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A dynamic analysis procedure for concrete-faced rockfill dams subjected to strong seismic excitation
Computers and Structures 72 (1999) 409±421
A dynamic analysis procedure for concrete-faced rock®ll dams subjected to strong seismic excitation Nasim Uddin Civil Engineering, University of Evansville, 1800 Lincoln Ave, Evansville, IN 47722, USA
Abstract There is presently little analytical and essentially no observational evidence on the behavior of the concrete-face of the very popular concrete-faced rock®ll (CFR) dams during strong seismic shaking. The choice of slab thickness and steel reinforcement is based solely on precedent, with performance under static loads being the only design consideration. To ®ll this gap, a dynamic ®nite element (FE) procedure is presented to design the concrete-face slab which involves a realistic modeling for the embankment material, the face slab, and the slab±rock®ll interface. A set of historic accelerograms, with peak ground accelerations (pga) of about 0.60 g, is used as excitation. Numerical results highlight key aspects of the seismic response of CFR dams with emphasis on the internal forces developing in the slab. It is shown that slab distress may be produced only from axial tensile forces, developing mainly due to the rocking component of dam deformation. For the 0.60 g shaking tensile stresses much higher than the likely tensile strength of concrete development in the slab. All analyses in this FE study are performed with the ADINA special interface elements to model the slip and Newmark's time-integration algorithm for a direct step-by-step solution. # 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction The concrete-faced rock®ll (CFR) dam has been used with increasing frequency in recent years, in many parts of the world. In addition to being a natural choice where suitable clayey core material is not available in the vicinity of the project, the CFR dam has in many cases been found to be the least-cost alternative dam design. As worldwide experience is accumulating on the long-term performance of CFR dams, their popularity may well increase in coming years. Current design trends and construction/performance records of many recent dams can be found in the proceedings of a 1985 ASCE symposium [6] and an accompanying
E-mail address: [email protected] (N. Uddin)
issue of the ASCE Journal of Geotechnical Engineering (Vol. 113, No. 10, October, 1987). The anticipated seismic response and performance of modern CFR dams has received only limited attention in the published literature [1,3,9±11]. Many engineers have argued that the CFR dam is inherently safe against potential seismic damage [15] since: (i) the entire CFR embankment is dry and hence earthquake shaking cannot cause porewater pressure buildup and strength degradation; (ii) the reservoir water pressure acts externally on the upstream face and hence the entire rock®ll mass acts to provide stability, whereas by contrast in earth-core rock®ll (ECR) dams in this may be true only for the downstream rock®ll shell. Notwithstanding the merit of these arguments, it is pointed out that, to date, no modern CFR dam has been tested under strong seismic shaking to prove or
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N. Uddin / Computers and Structures 72 (1999) 409±421
disprove the adequacy of its various design features. In fact, most CFR dams have been built in areas of extremely low seismicity, such as Australia and Brazil, and it seems that some of the design concepts and features have evolved with no consideration of their seismic performance. Bureau et al. [3] presented a study dealing with the seismic performance of rock®ll dams, in general, and
the possible modes of failure of CFR dams, in particular. A numerical formulation was outlined for computing the nonlinear response of CFR dams and evaluating the complete distribution pattern of permanent deformations, without the need to use the simpli®ed Newmark procedure. In addition, an equivalentlinear ®nite-element formulation was utilized to study the eect of ¯uid±dam interaction and to estimate the
Fig. 1. (a) Typical cross-section, details of the crest and material composition of a CFR dam. (b) Cross-section and detail of the `plinth' and perimetric joint [9].
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Fig. 1 (continued)
seismic axial forces and bending moments on the concrete-face slab. Among their conclusions are: (1) hydrodynamic eects can be safely ignored in the seismic response of CFR dams; (2) most of the dam section under strong base excitation (peak-ground acceleration pga=0.70 g) is in a state of plastic deformation, thus `distributed slumping', rather than failure along a discrete surface, may take place; (3) permanent deformations seem to concentrate in the upper third of the dam, a result con®rmed by observations on El In®ernillo dam in Mexico [4]; (4) crest deformations of the order of 1 m remain following this strong shaking. In general, they concluded that crest settlements of modern CFR dams would not exceed 1% or 2% of the dam height under severe earthquake shaking. A crude qualitative picture of the mechanism of seismic failure of CFR dams might be obtained through shaking-table tests on small-scale physical models. Such a study, reported by Han et al. [11], used a 1 m high model having both slopes equal to 1.4H:1 V, a 4 mm thick face slab consisting mainly of gypsum and having a tensile strength of up to 300 kPa, a 2.5 cm thick supporting zone of sand with mass density of 1.7 Mg/m3, and a main body consisting of sand-andgravel compacted to a 1.6 Mg/m3 density. Base acceleration reached 0.60 g, but permanent deformations started at 0.14 g. It was observed that initial sliding was con®ned to shallow wedges in the vicinity of the crest. With increasing acceleration amplitudes the size of sliding zone increased. At even greater amplitudes
the face slab lost support, deformed as a cantilever, and ruptured in violent vibration. The above observations support the concept of sliding mode of deformation predicted in the theoretical studies. However, in view of the inadequacy of such small-scale models to reproduce the signi®cant eects of gravity on material behavior, the results of this study should be viewed with great caution, and only qualitatively. It would be of interest to attempt realistic modeling of CFR dams in a large centrifuge; the author is not aware of any such study up to now. An important missing point in all the above articles is that no study has been made of the internal forces/ stresses developing in the face slab. The potential consequences of strong seismic shaking for CFR dams is explored herein with the help of state-of-the-art ®nite element (FE) analyses of a typical 100 m tall dam. Attempting to ®ll the apparent gap, particular emphasis is accorded to the internal forces developing in the face slab. 2. The concrete-faced rock®ll (CFR) dam The basic features of the CFR dam are outlined herein with the help of Fig. 1, which shows a cross-section and some characteristic details of a typical design. In contrast to the earth-core rock®ll (ECR) dam, the main body of the CFR dam consists exclusively of rock®ll, all of which is located downstream from the
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Fig. 2. The studied typical CFR dam: (a) dam geometry; (b) shear modulus and damping ratio versus cyclic shear strain of the rock®ll [14].
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water thrust; the latter acts externally on the upstream reinforced-concrete face and contributes to increasing the stiness and stability of CFR dams. Hence, much steeper slopes (ranging from 1:1.3 to 1:1.6) are attainable in CFR dams. The face slab is usually made of 20 MPa-strength concrete, with 0.4% reinforcing in each direction, placed in the middle. The slab thickness is variable along the height, starting at 0.30±0.4 m near the crest and increasing by approximately 0.002 hw, where hw is the depth of water (in meters). Crucial is the design and construction of the perimetric joint between the face slab and the so-called `plinth', as this joint always opens up and distorts moderately when the reservoir is ®lled. A double (and sometimes triple) line of defence is provided against this potential source of leakage. Face slabs are placed in vertical strips, typically 15 m wide, by slip form continuously from bottom to top, where they culminate in an L-shaped 3±5 m high cantilever crest wall, the cost of which is more than oset by saving a slice of downstream rock®ll [5]. The upstream zone supporting the face slab consists of smaller-size rock than the main body of the dam to facilitate slope trimming and compaction and thus minimize dierential slab movements. Another role of this relatively low permeability zone is to limit leakage into the dam to that which could safely be passed through the downstream zones, should the coerdam be overtopped before the concrete face slab is constructed. Compaction of the rock®ll to a high density is required for minimizing deformations and face-slab distress and leakage. One of the factors controlling the compression modulus of rock®ll is its gradation. Wellgraded materials, with smaller-size particles ®lling the voids between larger rocks, yet maintaining free-draining characteristics, have led to very satisfactory design. High moduli of deformation have in fact been achieved in CFR dams with rock ®ll having uniformity coecient of 20 or higher and containing about 30% of material smaller than 1 in (25.5 mm). Measurements have also shown that rock®ll is about three times stier in the horizontal than in the vertical direction. 3. Dynamic ®nite element analysis procedure The proposed dynamic analysis procedure is presented herein by including the response of a typical 100 m CFR dam subjected to strong seismic shaking. As described below, the proposed procedure involves the following steps: 3.1. Geometry and material modeling of the studied dam The typical 100 m tall dam studied herein is symmetric with two 1.5H:1 V slopes and with a 0.40 m
413
thick concrete face slab. The crest is 10 m wide and the reservoir is at its maximum level, 90 m above the base. The ®nite element model and geometry of the dam is shown in Fig. 2(a). The dynamic behavior of a rock®ll element is described through: (i) the small-strain shear modulus, Gmax; (ii) the decrease of secant modulus G with increasing strain g; (iii) the hysteric damping ratio, b, which is an increasing function of the amplitude of shear strain g; and (iv) the Poisson's ratio n. Published experimental results from the literature were utilized to assign realistic values to the material parameters [14]. Thus, the spatial distribution of Gmax was estimated as a function of the eective con®ning pressure, sm=(s1+s2+s3)/3, of each rock®ll element: G max 1000 K2 max sm 1=2 K2max has units of square-root of stress and its value for compacted gravels and rock®ll is in the range of 150±250 if stresses are in lb/ft2 (or about 40±70 if stresses are in kPa). Back analysis by Mejia et al. [12] of the response of the Orovile Dam (California) to a weak seismic shaking gave K2max=170. In view of the greater compaction likely to be achieved by modern equipment, K2max=200 is used as a typical best estimate in our dynamic response analyses. K2max is also varied parametrically between 150 and 250, if only to con®rm that the conclusions regarding the performance of the dam are not sensitive to this parameter. Static analyses are ®rst carried out using the FE code ADINA to obtain the eective mean principal stress sm in all elements. Poisson's ratio n for dry or nearly dry rock®ll is taken equal to 0.25. Note that while n has only a marginal in¯uence on lateral oscillations, it may play an appreciable role in rocking-type, as well as in longitudinal and especially vertical oscillations (e.g. [7,8]). Some limited data is available for estimating the decline of secant shear modulus, G, with increasing g, in rock®ll; they reveal a slightly faster rate of decline than for sandy soils, as shown in Fig. 2(b). On the other hand, the data for the dependence of b on g show a slightly faster rate of increase than for sands and clays. Having modeled the plane geometry and dynamic properties of the dam, iterative two-dimensional `equivalent linear' visco-elastic analyses were performed in which the shear modulus G and damping ratio b were obtained from the `eective' shear strain level of the previous iteration. The `eective' shear strain was obtained as the 2/3 fraction of the peak shear strain. All analyses were performed with ADINA, which uses Newmark's time integration algorithm for a direct step-by-step solution.
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Fig. 3. Schematic representation: `welded' contact versus `frictional' contact (allowing slippage).
3.2. The numerical model and ground motion The dam section is discretized in 150 ®nite elements as shown in Fig. 2a. To study the eect of type of slab-rock®ll interface behavior on the distribution of peak axial forces of the slab, two types of contact are used in the study: welded contact and frictional contact. Fig. 3 portrays schematic representation of the two types of contact used in the study: welded contact and frictional contact. Welded contact (sketched in
Fig. 3a) is used to represent the condition when separation is not allowed between the slab and the supporting soil. The frictional contact (which is more realistic) simulates the condition where the concrete face is in a simple tensionless contact with the upstream body of the rock®ll dam. This contact (sketched in Fig. 3b) obeys Coulomb's friction law, with the hydrostatic load providing the normal forces to resist sliding. The face slab is discretized into a set of plane-strain beam elements. To model the slip and separation at the interface during the strong earthquake shaking special joint elements in ADINA [2] are utilized for the frictional contact. These elements can reproduce realistically in the time domain slippage and reattachment between slab and the supporting soil, as well as separation (uplifting) of the slab from the soil whenever net tensile stresses are about to develop. The procedure used by ADINA is an iterative one. Any segment of the slab experiences sliding if the ratio of the computed tangential to the normal forces is about to exceed the coecient of friction. The tangential force is then updated to equal the local frictional capacity, which is essentially equal to the water pressure multiplied by coecient of friction. Implementation of this assumption requires a ®ne enough FE discretization and relatively small load steps during the solution. In this study accelerograms recorded in two historic earthquakes are used as the input ground motion. Information on the records and the earthquake events are summarized in Table 1. . GIC record in the San Salvador (October, 1986) earthquake; and . PV record in the Coalinga (May, 1983) earthquake. Note that the San Salvador record has higher peak ground acceleration (PGA) than the Coalinga record (0.69 versus 0.602 g), but it also has a shorter duration
Fig. 4. Response spectra for very strong earthquake records.
0.695 0.602 Bedrock Francisca Formation 4 11 Geotechnical Inv. Center (GIC) Pleasant Valley (PV) Strike±slip Reverse San Salvador (October 1996) Coalinga (May 1983)
5.4 6.5
pga (g) Site geology Distance to source (km) Record (station) name Ms Rupture mechanism Earthquake name
Table 1 Characteristics of records
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and its `dominant' frequency is much higher than that of the Coalinga record (Fig. 4). The frequency content of the chosen records is re¯ected in their acceleration response spectra, shown in Fig. 4. 3.3. Results of the Dynamic Analyses 3.3.1. Natural frequencies The ®rst 10 natural frequencies of the CFR dam, are calculated with and without the concrete face slab [16]. The results, as expected, show that the facing slab has only a minor restraining in¯uence on the characteristics of the dam. It is concluded that: (i) there is an increase of the natural frequencies of the dam due to presence of the slab by an insigni®cant 2±4%. (ii) The (transverse) modal shapes of the dam sections with and without slab are practically identi®ed (not shown in this paper for the sake of brevity; see Uddin [16] for details). 3.3.2. Seismic response Figs. 5 and 6 summarize the results of the parametric dynamic response analyses in the form of distribution along the vertical axis z of the dam of the peak absolute accelerations, peak relative `elastic' displacements and peak shear strains. The term `elastic' is used to distinguish from the sliding block `Newmark' type deformations. It is evident that the top third of the dam (the `near crest' region) experiences very strong crest acceleration averaging about 1.3 g with the very strong excitation. Peak values of `elastic' displacement at the crest are about 30 cm for the very strong records. Local shear strain amplitudes do not exceed the value of 3 10ÿ3 (or 0.3%), which is not very large given the intensity of shaking. 3.3.3. Response of the face slab Fig. 7 depicts the face slab response when Coulomb's friction law governs the behavior of the interface between face-slab and dam, and slippage is allowed to occur whenever the seismic contact shear stresses exceed the frictional capacity of that interface. It is found that the slab experiences very strong axial forces but very small bending moments and shear forces. (Fig. 7(a) summarizes the results of the dynamic response analyses in the form of distribution along the sloping face of peak axial forces in the slab. The implied maximum peak normal stresses are of the order of 12 and 10 MPa, respectively, for the two records, given the 0.40 m thickness of the slab. These are very large stresses which would undoubtedly produce severe tensile failure in the concrete slab. Therefore, when designing against very strong seismic motions (expected to produce crest acceleration greater than 1 g, it is recommended that a thicker and
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Fig. 5. Distribution along the z axis of the peak absolute acceleration.
better-reinforced slab be used along with a ¯atter upstream slab. The distribution of peak contact shear stresses along the slab-rock®ll interface is also depicted in Fig. 7(b). It is seen that the frictional capacity of this interface is mobilized for the two sets of excitation only in the upper 30 or 60 m of the dam, where of course the con®ning water pressure is small and the shaking is strong. Below that `sliding' depth, the contact shear stresses remain nearly constant or even decrease with depth, whereas of course the frictional capacity increases almost linearly. Fig. 8 shows the eect of the type of slab±dam interface behavior on the distribution of peak axial forces in the slab. The ®gure compares the peak axial force distribution in the slab obtained under the assumptions of a `welded' (allowing no slippage between slab and rock®ll) and a `sliding' interface. The response of the slab is found to be dierent in the two cases. The `welded' contact leads to an increase by about 20% of the maximum peak axial force in the slab. Fig. 9 shows the typical contact shear stress history at dierent locations, for the Coalinga excitation. Due to the presence of large water pressures onto the slab, the lower portion of the slab-rock®ll interface experiences stresses which ¯uctuate about a non-zero static stress (Fig. 9a). On the other hand, at the upper part of the slab (where low con®nement causes slippage and separation of the slab from the rock®ll) shear stresses ¯uctuate about a nearly zero static stress (Fig. 9b).
4. Conclusions A dynamic analysis procedure for CFR (concretefaced rock®ll) dams is proposed in this paper and described in the context of a ®nite element study of a typical 10 m CFR dam. The dam is subjected to strong seismic shaking and analysis has been presented using a realistic modeling for the embankment material, the slab, and the slab±rock®ll interface. The rock®ll is modeled as an equivalent-linear material, whose straindependent shear modulus is proportional to the square root of the con®ning pressure. Coulomb's friction law governs the behavior of the interface between face slab and dam, and slippage is allowed to occur whenever the seismic shear traction exceeds the pertinent frictional capacity. The presented results are thus believed to be realistic. The main conclusions: . The vibration characteristics of the CFR dams can be estimated with conventional methods, ignoring the slab. . Crest accelerations reach values 1.5±3.0 times the peak ground acceleration, depending on the frequency content of the motion relative to the dam's natural frequency(ies). . Despite the high levels of crest acceleration (up to 1.5 g) during the very strong excitation, shear strains do not exceed 3 10ÿ3, thanks to their sti (`unyielding') rock®ll structure. The con®ning pressure of the reservoir water plays a key role in such
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417
Fig. 6. Distribution along the z axis: (a) of the peak relative `elastic' displacement, and (b) of the peak shear strain in the rock®ll for very strong excitation (pga>0.60 g).
sti responses. . The consequences of the very high accelerations near the mid-crest of the dam are likely to be seriousÐnot so much for the overall safety of the dam, as for the face slab and the crest (`parapet') wall. . The face-slab experiences very strong axial forces, but insigni®cant bending moment and shear force. For the strongest shaking (pga 1 0.60 g) the faceslab experiences tensile stresses substantially exceeding the likely tensile strength of concrete along most of the slab. Severe cracking of the concrete and fail-
ure of inadequate construction joints are thus inevitable. Improved design is a necessity. The above conclusions apply to dams in very wide valleys, for which the plane-strain assumption is valid. Dams built in narrow canyons are likely to develop much higher midcrest accelerations for the same base excitation [9±13]. In such cases, slab cracking/failure along with other detrimental eects are even more likely, and must be faced in a prudent design, even when the peak ground acceleration is of the order of 1/3 g. Particularly vulnerable to such high accelerations
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Fig. 7. Distribution along the slab of: (a) the peak axial force, and (b) the peak shear traction along the slab±rock®ll interface for very strong shakings (pga>0.6 g), with frictional contact (allowing both slippage and separation).
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Fig. 8. Eect of the type of slab±dam interface behavior on the distribution of peak axial force in the slab: (a) San Salvador 1986, GIC, and (b) Coalinga 1983, PV excitations.
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Fig. 9. Shear stress history along the slab±rock®ll interface with `contact allowing slippage' for Coalinga 1983, PV: (a) H/10 from base; and (b) 9H/10 from base.
are the crest (`parapet') walls, which need signi®cant redesigning or must be omitted altogether. [4]
References [1] Arrau L, Ibarra, Nogurea G. Performance of Cogoti dam under seismic loading. In: Concrete face rock®ll damsÐdesign, construction and performance. New York: ASCE, 1985. p. 1±4.
[5]
[2] Bathe K-J, Mijailovich S. Finite element analysis of frictional contact problems (Special Issue). J Theor Appl Mech 1988;7:31±44 Supplement no. 1±(0750-7240/1988).
[6]
[3] Bureau G, Volpe RL, Roth W, Udaka T. Seismic analy-
[7]
sis of concrete face rock®ll dams. In: Concrete face rock®ll damsÐdesign, construction and performance. New York: ASCE, 1985. p. 479±508. Elgamal A-WM, Scott RF, Succarieh MF, Yan L. La Villita Dam response during ®ve earthquakes including permanent deformation. J Geotech Engng Div, ASCE 1990;116:1443±62. Fitzpatrick M, Cole B, Kinstler F, Knoop B. Design of concrete face rock®ll dams. In: Concrete face rock®ll damsÐdesign, construction and performance. New York, NY: ASCE, 1985. p. 410±34. Cooke JB, Sherard JL, editors. Concrete face rock®ll damsÐdesign, construction and performance. New York: ASCE, 1985. p. 656±70. Gazetas G. Longitudinal vibrations of embankment
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[8] [9] [10]
[11]
dams. J Geotech Engng Div ASCE 1981;107(GT1):21± 40. Gazetas G. Vertical oscillation of earth and rock®ll dams: analysis and ®eld observation. Soil Found 1981;21:265±77. Gazetas G, Dakoulas P. Seismic analysis and design of rock®ll dams: state of the art. Soil Dyn Earthq Engng 1992;7:27±61. Guros FB, Thiers GR, Wathen TR, Buckles CE. Seismic design of concrete-faced rock®ll dams. In: Proceedings of 8th World Conference on Earthquake Engineering, San Francisco, CA, vol. III, 1984. p. 317±23. Han G, Kong X, Li J. Dynamic experiments and numerical simulations of model concrete-face rock®ll dams. In: Proceedings of the 9th World Conference on Earthquake Engineering, Tokyo, Japan, vol. VI, 1988.
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[12] Mejia LH, Seed HP, Lysmer J. Dynamic analysis of earth dams in three dimensions. J Geotech Engng Div, ASCE 1982;108:1586±604. [13] Mejia LH, Seed HB. Comparison of 2D and 3D dynamic analysis of earth dams. J Geotech Engng Div, ASCE 1983;109:1383±98. [14] Seed HB, Wong RT, Idriss IM, Tokimatsu K. Moduli and damping factors for dynamic analysis of cohesionless soils. J Geotech Engng ASCE 1986;112:1016±32. [15] Sherard JL, Cooke JB. Concrete-face rock®ll dam: I. Assessment and II. Design. J Geotech Engng 1987;113:1095±291. [16] Uddin N. Seismic analysis of earth-core and concreteface rock®ll dams. Ph.D. Thesis, State University of New York, Bualo 1992.
A dynamic analysis procedure for concrete-faced rock®ll dams subjected to strong seismic excitation Nasim Uddin Civil Engineering, University of Evansville, 1800 Lincoln Ave, Evansville, IN 47722, USA
Abstract There is presently little analytical and essentially no observational evidence on the behavior of the concrete-face of the very popular concrete-faced rock®ll (CFR) dams during strong seismic shaking. The choice of slab thickness and steel reinforcement is based solely on precedent, with performance under static loads being the only design consideration. To ®ll this gap, a dynamic ®nite element (FE) procedure is presented to design the concrete-face slab which involves a realistic modeling for the embankment material, the face slab, and the slab±rock®ll interface. A set of historic accelerograms, with peak ground accelerations (pga) of about 0.60 g, is used as excitation. Numerical results highlight key aspects of the seismic response of CFR dams with emphasis on the internal forces developing in the slab. It is shown that slab distress may be produced only from axial tensile forces, developing mainly due to the rocking component of dam deformation. For the 0.60 g shaking tensile stresses much higher than the likely tensile strength of concrete development in the slab. All analyses in this FE study are performed with the ADINA special interface elements to model the slip and Newmark's time-integration algorithm for a direct step-by-step solution. # 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction The concrete-faced rock®ll (CFR) dam has been used with increasing frequency in recent years, in many parts of the world. In addition to being a natural choice where suitable clayey core material is not available in the vicinity of the project, the CFR dam has in many cases been found to be the least-cost alternative dam design. As worldwide experience is accumulating on the long-term performance of CFR dams, their popularity may well increase in coming years. Current design trends and construction/performance records of many recent dams can be found in the proceedings of a 1985 ASCE symposium [6] and an accompanying
E-mail address: [email protected] (N. Uddin)
issue of the ASCE Journal of Geotechnical Engineering (Vol. 113, No. 10, October, 1987). The anticipated seismic response and performance of modern CFR dams has received only limited attention in the published literature [1,3,9±11]. Many engineers have argued that the CFR dam is inherently safe against potential seismic damage [15] since: (i) the entire CFR embankment is dry and hence earthquake shaking cannot cause porewater pressure buildup and strength degradation; (ii) the reservoir water pressure acts externally on the upstream face and hence the entire rock®ll mass acts to provide stability, whereas by contrast in earth-core rock®ll (ECR) dams in this may be true only for the downstream rock®ll shell. Notwithstanding the merit of these arguments, it is pointed out that, to date, no modern CFR dam has been tested under strong seismic shaking to prove or
0045-7949/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 5 - 7 9 4 9 ( 9 9 ) 0 0 0 1 1 - 5
410
N. Uddin / Computers and Structures 72 (1999) 409±421
disprove the adequacy of its various design features. In fact, most CFR dams have been built in areas of extremely low seismicity, such as Australia and Brazil, and it seems that some of the design concepts and features have evolved with no consideration of their seismic performance. Bureau et al. [3] presented a study dealing with the seismic performance of rock®ll dams, in general, and
the possible modes of failure of CFR dams, in particular. A numerical formulation was outlined for computing the nonlinear response of CFR dams and evaluating the complete distribution pattern of permanent deformations, without the need to use the simpli®ed Newmark procedure. In addition, an equivalentlinear ®nite-element formulation was utilized to study the eect of ¯uid±dam interaction and to estimate the
Fig. 1. (a) Typical cross-section, details of the crest and material composition of a CFR dam. (b) Cross-section and detail of the `plinth' and perimetric joint [9].
N. Uddin / Computers and Structures 72 (1999) 409±421
411
Fig. 1 (continued)
seismic axial forces and bending moments on the concrete-face slab. Among their conclusions are: (1) hydrodynamic eects can be safely ignored in the seismic response of CFR dams; (2) most of the dam section under strong base excitation (peak-ground acceleration pga=0.70 g) is in a state of plastic deformation, thus `distributed slumping', rather than failure along a discrete surface, may take place; (3) permanent deformations seem to concentrate in the upper third of the dam, a result con®rmed by observations on El In®ernillo dam in Mexico [4]; (4) crest deformations of the order of 1 m remain following this strong shaking. In general, they concluded that crest settlements of modern CFR dams would not exceed 1% or 2% of the dam height under severe earthquake shaking. A crude qualitative picture of the mechanism of seismic failure of CFR dams might be obtained through shaking-table tests on small-scale physical models. Such a study, reported by Han et al. [11], used a 1 m high model having both slopes equal to 1.4H:1 V, a 4 mm thick face slab consisting mainly of gypsum and having a tensile strength of up to 300 kPa, a 2.5 cm thick supporting zone of sand with mass density of 1.7 Mg/m3, and a main body consisting of sand-andgravel compacted to a 1.6 Mg/m3 density. Base acceleration reached 0.60 g, but permanent deformations started at 0.14 g. It was observed that initial sliding was con®ned to shallow wedges in the vicinity of the crest. With increasing acceleration amplitudes the size of sliding zone increased. At even greater amplitudes
the face slab lost support, deformed as a cantilever, and ruptured in violent vibration. The above observations support the concept of sliding mode of deformation predicted in the theoretical studies. However, in view of the inadequacy of such small-scale models to reproduce the signi®cant eects of gravity on material behavior, the results of this study should be viewed with great caution, and only qualitatively. It would be of interest to attempt realistic modeling of CFR dams in a large centrifuge; the author is not aware of any such study up to now. An important missing point in all the above articles is that no study has been made of the internal forces/ stresses developing in the face slab. The potential consequences of strong seismic shaking for CFR dams is explored herein with the help of state-of-the-art ®nite element (FE) analyses of a typical 100 m tall dam. Attempting to ®ll the apparent gap, particular emphasis is accorded to the internal forces developing in the face slab. 2. The concrete-faced rock®ll (CFR) dam The basic features of the CFR dam are outlined herein with the help of Fig. 1, which shows a cross-section and some characteristic details of a typical design. In contrast to the earth-core rock®ll (ECR) dam, the main body of the CFR dam consists exclusively of rock®ll, all of which is located downstream from the
412
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Fig. 2. The studied typical CFR dam: (a) dam geometry; (b) shear modulus and damping ratio versus cyclic shear strain of the rock®ll [14].
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water thrust; the latter acts externally on the upstream reinforced-concrete face and contributes to increasing the stiness and stability of CFR dams. Hence, much steeper slopes (ranging from 1:1.3 to 1:1.6) are attainable in CFR dams. The face slab is usually made of 20 MPa-strength concrete, with 0.4% reinforcing in each direction, placed in the middle. The slab thickness is variable along the height, starting at 0.30±0.4 m near the crest and increasing by approximately 0.002 hw, where hw is the depth of water (in meters). Crucial is the design and construction of the perimetric joint between the face slab and the so-called `plinth', as this joint always opens up and distorts moderately when the reservoir is ®lled. A double (and sometimes triple) line of defence is provided against this potential source of leakage. Face slabs are placed in vertical strips, typically 15 m wide, by slip form continuously from bottom to top, where they culminate in an L-shaped 3±5 m high cantilever crest wall, the cost of which is more than oset by saving a slice of downstream rock®ll [5]. The upstream zone supporting the face slab consists of smaller-size rock than the main body of the dam to facilitate slope trimming and compaction and thus minimize dierential slab movements. Another role of this relatively low permeability zone is to limit leakage into the dam to that which could safely be passed through the downstream zones, should the coerdam be overtopped before the concrete face slab is constructed. Compaction of the rock®ll to a high density is required for minimizing deformations and face-slab distress and leakage. One of the factors controlling the compression modulus of rock®ll is its gradation. Wellgraded materials, with smaller-size particles ®lling the voids between larger rocks, yet maintaining free-draining characteristics, have led to very satisfactory design. High moduli of deformation have in fact been achieved in CFR dams with rock ®ll having uniformity coecient of 20 or higher and containing about 30% of material smaller than 1 in (25.5 mm). Measurements have also shown that rock®ll is about three times stier in the horizontal than in the vertical direction. 3. Dynamic ®nite element analysis procedure The proposed dynamic analysis procedure is presented herein by including the response of a typical 100 m CFR dam subjected to strong seismic shaking. As described below, the proposed procedure involves the following steps: 3.1. Geometry and material modeling of the studied dam The typical 100 m tall dam studied herein is symmetric with two 1.5H:1 V slopes and with a 0.40 m
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thick concrete face slab. The crest is 10 m wide and the reservoir is at its maximum level, 90 m above the base. The ®nite element model and geometry of the dam is shown in Fig. 2(a). The dynamic behavior of a rock®ll element is described through: (i) the small-strain shear modulus, Gmax; (ii) the decrease of secant modulus G with increasing strain g; (iii) the hysteric damping ratio, b, which is an increasing function of the amplitude of shear strain g; and (iv) the Poisson's ratio n. Published experimental results from the literature were utilized to assign realistic values to the material parameters [14]. Thus, the spatial distribution of Gmax was estimated as a function of the eective con®ning pressure, sm=(s1+s2+s3)/3, of each rock®ll element: G max 1000 K2 max sm 1=2 K2max has units of square-root of stress and its value for compacted gravels and rock®ll is in the range of 150±250 if stresses are in lb/ft2 (or about 40±70 if stresses are in kPa). Back analysis by Mejia et al. [12] of the response of the Orovile Dam (California) to a weak seismic shaking gave K2max=170. In view of the greater compaction likely to be achieved by modern equipment, K2max=200 is used as a typical best estimate in our dynamic response analyses. K2max is also varied parametrically between 150 and 250, if only to con®rm that the conclusions regarding the performance of the dam are not sensitive to this parameter. Static analyses are ®rst carried out using the FE code ADINA to obtain the eective mean principal stress sm in all elements. Poisson's ratio n for dry or nearly dry rock®ll is taken equal to 0.25. Note that while n has only a marginal in¯uence on lateral oscillations, it may play an appreciable role in rocking-type, as well as in longitudinal and especially vertical oscillations (e.g. [7,8]). Some limited data is available for estimating the decline of secant shear modulus, G, with increasing g, in rock®ll; they reveal a slightly faster rate of decline than for sandy soils, as shown in Fig. 2(b). On the other hand, the data for the dependence of b on g show a slightly faster rate of increase than for sands and clays. Having modeled the plane geometry and dynamic properties of the dam, iterative two-dimensional `equivalent linear' visco-elastic analyses were performed in which the shear modulus G and damping ratio b were obtained from the `eective' shear strain level of the previous iteration. The `eective' shear strain was obtained as the 2/3 fraction of the peak shear strain. All analyses were performed with ADINA, which uses Newmark's time integration algorithm for a direct step-by-step solution.
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Fig. 3. Schematic representation: `welded' contact versus `frictional' contact (allowing slippage).
3.2. The numerical model and ground motion The dam section is discretized in 150 ®nite elements as shown in Fig. 2a. To study the eect of type of slab-rock®ll interface behavior on the distribution of peak axial forces of the slab, two types of contact are used in the study: welded contact and frictional contact. Fig. 3 portrays schematic representation of the two types of contact used in the study: welded contact and frictional contact. Welded contact (sketched in
Fig. 3a) is used to represent the condition when separation is not allowed between the slab and the supporting soil. The frictional contact (which is more realistic) simulates the condition where the concrete face is in a simple tensionless contact with the upstream body of the rock®ll dam. This contact (sketched in Fig. 3b) obeys Coulomb's friction law, with the hydrostatic load providing the normal forces to resist sliding. The face slab is discretized into a set of plane-strain beam elements. To model the slip and separation at the interface during the strong earthquake shaking special joint elements in ADINA [2] are utilized for the frictional contact. These elements can reproduce realistically in the time domain slippage and reattachment between slab and the supporting soil, as well as separation (uplifting) of the slab from the soil whenever net tensile stresses are about to develop. The procedure used by ADINA is an iterative one. Any segment of the slab experiences sliding if the ratio of the computed tangential to the normal forces is about to exceed the coecient of friction. The tangential force is then updated to equal the local frictional capacity, which is essentially equal to the water pressure multiplied by coecient of friction. Implementation of this assumption requires a ®ne enough FE discretization and relatively small load steps during the solution. In this study accelerograms recorded in two historic earthquakes are used as the input ground motion. Information on the records and the earthquake events are summarized in Table 1. . GIC record in the San Salvador (October, 1986) earthquake; and . PV record in the Coalinga (May, 1983) earthquake. Note that the San Salvador record has higher peak ground acceleration (PGA) than the Coalinga record (0.69 versus 0.602 g), but it also has a shorter duration
Fig. 4. Response spectra for very strong earthquake records.
0.695 0.602 Bedrock Francisca Formation 4 11 Geotechnical Inv. Center (GIC) Pleasant Valley (PV) Strike±slip Reverse San Salvador (October 1996) Coalinga (May 1983)
5.4 6.5
pga (g) Site geology Distance to source (km) Record (station) name Ms Rupture mechanism Earthquake name
Table 1 Characteristics of records
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and its `dominant' frequency is much higher than that of the Coalinga record (Fig. 4). The frequency content of the chosen records is re¯ected in their acceleration response spectra, shown in Fig. 4. 3.3. Results of the Dynamic Analyses 3.3.1. Natural frequencies The ®rst 10 natural frequencies of the CFR dam, are calculated with and without the concrete face slab [16]. The results, as expected, show that the facing slab has only a minor restraining in¯uence on the characteristics of the dam. It is concluded that: (i) there is an increase of the natural frequencies of the dam due to presence of the slab by an insigni®cant 2±4%. (ii) The (transverse) modal shapes of the dam sections with and without slab are practically identi®ed (not shown in this paper for the sake of brevity; see Uddin [16] for details). 3.3.2. Seismic response Figs. 5 and 6 summarize the results of the parametric dynamic response analyses in the form of distribution along the vertical axis z of the dam of the peak absolute accelerations, peak relative `elastic' displacements and peak shear strains. The term `elastic' is used to distinguish from the sliding block `Newmark' type deformations. It is evident that the top third of the dam (the `near crest' region) experiences very strong crest acceleration averaging about 1.3 g with the very strong excitation. Peak values of `elastic' displacement at the crest are about 30 cm for the very strong records. Local shear strain amplitudes do not exceed the value of 3 10ÿ3 (or 0.3%), which is not very large given the intensity of shaking. 3.3.3. Response of the face slab Fig. 7 depicts the face slab response when Coulomb's friction law governs the behavior of the interface between face-slab and dam, and slippage is allowed to occur whenever the seismic contact shear stresses exceed the frictional capacity of that interface. It is found that the slab experiences very strong axial forces but very small bending moments and shear forces. (Fig. 7(a) summarizes the results of the dynamic response analyses in the form of distribution along the sloping face of peak axial forces in the slab. The implied maximum peak normal stresses are of the order of 12 and 10 MPa, respectively, for the two records, given the 0.40 m thickness of the slab. These are very large stresses which would undoubtedly produce severe tensile failure in the concrete slab. Therefore, when designing against very strong seismic motions (expected to produce crest acceleration greater than 1 g, it is recommended that a thicker and
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Fig. 5. Distribution along the z axis of the peak absolute acceleration.
better-reinforced slab be used along with a ¯atter upstream slab. The distribution of peak contact shear stresses along the slab-rock®ll interface is also depicted in Fig. 7(b). It is seen that the frictional capacity of this interface is mobilized for the two sets of excitation only in the upper 30 or 60 m of the dam, where of course the con®ning water pressure is small and the shaking is strong. Below that `sliding' depth, the contact shear stresses remain nearly constant or even decrease with depth, whereas of course the frictional capacity increases almost linearly. Fig. 8 shows the eect of the type of slab±dam interface behavior on the distribution of peak axial forces in the slab. The ®gure compares the peak axial force distribution in the slab obtained under the assumptions of a `welded' (allowing no slippage between slab and rock®ll) and a `sliding' interface. The response of the slab is found to be dierent in the two cases. The `welded' contact leads to an increase by about 20% of the maximum peak axial force in the slab. Fig. 9 shows the typical contact shear stress history at dierent locations, for the Coalinga excitation. Due to the presence of large water pressures onto the slab, the lower portion of the slab-rock®ll interface experiences stresses which ¯uctuate about a non-zero static stress (Fig. 9a). On the other hand, at the upper part of the slab (where low con®nement causes slippage and separation of the slab from the rock®ll) shear stresses ¯uctuate about a nearly zero static stress (Fig. 9b).
4. Conclusions A dynamic analysis procedure for CFR (concretefaced rock®ll) dams is proposed in this paper and described in the context of a ®nite element study of a typical 10 m CFR dam. The dam is subjected to strong seismic shaking and analysis has been presented using a realistic modeling for the embankment material, the slab, and the slab±rock®ll interface. The rock®ll is modeled as an equivalent-linear material, whose straindependent shear modulus is proportional to the square root of the con®ning pressure. Coulomb's friction law governs the behavior of the interface between face slab and dam, and slippage is allowed to occur whenever the seismic shear traction exceeds the pertinent frictional capacity. The presented results are thus believed to be realistic. The main conclusions: . The vibration characteristics of the CFR dams can be estimated with conventional methods, ignoring the slab. . Crest accelerations reach values 1.5±3.0 times the peak ground acceleration, depending on the frequency content of the motion relative to the dam's natural frequency(ies). . Despite the high levels of crest acceleration (up to 1.5 g) during the very strong excitation, shear strains do not exceed 3 10ÿ3, thanks to their sti (`unyielding') rock®ll structure. The con®ning pressure of the reservoir water plays a key role in such
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Fig. 6. Distribution along the z axis: (a) of the peak relative `elastic' displacement, and (b) of the peak shear strain in the rock®ll for very strong excitation (pga>0.60 g).
sti responses. . The consequences of the very high accelerations near the mid-crest of the dam are likely to be seriousÐnot so much for the overall safety of the dam, as for the face slab and the crest (`parapet') wall. . The face-slab experiences very strong axial forces, but insigni®cant bending moment and shear force. For the strongest shaking (pga 1 0.60 g) the faceslab experiences tensile stresses substantially exceeding the likely tensile strength of concrete along most of the slab. Severe cracking of the concrete and fail-
ure of inadequate construction joints are thus inevitable. Improved design is a necessity. The above conclusions apply to dams in very wide valleys, for which the plane-strain assumption is valid. Dams built in narrow canyons are likely to develop much higher midcrest accelerations for the same base excitation [9±13]. In such cases, slab cracking/failure along with other detrimental eects are even more likely, and must be faced in a prudent design, even when the peak ground acceleration is of the order of 1/3 g. Particularly vulnerable to such high accelerations
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Fig. 7. Distribution along the slab of: (a) the peak axial force, and (b) the peak shear traction along the slab±rock®ll interface for very strong shakings (pga>0.6 g), with frictional contact (allowing both slippage and separation).
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Fig. 8. Eect of the type of slab±dam interface behavior on the distribution of peak axial force in the slab: (a) San Salvador 1986, GIC, and (b) Coalinga 1983, PV excitations.
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Fig. 9. Shear stress history along the slab±rock®ll interface with `contact allowing slippage' for Coalinga 1983, PV: (a) H/10 from base; and (b) 9H/10 from base.
are the crest (`parapet') walls, which need signi®cant redesigning or must be omitted altogether. [4]
References [1] Arrau L, Ibarra, Nogurea G. Performance of Cogoti dam under seismic loading. In: Concrete face rock®ll damsÐdesign, construction and performance. New York: ASCE, 1985. p. 1±4.
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[2] Bathe K-J, Mijailovich S. Finite element analysis of frictional contact problems (Special Issue). J Theor Appl Mech 1988;7:31±44 Supplement no. 1±(0750-7240/1988).
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dams. J Geotech Engng Div ASCE 1981;107(GT1):21± 40. Gazetas G. Vertical oscillation of earth and rock®ll dams: analysis and ®eld observation. Soil Found 1981;21:265±77. Gazetas G, Dakoulas P. Seismic analysis and design of rock®ll dams: state of the art. Soil Dyn Earthq Engng 1992;7:27±61. Guros FB, Thiers GR, Wathen TR, Buckles CE. Seismic design of concrete-faced rock®ll dams. In: Proceedings of 8th World Conference on Earthquake Engineering, San Francisco, CA, vol. III, 1984. p. 317±23. Han G, Kong X, Li J. Dynamic experiments and numerical simulations of model concrete-face rock®ll dams. In: Proceedings of the 9th World Conference on Earthquake Engineering, Tokyo, Japan, vol. VI, 1988.
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[12] Mejia LH, Seed HP, Lysmer J. Dynamic analysis of earth dams in three dimensions. J Geotech Engng Div, ASCE 1982;108:1586±604. [13] Mejia LH, Seed HB. Comparison of 2D and 3D dynamic analysis of earth dams. J Geotech Engng Div, ASCE 1983;109:1383±98. [14] Seed HB, Wong RT, Idriss IM, Tokimatsu K. Moduli and damping factors for dynamic analysis of cohesionless soils. J Geotech Engng ASCE 1986;112:1016±32. [15] Sherard JL, Cooke JB. Concrete-face rock®ll dam: I. Assessment and II. Design. J Geotech Engng 1987;113:1095±291. [16] Uddin N. Seismic analysis of earth-core and concreteface rock®ll dams. Ph.D. Thesis, State University of New York, Bualo 1992.