Transactions on Modelling and Simulation vol 16, 1997 WIT Press, ISSN X

Transcription

1 A Comparison between Actual Displacements and Numerical Results from a Finite Element Model in an Arch Dam L.E. Romera, S. Hernandez E.T.S. Ingenieros de Caminos, Canales y Puertos University of La Coruna, La Coruna 15071, Spain ABSTRACT A comparative study between recorder displacement data of the Belesar arch dam in Spain and displacement fields provided by a structural analysis carried out of a finite element mesh is presented in this paper. In addition to the usual loads as weight material, water pressure and temperature changes, an expansive process of geochemical origin has been considered in the analysis. Numerical results showed good accuracy, with better performance in downstream displacement. 1. INTRODUCTION The Belesar Dam is an arch dam located in North West Spain. It has a height of 130 m and its maximum length at the top dam is about 600 m. Figure 1. Picture of Belesar Dam

2 60 Computer Methods and Experimental Measurements The dam has been monitored since construction works finished in The structure behaved as predicted at the beginning of its service life, but afterward the dam showed unexpected upstream displacements. This structural response was consecuence of an expansive process in the dam concrete due to chemical interaction between alkaline components of the cement and concrete aggregates. According with data from the monitoring system of the dam this phenomenon! was first located in the left side of the dam, and spread out to most of dam volume since MONITORING SYSTEM OF THE BELESAR DAM The dam posseses a quite complete system to obtain loading values, temperature data and structural responses. A summary description follows: Dam displacement are measured at six locations, distributed along dam volume at different heights. Altitude values are indicated in Table 1, and locations are presented in Figure 2. Table 1. Altitude of displacement monitoring devices Name RO Rl R2 R3 R4 R5 Altitude (m) RO (330 m) R1 (312m) R2 (292 m) Loc5 R3 (272 m) R4 (252 m) R5 (232 m) Loc3 Figure 2. Location of displacement monitoring devices Concrete and water data temperatures are obtained by termometers located on wall dam and inside the dam. The number of termometer locations is higher than 300 and provide a complete set of data temperatures along dam thickness. A number of 249 extensometers are located in the dam to control material strain. There are spreadout in the upstream and downstream walls and at half thickness of the dam.

3 Computer Methods and Experimental Measurements 61 Data provided by aforementioned devices are stored in computers, allowing any kind of printed output of the collected information. 3. TIME HISTORY OF DAM DISPLACEMENTS Usual values of dam displacements are related to reservoir level and material temperatures. Yearly variations present upstream displacement in summer, due to higher temperatures and lower amount of impounded water, and downstream values in winter due to the opposite situation. Displacement data form the Belesar dam presented earlier on this type of yearly variation, but with an average value moving continously upstream. The process was quite slow from 1963 to 1979 but it increased in intensity since that year. Historical evolution at position RO (330 m) of locations 1 and 2 are showed in Figure 3. Year numbering is printed on horizontal coordinate and displacement data are in vertical axis, with positive values coresponding to downstream values. a) Displacement (mm) at RO in location b) Displacement (mm) at RO in location 2 Figure 3. Historical evolution of dam displacements

4 62 Computer Methods and Experimental Measurements It was already mentioned the increase in upstream displacements was caused by volume expansion of dam concrete due to a geochemical phenomenon, which produced higher values of stresses and therefore diminished dam safety. Because of that, a study was conducted aiming to set up a finite element model to the dam, capable of emulate past behaviour of the dam and consecuently providing a tool to predict future evolution of dam displacement and global safety. 4. FINITE ELEMENTS MODEL OF BELESAR DAM Structural model used in the analysis of Belesar dam appears in Figure 4. Model is composed of dam and surrounding rock foundation, which turned out to be formed by three material of two different mechanical properties. The complete set of values of E and v is presented in Table 2. Figure 4. Finite element model of Belesar dam Table 2. Mechanical properties of materials Material 1. Concrete 2. Rock Foundation 3. Rock Foundation 4. Rock Foundation E (KN/m?) 3/7-10? ? ? ? v Structural model contained 5075 isoparametric finite element of 20 nodes [1, 2]. Total number of degrees of freedom after imposing boundary conditions was

5 Computer Methods and Experimental Measurements LOADING SET CONSIDERED The individual cases of loading set considered were the following: Self-weight (SW) of the dam. Water pressure at two different level: Average level: WP?&5 Full reservoir: W PJJQ h m h = 330 m Temperature variation: According with existing data temperature, variations of AT = ±10 C were taken in account. A coefficient of thermal expansion a= m/m C was defined for the concrete. Geochemical expansion fields: According with data presented in Figure 3, the historical evolution of this phenomenon can be divided into two phases. Initial phase from 1963 to 1979 (EXP1). This period is charactericed by a slow increment of displacement. A total value of expansion has been considered to represent this loading. Second phase from 1979 to 1994 (EXP2): Expansion fields in those years present a yearly rate quite constant. Therefore, this loading has been modeled identifying the annual rate and multiplying it by the number of years considered in the analysis. Figure 5 shows zones where data of total value of expansion field before 1979 exist and Figure 6 shows annual rate of expansion fields after a) Upstream side b) Downstream side Figure 5. Total values of expansion fields before 1979 (x 10*)

6 64 Computer Methods and Experimental Measurements a) Upstream side b) Downstream side Figure 6. Annual rate of expansion fields after 1979 (x 10*) The structural analysis of finite element model presented in Figure 4 subjected to load combination produced by the set of loading indicated was carried out using the COSMOS/M software [3, 4]. Expansion fields were introduced as thermal loadings in the finite element model by using the following relationship AT=^a where e is the value of expansion field, a the thermal coefficient of concrete and AT the equivalent temperature variation. 6. LOAD COMBINATIONS AND NUMERICAL RESULTS Several load combination were needed efficiently dam displacement history. to be accounted for representing Combination 1. SW + WP^Q - AT: This combination produces the maximum downstream displacement before the expansive process. Therefore, it must agree with the data record at the beginning of life service of the dam. Combination 2. SW + Wf^aj + AT: Simmilarly this combination corresponds to the maximum upstream displacement and it was compared with upstream displacement recorded at the early times of the dam.

7 Computer Methods and Experimental Measurements 65 Combination 3. SW + WP^g - AT + EXP1: This combination adds the total value of initial phase of expansion to Combination 1. Therefore, it needs to be compared with the maximum downstream displacement of the dam in Combination 4. SW + W/^aj + AT + EXP1: It adds the expansion phase until 1979 to Combination 2. It will be checked with maximum data values of upstream displacement in that year. Combination 5. SW + WP^ - AT + EXP EXP2: This combination considers 15 years of the second phase of expansive process ( ) and includes them to the values in Combination 3. It simulates the maximum downstream values in Combination 6. SW + M^SJ + AT + EXP EXP2: Simmilarly it adds 15 years of the second phase of expansion to Combination 4 and its results have to be compared with maximum upstream values in Numerical results obtained in the structural analysis were checked up with displacement data recorded using the monitoring system of Belesar dam. Both types of data showed quite good simmilarity. Figure 7.a presents data in location 1 at elevation RO and Figure 7.b shows the same kind of data at location 1 in elevation R3. Numbers 1 to 6 appearing in Figure 7 corresponds to the displacement values obtained and Combinations 1 to 6 respectively. a) Location 1 at elevation RO Figure 7. Comparison between actual data and results from finite element model

8 Computer Methods and Experimental Measurements b) Location 2 at elevation RO Figure 7. Comparison between actual data and results from finite element model (cont.) 7. CONCLUSIONS Some conclusions can be extracted from the research worked out: Monitoring system of dams provide a very comprehensive set data about structural responses which can be used to stablish comparisons with computer simulations. Finite element models are a valuable tool to represents large structural typologies as arch dam very adecuately. Geochemical process present in dams may be represented as temperature fields and this techniques allows to include this phenomenon as a loading case in structural analysis. Dam displacement data can be obtained with adecuately accuracy by using proper load combinations. Downstream displacement show better approximation than upstream values. This disimmilarity is due that upstream displacement corresponds to lower ratios of reservoir water level and this ratio may be different every year, on the opposite downstream displacement are related with full reservoir and cold temperatures which is an usual situation in winter. REFERENCES 1. BATHE, K.J.: Finite element procedures in Engineering Analysis. Prentice Hall, HUGHES, T.J.R.: The Finite Element Method. Linear Static and Dynamic Finite Element Analysis. Prentice Hall, COSMOS/M 1.71 version. User's Manual, SRAC. Santa Monica, California, ROMERA, L.E. and HERNANDEZ, S.: Resolucion de modelos estructurales de elementos finitos con el programa COSMOS/M. Universidad de La Coruna, 1997 (in Spanish).