NON-LINEAR STATIC AND DYNAMIC ANALYSIS OF THE
CUSHMAN ARCH DAMS USING DISTINCT ELEMENTS
埋点
D. D. Curtis1J. P. Aglawe2
E. B. Kollgaard3 D. E. Bowes4
S. H. Fischer5
ABSTRACT
The paper presents the detailed non-linear static and dynamic analysis of the Cushman No. 1 arch dam. The Cushman No. 1 arch dam is owned and operated by the City of Tacoma, Department of Public Utilities. The analyses were undertaken as part of the F.E.R.C. Part 12 investigations. The static and dynamic analyses are unique in that opening, closing, and sliding along joints is modeled in considerable detail. The distinct element program 3DEC is used in the non-linear analysis of the dam and foundation. We believe that the sophisticated non-linear analyses that have been carried out on these dams’ advances the state-of-the-art of dam assessment under seismic loading.
In the 3DEC analysis, all the dam contraction joints and the dam-foundation interface joints are allowed to open, close, and slide under static and dynamic loading. In addition, joints in the foundation rock are modeled such that stability analysis of the dam and foundation are made within one 3DEC model. The static analysis simulates dam construction, grouting of contraction joints, and reservoir impoundment. The static stability of the dam is checked by gradually reducing the frictional strength of the joints until displacements become excessive. A detailed non-linear static analysis was undertaken to investigate slip on the dam-foundation interface, particularly at the right abutment where the contact geometry is adversely sloped downstream.
In the non-linear seismic analysis, the dam joints and dam-foundation interface open and close during the earthquake. At several time instances during the earthquake, the shear strength along various joint surfaces was exceeded and this caused relative shear slip displacements. The post-earthquake stability of the dam was assessed by increasing uplift and gradually reducing the strength of the joints. By this means the dam was found to be safe.
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1 Senior Civil Engineer, Acres International, 434
2 Queen St., P.O. Box 1001, Niagara Falls, Ontario Canada, L2E 6W1, Tel: 905-374-5200, Fax: 905-374-1157, dcurtis@acres.
2 Senior Geotechnical Engineer, Acres International, 4342 Queen St., P.O. Box 1001, Niagara Falls, Ontario Canada, L2E 6W1, Tel: 905-374-5200, Fax: 905-374-1157, jaglawe@acres.
3 Consulting Engineer, 4820 Eagle Way, Concord, CA, USA, 94521, Tel: 925-798-9475, Fax: 925-689-网络新闻编辑 华硕易pc3456, ebkollgaard@ca.astound.
4 Consulting Engineer, 2922 78th Ave. Ct. N.W., Gig Harbor, WA, USA, 98335, Tel: 253-265-0811, Fax: 253-265-0812, bowespe@halcyon.
5 Senior Principal Engineer, Tacoma Power, Generation, 3628 South 35th Street, Tacoma, WA, USA, 98409, Tel: 253-502-8316, Fax: 253-502-8136, sfischer@ci.tacoma.wa.us.
INTRODUCTION
The Cushman Dams are on the lower stretch of the North Fork of the Skokomish River on the south
eastern side of the Olympic peninsula near the southern end of the Hood Canal. The City of Tacoma owns both the dams.
Cushman Dam 1 is a single curvature concrete arch dam with an overall height of 260 ft above the streambed. The 400 ft-long crest of the dam is at El. 741.5. The reservoir normal maximum storage level is El. 738.0. The dam was completed and placed into operation in 1926.
The Cushman 1 dam/foundation contact is poorly shaped especially at the right abutment where it is sloped adversely in the downstream direction. This fact led to the question of ability of the dam to withstand the strong ground motions associated with the seismic loading. It was recommended to perform a sophisticated non-linear numerical analysis to ascertain the seriousness of the seismic response and evaluation of remedial modifications.
The non-linear static and dynamic analyses were performed with 3DEC, a three dimensional distinct element analysis program. The 3DEC program was used to perform a non-linear static analysis of dam followed by a non-linear dynamic time history analysis. The 3DEC program was used to analyze both Cushman 1 and 2 dams, but due to space limitations, the main results from the Cushman 1 analysis are presented herein.
MODELING APPROACH
林州地震
Brief Description of 3DEC
The 3DEC (3-Dimensional Distinct Element Code) program is the three-dimensional extension of Itasca's two-dimensional code UDEC. It is specifically designed for simulating either the quasi-static or dynamic response to loading of rock media containing multiple, intersecting joint structures.
The 3DEC model is an assemblage of discrete polyhedras representing discontinuous medium. Discontinuities are treated as boundary conditions between blocks. Large displacement on the discontinuities such as slip and opening is simulated in a discontinuous medium. Relative motion along discontinuities is governed by linear and non-linear force-displacement relations for movement in both the normal and shear directions. The program uses an explicit solution scheme, which gives a stable solution to unstable physical processes.
3DEC is particularly well suited to simulate blocky structures, such as stone masonry arches. Assessment of the safety conditions of old masonry bridges (Lemos, 1997) and the seismic behavior of stone masonry arches (Lemos, 1995) has been done using 3DEC. It has been successfully employed to simulate the behavior of a concrete arch dam
constructed on a jointed rock foundation (Lemos, 1996) and also to perform stability analysis of underground powerhouse station (Dasgupta and Lorig, 1995, Dasgupta, et al., 1995).
Geological Setting
The brief review of the engineering geology of Cushman Dam No 1 is given by Coombs (1972). Recent geological compilation and review was done by Hamilton (2001) for the right abutment of Cushman Dam 1. The bedrock in the area of Cushman projects consists of thick sequence of basalt and andesite flows with local interflow layers of tuff and agglomerate, of the Eocene age Crescent Formation. At the dam site the Crescent Formation layering strikes about NE-SW, crossing the canyon at a high angle and dips 45 to 60 degrees SE downstream. Various joints in the foundation rock are present. Strike and dip angles for the various joints are given in Table 1. The joint plane A1 intersects near the contraction joint at station 3+64.79 of the dam. Figure 1 shows the joint planes D, A1, A2 and B. The right abutment wedge is formed by an assumed vertical plane D on the upstream, ramp fracture plane B below the dam-foundation contact, and the joint planes A1 and A2. These joint planes form a right abutment wedge with a total weight of about 30,000 tons.
Table 1. Orientations of the Discontinuities
Joint Plane Strike Dip
Vertical
D N25W
NW
B N56E
53
55SE
A1 N67E
A2 N67E
Model Development
3DEC model was developed as an assemblage of discrete blocks using commercially available program DISPLAY (EMRC, 1997). Foundation rock, concrete dam, and reservoir water elements were discretized. An exploded view of foundation rock, concrete dam, and the reservoir is shown in Figure 2. In Figure 2, the reservoir is shown in the upper part of the figure, the dam in the middle and the reservoir in the lower part of the figure. The reservoir was extended more than three times the dam height in the upstream direction. It is noted that the bulk of the model was created using a 3D AutoCad model, which was supplied by Tacoma Power. In the foundation rock, four joint sets were used. In the concrete dam, the seven vertical contraction joints and the dam/foundation contact joints were modeled. Various rock joints forming a right abutment wedge are shown in Figure 1. Figure 3 provides an illustration of right abutment wedge along with dam. Right abutment gravity sections and the start of the arch section of the dam are also shown to obtain spatial location and orientation of the wedge with respect to the dam.
Figure 1. Dam-Foundation Contact, Contraction Joints and
Foundation Rock Mass Discontinuities
Figure 2. Exploded View of Foundation, Dam and Reservoir Figure 9a.
Figure 1 3DEC model of Cushman Arch Dam No. 1
R k
Figure 3. Right Abutment Wedge Geometry and the Dam.
The Rock Wedge Alone is shown in the Inset.
Various FISH functions were written to simulate the effect of grouting of the independent cantilever monoliths at the contraction joints, the uplift pressure distribution at the dam-foundation contact and water pressure in the joints on the right abutment wedge surfaces. FISH functions provide a programming capability in 3DEC that allows the user to program such features as grouting joints, i.e., closing gaps at the dam joints.
Figure 4 presents various stages during the modeling sequence to establish initial state of stress. Initial rock stresses were computed using gravity loading. The dam monolithic blocks were then con
structed. Grouting of the independent cantilevers was simulated by specifying a closed gap between the contraction joints after gravity loads were equilibrated. The reservoir elements were turned on to load the dam hydrostatically. Parametric studies were performed to examine the sensitivity of the 3DEC to reduced frictional strength at the dam-foundation contact and on the joints forming the right abutment wedge. Finally, the dynamic analysis was performed using Juan de Fuca and Cascadia seismic records for MCE loading.
Properties
The joints between the dam-reservoir and reservoir-foundation are assumed to be elastic. Contraction joints within the dam and dam-foundation contact are assumed to have zero cohesion and 55 degrees friction angle. The dam foundation was quite rough, therefore, the assumed friction angle is considered conservative. In the right abutment wedge analysis, the cohesion on the joint planes was set to zero. The assumed total combined (cohesive and frictional) shear strength on joints B, D, A1 and A2 is taken as 55 degrees.
It was assessed that the total shear strength of the joint planes is at least equivalent to that with a combined friction angle of 55 degrees.
of Cushman-1 Arch Dam
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