cases, the value of 0.45sec

was selected as the fundamental period; consequently, the values of Tmin and Tmax were

determined as 0.09sec and 0.9sec, respectively. As seen in Figure 6, an acceptable level of

consistency is reached between ground motions and target spectrum over both the selected

period range and fundamental period. The scaling factor is defined in a way that satisfies the

following equation within the selected period range:

(12)

where SaEQGM and SaTARGET are the acceleration response spectrum of selected ground motions

and (targeted) site spectrum, and ψ is the linear scaling factor for each ground motion.It is noted that other methods may be used to fit the ground motion response spectrum on the

target spectrum to any desired accuracy. However, these methods alter the intrinsic nature of

ground motion and additional corrections are usually required on the acceleration time-histories.

Based on Table 2, the originally selected near-fault ground motions are stronger than far-field

motions, yet comparing the PGV-to-PGA ratio for all ground motions reveals that this

ratio tends to be higher for far-field motions. All ground motions were proposed herein

for selection within the same magnitude range, i.e. M = 7.3 ± 0.4, and surface magnitude

range, i.e. Ms = 7.4 ± 0.4. Near-fault ground motions were also selected at a distance of

less than 12km from the centre of the rupture, while far-field motions were chosen to be

at a distance greater than 50km. From Figure 5, the original duration of near-fault

motions equals approximately 30-40sec, while their value reaches 60-130sec in far-field

motions. As previously mentioned, in order to reduce the computational effort for the

present case the significant ground motion duration was calculated based on 90% of

their total energy. This significant duration equals approximately 9-14sec in near-fault

and 30-31sec in far-field motions.



–





Figure 6. a) Scaled acceleration time-histories; b) scaled velocity time-histories for near-fault andfar-field ground motions

(a) (b)

Figure 7. Scaled acceleration response spectra of selected records based on the target spectrum



Figure 8 represents the general flowchart used in the present paper to conduct the seismic

safety assessment of a concrete dam, as based on USACE methodology[20]. This procedure

constitutes a standard method available for use with any other concept in dam engineering

for the purpose of assessing the seismic behaviour of a dam.

In this paper such a method has been combined with the concept of near-fault/far-field

ground motions, as well as with the foundation type effect. It is clearly apparent that this

methodology starts with a seismic hazard analysis of the dam site to identify the site’s

seismic characteristics along with the condition of the various faults, their activities,

maximum credible level, and a set of suitable near-fault and far-field ground motions for

seismic analyses.

Earthquake ground motions should be selected based on source characteristics, source-to-site

transmission path properties, and site conditions. Current practice usually dictates using at

least three ground motions and then taking their maximum results, or using up to seven

ground motions and taking their average responses. The finite element model of the

dam-reservoir-foundation system is then developed, based on previous instructions offered

for the various foundation types.

Three component ground motions (i.e. two horizontal and one vertical) are required

for 3D seismic analysis of arch dams. The structure must be capable of resisting maximum

earthquake ground motions occurring in any direction. In time-history analysis it may

be necessary to identify the stronger horizontal component in order to obtain the

highest-magnitude system response.

The orthogonal components of earthquake ground motion are commonly applied

along the principal axes of the structure[20], while the maximum response may occur in

any direction other than the principal axes. This effect can be determined from component

rotation, and may be significant in some cases, especially when the second ground

motion component is not as strong as the first, and when the arch dam is not symmetric

along the dam axis.

This effect is shown schematically in Figure 9, which also displays the maximum first

principal stress of the Karaj Dam under an N1 ground motion for the massless foundation

case, with the rotation of horizontal components. In this case, applying the orthogonal

components along the principal dam axes (x and y) leads to the generation of a maximum

first principal stress in the dam body equal to 3.96MPa, whereas applying ground motion

at an angle of θ = 45º with respect to the principal axes (x45 and y45) leads to a highermaximum first principal stress of approximately 4.59MPa. A θ = 315º angle of applicationwith respect to the principal axes (x315 and y315), yields a lower maximum first principal

stress (i.e. about 3.01MPa).

For 3D time-history analysis of arch dams a complete permutation of all three components,

with positive and negative signs, may be required to obtain the most critical directions causing

the greatest structural response[20]. Figure 10 shows the effects of considering all eight

permutations of an N1 ground motion on the massless foundation for both stress and




displacement responses. As can be observed, despite some differences between results, these

responses are negligible for the current case due to a completely symmetric dam. In this

figure, the displacement response differs for all load combinations, while the stress response

no longer seems to be sensitive to the direction of the second horizontal ground motion

component. This finding suggests that the load combinations are reduced to four different

cases under this condition. Let us note that in the present paper, the criterion for selecting a

critical direction (for both component rotations and permutations) consists of the higher

maximum first principal stress.

The last step entails scaling ground motions, based on the site response spectrum for the

predefined period range. This scaling step may be either linear, by means of multiplying the

ground motion response spectrum by a scalar factor that reasonably matches the target

spectrum, or non-linear by changing the original shape of the ground motion response

spectrum to better match the target spectrum, and then generating some kind of artificial

ground motion that uses the original motion. These scaled ground motions should then be

used for linear analysis of the coupled system, with all required results being extracted to

perform a seismic safety assessment of the dam. The most common required responses are:

displacement and tensile stress time-histories, cumulative inelastic duration (CID) for the

most critical node within the dam body, and a 20% limitation of the overstressed area (i.e.

the area where tensile stresses exceed the tensile strength of concrete) on both the upstream

and downstream faces.

The last two major criteria are shown in Figure 8. In these two plots the curve calculated

from our case study is compared with the threshold: the case is deemed to be safe if the

curve lies below the threshold[21].






Figure 8. General flowchart for the seismic safety assessment of concrete dams consideringvarious foundations and ground motion types





Figure 9. a) Rotational effect of horizontal ground motion components; b) variation inmaximum first principal stress due to N1 with respect to component rotation

(a)

(b)




Figure 10. Effects of considering permutations of all three earthquake components on:a) maximum first principal stress; b) displacement along the crest

(a)

(b)



10. RESULTS AND DISCUSSION

In this section the results obtained from the seismic analyses of the coupled system, considering

various foundation types, will be compared under near- and far-field ground motions. The

comparison of displacement time-histories for the crest point have been omitted, but the

non-concurrent envelope of displacement in the stream direction for the central cantilever is

shown in Figure 11.

Based on this figure the massless foundation leads to higher displacement values than the

massed foundation, with both values exceeding the rigid foundation displacement. An analysis

of the coupled system using the massless foundation model thus yields a more conservative

response than the actual massed foundation model. The rigid foundation model, considering

no relative displacement at the dam-foundation interfaces, would be expected to output

lower displacement values than the other two models.

In all cases near-fault ground motions generate greater responses than far-field motions,

especially over the upper half of the cantilever. The scaled near- and far-field ground motion

differences for the rigid foundation model are wider than either the massed or massless

foundation model.

Figure 11d shows the average displacement response for two types of ground motions.

The percentage difference at the crest point equals 57%, 38% and 31% for the rigid, massed

and massless foundation models, respectively. Generally speaking, far-field ground motions

produce results closer to each other than near-fault ground motions. The scattering of results

in near-fault ground motion is greater than that for far-field motion, yet still lies within an

acceptable range. For both massless and massed foundation models, N3 provides a greater

response than either N1 or N2, while in the rigid model (even though all ground motions

exhibit nearly the same crest point response), N1 leads to higher values than N3 or N2 over

the middle part of the cantilever.





Figures 12 to 14 present the non-concurrent envelope of maximum first principal stress

(MFPS), and minimum third principal stress (MTPS), on the upstream dam face for three

types of foundations. For the massless configuration, the higher MFPS values typically occur

on the lower parts of the upstream face near the foundation; moreover, these tensile stresses

are primarily characterized by cantilever stresses due to hydrodynamic pressure of the reservoir

being transferred to the bottom of the dam.

The upper part of the dam, near the crest, also experiences tensile stress (but less than the

bottom part), whose primary characteristic is the arch stresses due to the arch action of the

monolithic body. The central part of the dam generally exhibits low tensile stresses and, in

some cases, these parts are completely equivalent. The central and upper parts of the

upstream face have a higher compressive stress (in terms of MTPS); also, the central parts of

the downstream face, in the vicinity of the foundation (not shown in these figures), experience

high compressive stresses.


Figure 11. Non-concurrent envelope of displacement in the stream direction at the central cantilever for:a) massless foundation; b) massed foundation; and c) rigid foundation – d) shows the average results

(a) (b)

(c) (d)





Figure 12. Non-concurrent envelope of maximum first principal stress and minimum third principalstress on the upstream face for the massless foundation (Pa)




Figure 13. Non-concurrent envelope of the maximum first principal stress and minimum third principalstress on the upstream face for the massed foundation (Pa)





Figure 14. Non-concurrent envelope of the maximum first principal stress and minimum third principalstress on the upstream face for the rigid foundation (Pa)



Table 3 summarizes the MFPS and MTPS for all cases, along with their comparisons.

As can be seen in all cases, the rigid foundation model leads to higher MFPS and MTPS

values than the massless and massed models. In adopting the massed foundation model

as the basis, it can be concluded that using a massless foundation model leads to a difference

in the range of 17-20% under near-fault ground motions, and 21-28% under far-field

motions.

On the other hand, using a rigid foundation model increases the percentage of MFPS

differences to about 57-86% for near-fault motions, and 33-53% for far-field motions.

The percentage increase in compressive stress (in terms of MTPS), due to the use of a

massless foundation, amounts to about 13-20% and 16-24% for near- and far-field

ground motions, respectively, while these results equal 16-50% and 30-35% for the

rigid foundation model.

In all cases, the assumption of a massless foundation is closer to the benchmark model

(i.e. massed foundation) than the rigid foundation. The percentage error in the difference

between massless and massed foundation models under near-fault ground motions is less

than that under far-field motions for both MFPS and MTPS; in contrast, these results are

completely reversed for the percentage of difference between rigid and massed foundation

models (except for N3 ground motion, which produces a lower percentage of difference than

for far-field motions).

Table 3 also lists the values of the maximum demand-capacity ratio, DCRmax, for the

various models. Based on USACE guidelines[20] the dam response to MCE is assumed to

be linear elastic, with little or no possibility of damage if the computed DCR values are

less than or equal to 1. The amount of contraction joint opening at DCR ≤ 1 is expected,

however, to be small with negligible or no effect on the overall stiffness of the dam. The

dam is considered to exhibit a non-linear response, in the form of contraction joint

opening/closing, and lift line cracking provided the estimated DCR > 1. The level of non-linear

response or joint opening and cracking is deemed acceptable if DCR < 2, and the overstressed

region is limited to 20% of the dam surface area. For cases where DCR ≥ 2, the dam

body is expected to behave in a strong non-linear manner in terms of mass concrete damage

and/or permanent relative drifts between blocks.

Based on this table DCR > 1 in all cases, yet remains limited to 2 for the massless and

massed foundation cases, while approaching or even exceeding 2 for some ground motions

in the rigid foundation model. Using a massed foundation leads to lower DCRmax values,

in comparison with the massless foundation model. Comparing near-fault with far-field

ground motion effects on numerical models reveals that far-field motions tend to yield a

higher DCRmax than near-fault motions on both the massless and massed foundations. No

general rule is available for comparing ground motion type on the rigid foundation model,

though near-fault motions show a slightly higher value.

Figure 15 presents the percentage of the overstressed area of the dam under various

conditions, with respect to the pre-defined threshold curve proposed by USACE[20]. Even




though the demand curves for all models lie below the threshold curve, the rigid foundation

generally produces a greater overstressed area than either the massless or massed foundation

at various DCR values. Moreover, Figure 14d compares these curves for near- and far-ground

motion recordings. It is clearly apparent that the difference between these two types

remains small for massless and massed foundation models; nonetheless, near-fault

motions show a bigger jump than far-field motions for the rigid foundation model.



Table 3. Comparison of extreme stresses within the dam body for different cases



11. CONCLUSION

This paper has provided a discussion on foundation numerical models, i.e. massless, massed and

rigid models, relative to the seismic safety analysis of a dam-reservoir-foundation system.

Two sets of near- and far-field ground motions, consistent with the site characteristics of the

Karaj Dam in Iran, were chosen for the purpose of dynamic analysis. The results were compared

in terms of displacements, principal stresses and demand-capacity ratio for the dam.

The rotational effects of horizontal components were closely investigated for this specific

case. It was found that applying the orthogonal components at an angle of θ = 45º, withrespect to the principal axes, leads to an increase in the maximum first principal stress of

approximately 16% within the dam body. It was also determined that the current case is

rather insensitive to the component permutation rule.


Figure 15. Percentage of overstressed area on the dam face at various DCR values: a) masslessfoundation; b) massed foundation; c) rigid foundation – d) shows the average results

(a) (b)

(c) (d)



Based on the analyses conducted herein, the massless foundation yields higher displacement

values along the central cantilever of the dam than the massed foundation, with both these

values exceeding the rigid foundation displacement. In all foundation types, near-fault ground

motions lead to a greater response than those generated by far-field motions, especially over

the upper half of the cantilever. The scattering of results in near-fault ground motion is more

pronounced than that in far-field motion, yet remain within an acceptable range.

For the massless foundation, higher MFPS values typically occur at lower parts of the

upstream face, near the foundation. The central part of the dam generally exhibits very low

tensile stresses and, in some cases, these parts are completely equivalent. The central and upper

parts of the upstream face, and the central parts of the downstream face in the foundation

vicinity, revealed high compressive stresses.

For all ground motions, the rigid foundation model leads to higher MFPS and MTPS than

either the massless or massed models. The percentage differences between massless and

massed foundation models for stress response under near-fault ground motions is less than

the corresponding percentage differences under far-field motions, while these results are

completely reversed for the percentage differences between rigid and massed foundation

models, with the exception of N3 ground motion (which has a lower percentage of difference

than far-field motions).

Based on current research, DCRmax > 1 in all cases; however, it is limited to 2 for the massless

and massed foundation cases, while it approaches or even exceeds 2 for some ground motions in

the rigid foundation model. In contrast, the overstressed area demand curves lie below the

threshold curve in all ground motion cases. The rigid foundation tends to produce a greater

overstressed area than either the massless or massed foundation model at various DCR values.

It can be concluded that use of the massed foundation model with infinite elements at far-end

boundaries is more appropriate for simulating the seismic behaviour of arch dams than the

massless model. In addition, introducing a rigid foundation increases stresses within the dam

body, and would not be a suitable model for assessing the safety response of arch dams under

earthquake conditions.

Lastly, near-fault ground motions may generate different responses than conventional far-field

ground motions; hence their effects should be investigated separately should an active fault be

identified near a dam site, or should a new fault be detected after the construction of a dam.

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