Thermal-Structural Modeling and Temperature Control of Roller Compacted Concrete Gravity Dam Abdallah I. Husein Malkawi1; Saad A. Mutasher2; and Tony J. Qiu3 Abstract: A coupled thermal-structural analysis is carried out using both a two- and a three-dimensional finite-element method. The computer program ANSYS is used and simulates the construction process of a roller compacted concrete 共RCC兲 dam. Thermally induced stresses are computed for the 60 m high RCC Tannur Dam in Jordan. The actual temperature distribution in the body of the dam measured by thermocouples is compared with that obtained by ANSYS; generally, a good agreement is obtained. The study demonstrates that detailed thermal stress analysis should be performed for large RCC dams to provide a basis to minimize and control the occurrence of thermal cracking. DOI: 10.1061/共ASCE兲0887-3828共2003兲17:4共177兲 CE Database subject headings: Thermal stresses; Finite element method; Dams, concrete; Cracking; Temperature effects.
Introduction In roller compacted concrete 共RCC兲 dams, large quantities of concrete are usually placed to form a monolithic mass-concrete structure. During placement of RCC, heat will generate by the hydration of cement. Cement tends to liberate a substantial amount of heat, which leads to a rise in the temperature in the body of the dam. After the peak temperature is reached, the concrete, sometimes over a period of years, cools, to a stable temperature. Such reductions in the temperature usually lead to the following. 1. Surface gradient cracking. This generally occurs when the reservoir is first filled. A thermal gradient develops between the cooled surface and the hot concrete core. This change in the temperature can generate undesirable surface thermal stresses, which can lead to cracking at the surface of the dam. 2. Mass gradient cracking. This occurs well after the dam is completed, with the cooling of the central mass of the dam. A volume reduction will occur and if such a reduction of the volume is externally restrained, as it will be by the rock foundation, sufficient strain can develop, causing cracking through the dam body. 1
PhD, Professor of Geotechnical Engineering and President of ASCE—Jordan International Group, Civil Engineering Dept., Jordan Univ. of Science and Technology, Irbid 22110, Jordan. E-mail:
[email protected] 2 Research Assistant, Civil Engineering Dept., Jordan Univ. of Science and Technology, Irbid 22110, Jordan. E-mail:
[email protected] 3 Senior Engineer, Gutteridge Haskins & Davey Pty Ltd., 15 Astor Terrace, Brisbane Qld 4000, GPO Box 668, Brisbane Qld 4001, Australia. E-mail: tonyគ
[email protected] Note. Discussion open until April 1, 2004. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on May 15, 2001; approved on July 3, 2002. This paper is part of the Journal of Performance of Constructed Facilities, Vol. 17, No. 4, November 1, 2003. ©ASCE, ISSN 0887-3828/2003/4177–187/$18.00.
Several techniques are reported in the literature for designers to evaluate the thermal performance of concrete, the structural configuration, and construction requirements. These techniques range from complex three-dimensional finite-element analysis methods to simple manual computation. Tatro and Schrader 共1992兲, for example, provide specific guidance for performing a thermal study for RCC structures. The U.S. Army Corps of Engineers, in Engineering Technical Letter 共ETL兲 1110-2-542 共U.S. 1997兲, provides design guidance for implementing a range of thermal analysis techniques. In this ETL, background and examples for performing several levels of less complex analyses are presented. Zhang and Garga 共1996兲 used a two-dimensional finite-element method for simulating the construction process of an RCC dam. Concrete temperature and the thermally induced stresses were determined with a personal microcomputer. Truman et al. 共1991兲 used the finite-element program ABAQUS along with user developed subroutines and experimentally derived material properties to analyze by incremental construction the thermal loads of a pile-founded mass concrete lock and dam structure. Forbes and Williams 共1998兲 discussed thermal stress modeling, use of high sand RCC mixes, and in situ modification of RCC for the Cadiangullong Dam. They provided a good understanding of the thermal condition, and, as a result, thermal stresses and contraction joint spacing were determined. Ishikawa 共1991兲 demonstrated numerically that thermal cracks might be avoided to a certain degree by determining the optimum construction method. Ayotte et al. 共1997兲 presented details of the experimental and numerical thermal studies undertaken for a large-scale mass concrete structure. The study presents a modified step-by-step approach, which improved the stress modeling within the available commercial software. Crichton et al. 共1999兲 presented a thermalstructural analysis using the ANSYS computer program to assess the effect of heat of hydration in RCC structural stresses. The effect of using simple linear elastic material properties on the calculated stresses has been compared to a more complex time variant material modulus and creep analysis. They concluded that the simple models overestimate the initial stresses and underestimate or cannot predict the long-term tensile stresses.
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Fig. 1. Typical cross section and thermocouple locations
In this paper, the determination of the thermal and structural stresses and temperature control requirements is described for the 60 m high Tannur RCC Dam in Jordan. Temperature distribution with time, concrete placement temperature limits, and joint spacing requirements to minimize cracking are also discussed.
Description of Dam The Tannur Dam is the first completed RCC dam in the Middle East. It is a concrete gravity dam, approximately 60 m high, built to impound the floodwater of the Wadi Al Hasa. It retains a reservoir at an elevation of 400 m above sea level 共ASL兲 with a 16.8⫻106 m3 capacity. The dam is situated some 50 km south of Karak. The yield of the reservoir will help satisfy the future water demand for industry and agriculture in the southern Ghors. The
Tannur Dam is constructed of high paste content RCC, placed in 300 mm thick layers with a facing made of grout enriched roller compacted concrete 共GE-RCC兲. The concrete is designed to have a very low air void content and to achieve maximum strength and density with minimum permeability and with a good bond between layers. The dam is founded on limestone of the Wadi As Sir and Fuheis, Hummar Shueib Formation. A two-layer cement grout curtain will limit the quantity of seepage. The upstream face of the dam is vertical, with a batter of 1:1 below Elevation 356 to the foundation level. The stepped downstream face has a slope of 0.8共H兲: 1共V兲 共Fig. 1兲. This profile has been adopted to reduce vertical stresses by a more distributed loading, and to achieve higher compressive stresses at the upstream heel due to the vertical loading—thus reducing tensile stresses at the location under seismic loading. The dam is a straight structure 242 m long at the crest.
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Table 1. Predicted Rolled Compacted Concrete Placement Temperature
Month January February March April May June July August September October November December a
Mean monthly temperature 共°C兲
Mean annual 共°C兲
Difference 共°C兲
10 11.1 13.6 17.8 21.5 24.5 25.5 25.6 24.2 21.3 16.4 6.7
18.2 18.2 18.2 18.2 18.2 18.2 18.2 18.2 18.2 18.2 18.2 18.2
⫺8.2 ⫺7.1 ⫺4.6 ⫺0.4 3.3 6.3 7.3 7.4 6 3.1 ⫺1.8 ⫺11.5
2 3
Difference 共°C兲 ⫺5.47 ⫺4.73 ⫺3.07 ⫺0.27 2.2 4.2 4.87 4.93 4 2.07 ⫺1.2 ⫺7.67
Subtotal 共°C兲
Aggregate crushing added 共°C兲
Aggregate stocking temperature 共°C兲
Mixing added 共°C兲
Transportation added 共°C兲
Final temperaturea 共°C兲
12.73 13.47 15.13 17.93 20.4 22.4 23.07 23.13 22.2 20.27 17 10.53
1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1
13.83 14.57 16.23 19.03 21.5 23.5 24.17 24.23 23.3 21.37 18.1 11.63
1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1
⫺0.6 0 0.6 0.6 1.1 1.1 1.7 1.7 1.1 0.6 0 ⫺0.6
14.3 15.7 17.9 20.7 23.7 25.7 27 27 25.5 23 19.2 12.2
Average⫽21.
Temperature Control Requirements Significant thermal induced stresses are developed as a result of the heat of hydration of the cementitious materials in RCC dams. The temperature distribution through the dam and its evolution with time depend on the following: • RCC concrete properties, • Climatic factors, • Construction procedure, • Thickness of lifts, • Initial temperature of lifts, and • Interval between their successive placements. These thermally induced stresses can be significant enough to induce cracks in the RCC. Recent developments in sophisticated software based on advanced numerical methods, together with the continually increasing power of computers allow complex analyses for such thermalstructural problems. The ANSYS computer program based on the finite-element method was used to analyze the thermal behavior of the Tannur Dam. The desired outcome of the numerical analysis was • To determine the spatial distribution of temperature and its evolution with time, • To determine the stress distribution during and following the dam construction and at the time of reservoir filling, • To identify the appropriate joint spacing to minimize the development of transverse cracking, and • To determine the concrete placement temperature limits.
Table 2 shows the actual data recorded for the RCC placement temperature for the time period between June and October of 2000. It is shown, for example, that the month of June had an average recorded temperature of 25.5°C, whereas the calculated temperature for the same month 共Table 1兲 is about 25.7°C. The average monthly ambient air temperature is shown in Table 3. RCC placement was assumed to take place in the cooler months of the year—i.e., from December of 1999 to the end of April of 2000. The aggregate production and stockpiling started in the summer. Based on the average ambient air temperature from December to April of 12°C, an average RCC placement tempera-
Table 2. Average Actual Data Record of Rolled Compacted
Concrete Placement Temperature during Construction Month 共2000兲 May June July August September October
The temperature of the concrete aggregate has the greatest influence on the initial temperature of the fresh RCC. Due to the low volume of mix water and the minor temperature difference of the water compared to the aggregate, the water temperature has a much less significant effect on the overall temperature. Table 1 provides the basis for estimating the aggregate temperature and approximating the RCC placement temperature used in the analysis. Since aggregate production will be done concurrently with the RCC placement, stockpile temperatures should closely parallel the average monthly ambient temperatures. Some heat is added because of screening, crushing, and transportation activities.
Temperature at night 共°C兲
24.28 25.52 25.8 26.15 24.4 24.7
23.2 25.16 25.7 25.7 23.4 24
Table 3. Average Monthly Air Temperature Month
Concrete Placement Temperature
Temperature at day 共°C兲
January February March April May June July August September October November December
Ambient air temperature 共°C兲 10 11.1 13.6 17.8 21.5 24.5 25.5 25.6 24.2 21.3 16.4 6.7
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Table 4. Properties Adopted for Thermal Analysis Property
Value
Density Elastic modulus Poisson’s ratio Coefficient of thermal expansion Specific heat Thermal conductivity Film 共convection兲 coefficient 共air兲 Film 共convection兲 coefficient 共water兲 Heat generation of RCC Placement temperature Foundation rock temperature
2,400 kg/m3 18 GPa 0.2 6.5E⫺6/°C 963 J/kg °C 2.6 J/s•m °C 15 J/s•m2 570 J/s•m2 309 J/g at 28 days 20 °C 18 °C
ture of 20°C was adopted. A water temperature of 18°C was assumed in the reservoir upon filling and 18°C was assumed for the foundation rock.
Material Properties and Environmental Conditions The model properties used were assessed from available data and typical RCC properties. The density, modulus, Poisson’s ratio, specific heat, and thermal conductivity are given in Table 4. A convection coefficient for air was used, which is consistent with moderate wind speed. A typical coefficient of thermal expansion of 6.5⫻10⫺6 /°C was adopted for the concrete. Heat generation rates adopted for the 125 kg/m3 cement ⫹75 kg/m3 pozzolan mixture were based on the heat of hydration of the Jordanian ordinary portland cement 共OPC兲 plus that of the pozzolan being 20% of that for the OPC. Heat of hydration of 309 J/g at 28 days was determined from testing the Jordanian OPC.
Fig. 3. Experimental results of heat of hydration for Jordanian cement
analysis. The element has one degree of freedom for temperature at each node. This is a higher-order element that has eight nodes, is suitable for simulating irregular shapes, and is applicable to the study of a two-dimensional steady-state or transient thermal analysis. Also, the model can be analyzed structurally by replacing it with the equivalent structural element PLANE82. This is a higher-order element; it also has eight nodes but has two degrees of freedom, allowing movement in both the x direction and the y direction. This is a powerful tool available in the ANSYS program that allows the stresses to be obtained in a coupled thermalstructural analysis due to a change in temperature with time. A plane strain model was adopted for the two-dimensional analysis of the maximum cross section of the dam. Fig. 2 shows the mesh of the cross section of the dam.
Two-Dimensional Model Analysis The dam was modeled as a two-dimensional transient heat transfer model using a birth and death procedure to simulate the real construction process of the dam. The dam is divided into 19 layers. Each layer has a thickness of 3 m, constructed in 10 days, and the last layer has a thickness of 2 m. The PLANE77 element type, available in the ANSYS library, was used in the finite-element
Fig. 2. Two-dimensional finite-element model—mesh
Heat of Hydration Heat of hydration as a function of time was obtained from several tests performed in the laboratory. Fig. 3 shows the heat of hydration produced with time for Jordanian cement with and without the addition of pozzolan. In this study, the heat of hydration was simulated as a ramp input, as shown in Fig. 4.
Fig. 4. Heat of hydration as ramp input
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induced strain⫽ 共 C th 兲共 dT 兲共 K R 兲共 K f 兲
Fig. 5. Predicted adiabatic temperature for Jordanian cement
Adiabatic Temperature Rise „ T ab … An adiabatic system is a system in which heat is neither allowed to enter nor leave. Therefore, adiabatic temperature rise is the change in the temperature of the concrete due to heat of hydration of the cement under adiabatic conditions. It is the measure of the heat evolution of the concrete mixture in a thermal analysis. In a very large mass of concrete, temperatures near the center of the mass will be approximately equal to the sum of the placement and adiabatic temperatures. However, near the surfaces, the temperature will be close to the ambient air temperature. The magnitude of the adiabatic temperature rise and the shape of the curve can vary significantly for different concrete mixtures. Typical values for the adiabatic temperature rise of the mass of concrete range from 11–19°C at five days to 17–25°C at 28 days. Fig. 5 shows the predicted adiabatic temperature rise for RCC in the Tannur Dam determined by the ANSYS program for a placement temperature of 20°C, where the rate of heat of hydration was simulated as a ramp input as shown in Fig. 4.
Crack Analysis RCC, like other concrete, has an ability to absorb some of the strain resulting from the tensile stresses generated by the cooling process. This ability is referred to as the tensile strain capacity. The laboratory test reported by Dunstan 共1981兲 showed that a typical value of the tensile strain capacity is 80 mm. The tensile strain capacity of the RCC is not large enough to withstand this strain without cracking; therefore, joints are required in the concrete to avoid cracking.
(1)
where C th ⫽coefficient of thermal expansion; dT⫽temperature difference; K R ⫽structure restraint factor; and K f ⫽foundation restraint factor. To determine the spacing of the RCC blocks, the following parameters are adopted. The peak internal temperature⫽37.7°C 共determined from 2D analysis兲. The minimum temperature 共based on the annual temperature cycle兲⫽6.7°C 共taken from Table 3兲. The coefficients K R and K f are both equal to 1.0 for a conservative assumption and the maximum strain at the foundation base 共Tatro and Schrader 1992兲. The coefficient of thermal expansion (C th ) is strongly influenced by the type of aggregate in the RCC mix; for the Tannur Dam, the aggregate is limestone/dolomite limestone. A typical value for the coefficient of thermal expansion for the RCC mass for the Tannur Dam is taken as 6.5 E-6/°C 共Neville and Brooks 1994兲. The calculated induced strain is 201.5 mm. Therefore, the excess strain is 121.1 mm. Based on the crest length of the Tannur Dam being 242 m, the total crack width expected is about 29.4 mm. Assuming a permissible crack width of 2.5 mm, the estimated total number of RCC blocks is 12. Each would have a length of 20 m. However, the actual size of the constructed blocks was about 15 m. This number was established earlier in the design report 共Howard Humphreys 1995兲 considering a presumptive value for the heat of hydration rate of 440 J/g at 28 days.
Surface Gradient Cracking In an RCC dam, the surface of the dam cools faster than the interior body. This causes a temperature gradient between the cooled surface and the hot interior mass. Such a difference will result in a thermal gradient that is likely to generate undesirable thermal stresses and that may cause cracks to develop at the exterior surface. This is not expected to be a structural problem unless the cracks extend through to the drainage gallery, where the leakage of water may increase. The method proposed by Tatro and Schrader 共1992兲 was used in the analysis to calculate the surface gradient cracking. Table 5 shows the cracking analysis for a depth of 9.0 m. It is observed that no surface cracking occurs during the first three days. However, by 14 days the cracking is apparent, based on the RCC tensile strength quoted by Tatro and Schrader 共1992兲. Therefore, appropriately spaced joints are necessary to control the cracks that are predicted to occur. From Table 5, the incremental strain is 111.36 mm; therefore, the excess strain is 31.36 mm. Based on a crest length of 242 m for the Tannur Dam, and considering a crack width of 2.5 mm, the total number of blocks to avoid such cracks is about four, at a spacing of 60 m.
Mass Gradient Cracking
Three-Dimensional Model Analysis
The mass gradient strain usually is determined by the following equation:
A 3D analysis was also carried out for the Tannur RCC Dam. Fig. 6 shows the geometry of the dam and its main dimensions. The
Table 5. Surface Cracking Analysis for Depth of 9 m Period 共days兲
Temperature difference 共°C兲
Incremental strain 共mm兲
Modulus of elasticity 共MPa兲a
Incremental stress 共MPa兲
Total stress 共MPa兲
Maximum tensile stress 共MPa兲a
0–3 3–14 14 –28
8.6 7.8 0.77
55.93 50.43 5.0
9,655 17,310 18,758
0.54 0.873 0.09
0.54 1.413 1.5
0.62 1.13 1.45
a
Adopted from Tatro and Schrader 共1992兲. JOURNAL OF PERFORMANCE OF CONSTRUCTED FACILITIES © ASCE / NOVEMBER 2003 / 181
Fig. 6. Geometry of Tannur Dam for 3D analysis; L⫽15, 30, and 45 m Fig. 8. Thermal boundary conditions for thermal analysis
length of the dam is divided into 12 blocks. Each block is 20 m long, and one of these blocks, with different lengths of 15, 30, and 45 m, was modeled with finite-element mesh, as shown in Fig. 7. A Solid70 element type was used for the thermal analysis. This element has eight nodes, with a single degree of freedom temperature at each node. Fig. 8 shows the boundary conditions for the thermal analysis. A Solid65 element type was used for the structural analysis. This element has three degrees of freedom, permitting movements in the x, y, and z directions. Fig. 9 shows the boundary conditions for the structural analysis. The step-bystep analysis of the construction simulation process allows the determination of the temperature and stress distributions for each added lift.
Fig. 9. Structural boundary conditions for structural analysis
Fig. 7. Three-dimensional finite-element model—mesh
Fig. 10. Temperature prediction at center of dam at 355 m elevation with 20°C rolled compacted concrete placement temperature
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Fig. 11. Comparison of thermal analysis predictions and actual readings of thermocouples from April until end of June at elevation of 365 m ASL
Finite-Element Results
Fig. 13. Actual temperature contours at end of rolled compacted concrete placement
Two-Dimensional Results The temperature distribution shown in Fig. 10 is for the specific location at an elevation of 355 m ASL—i.e., 12 m above the base of the dam. This shows that the maximum RCC temperature is approximately 37.7°C. It is shown that the temperature reached its maximum in the first 10 days due to the high rate of hydration that remained constant for a long period of time because heat transfer from the core of the dam to the surface is very slow. Further, the heat conduction due to the construction of the overlying layers of RCC prevents internal heat loss from the constructed lift surface. Fig. 11 shows a comparison between the predicted temperature rise and the actual thermocouple readings at an elevation of 365 m ASL, covering a period of 90 days between April and the end of June. Generally, a good agreement has been obtained. The small differences between the predicted and the actual readings could be attributed to the change of the RCC placement temperature. The placement temperature used for the analysis is 20°C. The actual maximum temperature in the dam by November 7 was about 40°C. This rise in temperature is attributed to the change of RCC placement temperature during the hot summer months, starting from June through September. The placement of RCC continued until August 8, 2000 and resumed on September 24, with the variation of RCC placement temperature reaching a
maximum of 26°C and with the reduction of the cement content to 120 kg/m3 starting in July. In all cases, the overall temperature in the body of the dam did not exceed 43°C. Fig. 12 shows the measured temperature through November 7 compared to that predicted by ANSYS. It should be clearly understood that during the months of August and September no RCC placement took place, and consequently readings of thermocouples were not made. Fig. 13 shows the actual temperature contours measured at the end of construction of the dam. Heat of hydration testing during the construction of the dam established that the actual heat of hydration of the cement in use is 309 J/g. Fig. 14 shows the predicted temperature for different nodal points at different locations. The results demonstrate that the temperature at the surface is affected by the environmental conditions, and the temperature in the center of the dam is essentially unaffected by the ambient temperature. From the two-dimensional analysis, plots for the temperature contour and stress distributions in the body of the dam for the different constructed lifts are shown in Fig. 15. The maximum temperature recorded after the end of construction was 37.7°C in the core of the dam.
Fig. 12. Comparison of thermal analysis predictions and actual readings of thermocouples until November 7 at elevation of 365 m ASL
Fig. 14. Predicted temperature history at 365 m ASL elevation measured from upstream face
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Fig. 15. Two-dimensional temperature and stress distribution for different constructed lifts: 共a兲 temperature distribution at Lift 3; 共b兲 stress distribution at Lift 3; 共c兲 temperature distribution at Lift 6; 共d兲 stress distribution at Lift 6; 共e兲 temperature distribution at Lift 12; 共f兲 stress distribution at Lift 12; 共g兲 temperature distribution at Lift 19; 共h兲 stress distribution at Lift 19
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Fig. 16. Three-dimensional temperature and principal stress distribution in body for block length of 15 m: 共a兲 temperature distribution at end of casting for half of 15 m block length; 共b兲 principal stress at end of casting for half of 15 m block length; 共c兲 temperature distribution at end of heat of hydration for half of 15 m block length; 共d兲 principal stress at end of heat of hydration for half of 15 m block length; 共e兲 temperature distribution after one year for half of 15 m block length; 共f兲 principal stress after one year for half of 15 m block length
Three-Dimensional Results Three different blocks of 15, 30, and 45 m lengths were modeled. These blocks were taken at the central monolith in the dam. The maximum temperature recorded after the end of construction was 37.7°C for a 15 m block length, as shown in Fig. 16. After one year, a gradual decrease in temperature of the dam core is observed. Similar trends were observed for block lengths of 30 and 45 m. It is predicted that the temperature of the inner core of the dam will coincide with the mean annual temperature, but this will take many years. Fig. 16 shows the predicted temperature and principal stress contours developed in the dam body for a block length of 15 m. The results indicate that the maximum principal stresses decrease with decreasing temperatures of the dam.
Fig. 17. Predicted temperature at elevation of 355 m ASL for threedimensional model
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Fig. 18. Principal stresses at center of dam for 15 m block length
Fig. 17 shows the predicted temperature for two different nodal points at two locations for the three-dimensional model. Again the results demonstrate that the temperature at the surface is affected by the environmental conditions and the temperature in the center of the dam is almost unaffected by air temperatures. Fig. 18 represents the principal stresses at the center of the dam for a block length of 15 m for different heights of the dam. The results indicated that the first peak tensile stress occurs shortly after placement of the RCC layers. The tensile stress then increases and remains nearly constant during construction before reducing because of the effect of the reservoir load on the upstream face. It also shows that the peak tensile stresses occur within 10 days of placement. Fig. 19 represents the cross-valley stress 共z direction兲 for a point at the center of the base of the dam for different block lengths. Again, the first peak stresses occur shortly after the placement of the RCC layers. Fig. 20 shows the principal stress path along the upstream face for different block lengths. The results indicated that the stress developed for a block length of 15 m is lower than that for block lengths of 30 and 45 m. At a location of 30 m elevation above the base of the dam, the peak value of the principal stress is 0.42 MPa for a 15 m block length, whereas for 30 and 45 m block lengths the peak stress increases to 0.94 and 1.1 MPa, respectively.
Fig. 19. Cross-valley stress 共z direction兲 at center of base of dam for different block lengths
Fig. 20. Principal stress path along upstream face for different block lengths
Conclusion The Tannur RCC Dam is constructed with a crest length of 242 m and 17 contraction joints at approximately 15 m spacing. However, from the computational results presented in this study, it is concluded that a 20 m average joint spacing is satisfactory to accommodate contraction openings of up to 2.5 mm if cracking is to be avoided. It was observed that if the RCC temperature is being raised to 26°C, the maximum peak temperature in the core of the dam could reach 43°C, which is less than the predicted peak temperature of 45°C established in the design report to cause cracks in the dam. Furthermore, in the design report 共Howard Humphreys 1995兲, it was concluded that the design criteria require that the RCC have a compressive strength of 20 MPa, and a tensile strength of over 1.35 MPa. The dam does not experience tensile stresses in excess of the tensile strength of the concrete. The tensile thermal stresses due to a temperature drop in the interior of an RCC gravity dam are partially compensated by the action of the weight of the concrete and water pressure. Results are very sensitive to the time of the year, the ambient air temperature, the RCC placement temperature, and the rate of heat of hydration. In conclusion, a thermal stress analysis using a finite-element method showed that the method is efficient and reliable. The temperatures and the stress distribution in the dam as predicted by the finite-element method are reasonable and predict the evolution of temperature and thermal stress with time. Using a commercially available finite-element program and the available laboratory data, the incremental construction process of a mass-concrete structure can be modeled to produce results that can be used in practical applications. The results from the analysis correlate closely with the actual thermal data obtained from the construction instrumentation.
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Acknowledgments The writers thank Brian Forbes and Francisco Andriolo for their discussions, advice, and ideas given at the start of and during the preparation of this paper. The writers also thank the owner of Tannur Dam, the Jordan Valley Authority, for allowing them to prepare this paper for publication.
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high sand RCC mixes and in-situ modification of RCC used for construction of Cadiangullong Dam NSW.’’ ANCOLD Bulletin, Sydney, Australia. Howard Humphreys Consulting Engineers. 共1995兲. ‘‘The study and design of Tannur Dam.’’ Design Rep., Vol. III, prepared for Jordan Valley Authority. Ishikawa, M. 共1991兲. ‘‘Thermal stress analysis of concrete dam.’’ Comput. Struct., 40共2兲, 347–352. Neville, A. M., and Brooks, J. J. 共1994兲. Concrete technology, Longman’s, Singapore. Tatro, S., and Schrader, E. 共1992兲. ‘‘Thermal analysis for RCC—A practical approach.’’ Proc., Roller Compacted Concrete III, ASCE, New York, 389– 406. Truman, K. Z., Petruska, D., Ferhi, A., and Fehl, B. 共1991兲. ‘‘Nonlinear, incremental analysis of mass-concrete lock monolith.’’ J. Struct. Eng., 117共6兲, 1834 –1851. U.S. Army Corps of Engineers. 共1997兲. ‘‘Thermal studies of mass concrete structures.’’ Engineering Technical Letter 1110-2-542, Washington, D.C. Zhang, Z., and Garga, V. K. 共1996兲. ‘‘Temperature and temperature induced stresses for RCC dams.’’ Dam Eng., VII共2兲.
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