# Simulation of Temperature Field – RCC arch dam

30 April 2008

Use of a 3-D FE method to simulat the temperature field of a roller compacted concrete (RCC) arch dam during both construction and operation

Based on the physical properties of roller compacted concrete (RCC) arch dam, a three-dimensional (3-D) finite element (FE)?relocating mesh method is used to simulate the temperature field during the periods of construction and operation.

The effect of the change of thermal insulation along with age, the progress of pouring by layer, summer shutdown and water storage on temperature field are considered in the simulation analysis. The distributions of temperature field and the change laws with time are provided, offering the reference for the dam design and the temperature control measures adopted during construction of the dam.

### Introduction

The Lin Hekou arch dam is near Langao town in Shaanxi province, China, is a double-curvature structure with a single circle centre. It has a maximum height of 100m, a crest width of 270m at elevation 515m and the normal pool level of the reservori is 512m. The total installed capacity of the power plant is 72MW.

Although the foundation bed used normal concrete with triple-graded CC2820MPa, other segments were built with RCC. The block of the upstream face was built with two-graded RCC9020MPa while the rest of the segments were poured with triple-graded RCC9020MPa.

### Parameters

Based on some RCC dam experimental data, the thermal parameters are showed in Table 1.

The data of air temperature:

Ta(t) = 17 + 11.5 cos(3.1415926(t – 6.6)/6.0)

The water temperature data in the reservoir:

watert(t,z)=4.53+14.49(1–2.08z/60.0+1.16z2/3600.0–0.08z3/216000.0)

+ 11.45 cos(3.1415926(t – 8.75 + 1.3e–0.085z)/6.0)

Where, t is the temperature of water (°C), z is depth, (m).

### Construction schedule

Each layer of the RCC dam was placed with a thickness of 300mm. After the placement of 5-10 continuous roller compacted layers there were intermissions of 8-15 days. Normal concrete was poured from 1st to 20th on February in 2001; RCC was poured immediately afterwards and that work was finished by the end of April at El. 418.5m, and pouring stopped forg 210 days.

At the end of May the following year, pouring resumed at the dam to El. 468m, then stopped for 90 days. The next phase of pouring, to the El. 515m design elevation, was started at the end of January, 2003. The pouring temperature of concrete in the calculations adopted a period of 10 days’ average air temperature, which is showed in Table 2.

### Calculation method

The 3-D FE floating mesh method[2] was adopted to analyse the temperature field during the construction period and operating period. The FE calculation methods and formula are those taken from Bofang[1]. The arch dam is a space shell structure, its geometry and boundary conditions being relatively complex with both upstream and downstream surfaces curved surfaces. Consequently, to achieve the correct simulation of the geometry and guarantee the calculation accuracy, 20 isoparametric element nodes were adopted as a fundamental discrete units. In the grid cutting process, considering the impacts of the foundation and abutment on the two sides of dam, a certain number of elements were taken in those places. Evidently, in the simulation of the construction process, because of a mass of elements and nodes, high order equation and many calculations, the workload was very heavy. In this paper, 3-D FE floating mesh method was adopted for simulation.

The so-called 3-D FE floating mesh method, on the basis of the relation of material characteristics and age, combines many layers of small unit mesh size, in which the concrete can be taken as a homogeneous body with its elastic modulus and temperature rise caused by the heat of hydration heat, and the degree of creep, calculated with the average age.

Compared to the fixed mesh method, the number of finite mesh and nodes is significantly less in the relocating mesh method with the increasing height of a dam, thus lowering the order of the calculation. The influence on calculation accuracy is not great, due to the comparatively small changes of elastic modulus and concrete heat emissions in big meshes.

### Calculation model

The boundary conditions were: the transverse joint side of the monolith, the underside and four sides of the foundation were the thermal insulation boundary.

In the monolith upstream, above the water level the calculated boundary conditions were defined as solid-air boundary and below the water level were defined as solid-water boundary, and so too was the monolith downstream. The solid-air boundary belonged to the third boundary condition, and the solid-water boundary belonged to the first boundary condition.

The calculated result analysis on the temperature field

The calculated result analysis on the stability temperature field

According to the upstream and downstream normal water level of reservoir, air temperature distributing and annual mean temperature at dam site, the stability temperature field which was calculated at crown section and vertical section is showed in Fig.1 and Fig.2. The calculated result of stability temperature field was accorded with the general law. In Fig.1, the temperature was lower in the central and bottom of upstream, which was about 5°C and close to the deep water temperature of reservoir; it was about 17°C above the normal water level and close to annual mean temperature adding 2-3°C solar radiation heat. In Fig.2, in the case of equal elevation at dam, the temperature in the interior of dam was higher than upstream face, but lower than downstream face, which was also accorded with temperature distribution at dam.

The calculated result analysis on the unstable temperature field

Distribution of maximum temperatures with time

According to the material characteristics of the RCC, for the newly-poured lift, whose thermal gradient was relatively large, smaller calculation step length should be adopted in the calculation, e.g. 0.25 days as used in this analysis. When it came to the operating period, the parameters changed slowly with age, then step length from 0.5 to 30 days varied regularly. With so much calculation required, in order to reduce the working capacity of data ordering only the values of maximum temperature were taken on a monthly basis during construction. During the operating phase, the annual maximum temperature value was given.

The duration curve of maximum temperature of the dam is shown in Fig.3. The maximum temperature of dam, 38.96°C, appeared near the 4m away from upstream surface at the elevation of 465.7m with the occurring time of 499.75 days (19 June, 2002), the pouring time of the concrete here is 480.75 days (31 May, 2002).

Based on the construction schedule, the work was ceased from June to August, and the maximum temperature appeared just in the intermittent period. It was seen from the average temperature table that the mean temperature in late May was 21.1°C, the adiabatic rise of temperature of the upstream surface concrete was 19.18°C and that the internal temperature of the dam was comparatively high in the intermittent period which reached the summit value after 20 days as heat was dispersed into surroundings. Then it was known that the higher the pouring temperature was and the higher grade the concrete was of, the higher the maximum temperature of the dam was. Moreover, it was seen from the occurring times of the maximum temperature, as the hydration heat of RCC was dissipated slowly, the maximum temperature appeared lag of the pouring time of lift.

Seen from Fig.3, the maximum temperature in April, 2001 was 31.16°C with the occurring time 19 April, 2001. The pouring work came to a stoppage from 10 April, 2001 to 5 December, 2001. During the intermittent period, the dam maximum temperature gradually decreased, as the dam emanated heat into the external environment. After 5 December, concrete-pouring resumed, but the dam was prone to exchange heat with the surroundings, due to the low temperature outside, thus the dam maximum temperature remaining relatively low, about 22°C. Then it was obvious that when both of the temperature outside and the pouring temperature were low, it was suitable for pouring the strong restraint district, without the maximum temperature increasing greatly. Since 4 April, 2002 with the rise in air temperature, the pouring temperature increased, leading to an obvious increase in the maximum temperature of the dam, which came to a peak in mid-May. As the temperature outside gradually descended, the pouring temperature decreased as well, strengthening the heat exchange between dam and external environment, then the maximum temperature reduced apparently.

During the operating period, with the dam emanating heat into surroundings, the maximum temperature gradually decreased, reaching a steady value of 30.16°C. From the data of the time and location of the maximum temperatures, it was clear that the peak value in the operating period appeared on the downstream surface on 9 August each year. The mean air temperature of the early August was 27.1°C with the average temperature rise due to radiation 3-4°C. Seen from above, the dam peak temperature in the operating period occurs on dam surface, which was just related to air temperature, about the maximum air temperature added to the radiation temperature rise.

Distribution of temperature - crown section, vertical section

The temperature isoline maps during construction (1 April, 2002 and 1 January, 2003) and operation period (31 January, 2005) at crown section and vertical section of dam are shown in the figures. As Fig.4 shows, the higher the pouring temperature then the higher the regional temperature near the new pouring concrete; and, on the upstream and downstream, because of the dam dispersing heat into surroundings, temperature was relatively low. As Fig.5 and Fig.7 disshow, the temperature at center of dam was equal at same elevation. Before water storage the upstream surface temperature of dam was almost the same as downstream and, afterwards, the surface temperature was equal with water temperature, but a little lower than the air temperature, as Fig.6 shows.

From the end of construction period to operating period, in the centre of dam appeared a high temperature zone which was about within the scope of 40m-60m of the height of the dam. This high temperature zone was poured in April to May, 2002, and showed that the higher the outside temperature and pouring temperature, and the poorer the heat dissipation, the higher the temperature rise.

During the operating period, with the dam dispersing heat into surroundings, the interior maximum temperature in dam gradually decreased, but the exterior maximum temperature varied with air temperature. The interior maximum temperature needed about 30 years to receive the stability temperature field.

### Conclusion

(1) When the pouring temperature equaled to the 10-day mean temperature, the maximum temperature of dam was 38.96°C. Because of temperature load was the main load of arch dam, strict temperature control measures should be adopted to reduce the maximum temperature of dam, and so decrease thermal stress of dam.

(2) Pouring temperature and material grade were the main factors at the influence on maximum temperature of dam. When material grade was decided, the lower the pouring temperature was, the smaller the maximum temperature of the dam was. Therefore, in strong restraint area, pouring concrete in period of low temperature was better, which was of benefit for temperature control measures.

(3) The maximum temperature of the dam appeared in the area of pouring in high temperature season, because the outside temperature and pouring temperature were high, and the heat dissipation condition in dam was poor.

Shouyi Li Jinke Ren Zhongming Wu Lijuan Zhao

Xi’an University of Technology, Xi’an 710048, Pepole’s Republic of China

Tables

Table 1: The thermal parameters of some RCC dam
Table 2 The ten-day average air temperature in each month(?)

Figures 4 and 5
Figures 6 and 7
Figures 1 and 2
Figure 3
Figures 8 and 9