Discussion of method for computing temperature……

Discussion of method for computing temperature load during operation period on high arch dam

Wang，Zhiqiang

Jiangxi Provincial Institute of Water Sciences

College of Hydrodynamic and Ecology Engineering，Nanchang Institute of Technology

Wu，Xiaobin

College of Hydrodynamic and Ecology Engineering，Nanchang Institute of Technology

1 Introduction

The temperature load is one of main design loads on arch dam.According to the existing arch dam design specification in our country，it only considers average temperature and equivalent linear temperature difference of dam section in operation period，the influence of non-linear temperature difference has not been considered ^［1］.How much of the error caused by not considering non-linear temperature difference and how to consider non-linear temperature difference have been people’s concern.After hydration heat of dam concrete and impact of initial temperature difference disappeared，the dam enters into quasi-steady temperature field；temperature load is the difference between quasi-steady temperature field and joint closure temperature field.This method can consider the influence of non-linear tempera Based on introducing the relevant calculation principles，this paper first takes free plate as an example，has calculated the temperature field corresponding to analytical method，finite element method，standard method，explains the rationality of using written program to carry on finite element analysis.Then takes Xiluodu arch dam as an example，the dam temperature load and temperature stress has been calculated by using finite element method and standard method，the difference between both has been discussed.

本文发表于2013年。

2 Calculation Principles

2.1 Temperature load corresponding to analytical method

Temperature load corresponding to analytical method is obtained for an infinite free plate；the infinite long free plate sees reference ^［3］..

Among them，the temperature of plate surface point on upstream and downstream is equal to boundary temperature.

When calculating plate internal point temperature，multi-annual average temperature on upstream and downstream side is reflected by linear interpolation，multi-annual average temperature amplitude on upstream and downstream side is reflected by the following formula.

For the plate satisfying heat conduction equation and boundary conditions，the theoretical solution sees reference ^［3］.

After calculating the temperature of various points，the temperature load of various points is obtained by subtracting initial temperature.

2.2 Temperature load corresponding to finite element method

Based on heat conduction equation，considering initial conditions and outside air temperature，water temperature，ground temperature and other boundary conditions，annual change quasi-steady temperature field is calculated by finite element method，temperature load is the difference between quasi-steady temperature field and joint closure temperature field ^［3］.Here the quasi-steady temperature field is non-heat-source non-steady temperature field，it is different from non-steady temperature field that considering concrete hydration heat of construction process.

2.3 Temperature load corresponding to standard method

After T_m and T_d of cross-section has been computed using standard method，the temperature load at various points of cross-section is obtained through the following method.Equivalent linear temperature is T_e（x）=T_m+T_d·x/L，in dam upstream surface，x=-L/2，equivalent temperature is T_e（x）=T_m-T_d/2，in dam downstream surface，xturefieldandjointclosuretemperaturefield.This methodcanconsidertheinfluenceof non-lineartemperaturedifference.Basedonactualairtemperatureandwatertemperature，etc.，dam quasi-steadytemperaturefieldcan beobtained usingfiniteelement simulation^[2].

=L/2，equivalent temperature is T_e（x）=T_m+T_d/2，in dam interior，equivalent temperature is obtained by linear interpolation.

2.4 Temperature stress corresponding to finite element method

The actual project is often complex，its temperature stress is very difficult to be obtained by analytical method，at present it is mainly obtained by finite element method.The principle of using finite element method to calculate temperature stress sees reference ^［3］.

3 Example confirmations

In order to explains the rationality of using written program to carry on finite element analysis，this paper takes free plate as an example，has calculated the temperature load by analytical method，finite element method，standard method.

The plate height is 400m，thickness is 40m，annual average temperature is 18℃，annual amplitude of air temperature is 10℃，initial temperature is 16℃，upstream water level is 400m，downstream is no water，water depth of constant temperature strata is 60m，concretes thermal diffusivity is 3m²/month.

Finite element mesh is divided into 20 along horizontal direction and vertical direction.Temperature load of temperature rise in mid-July on upper 380m and lower 20m elevation is shown in Fig.2.In which the time of calculating temperature field by finite element method is 50 years，the temperature tends to be stable 20 years later，and this paper takes the temperature in mid-July of 49 years as the temperature corresponding to temperature-rise.

Fig.2 Temperature load in mid-July at different elevation of plate

From the above results we can see that：①the results obtained by finite element method and analytic method are basically same，explaining the finite element analysis program in this paper is reasonable；②in the place not far away from the downstream surface，the result obtained by analytic method has catastrophic phenomenon，it is not the real case，it may be numerical singularity occurred in the area，needing further study.

4 Example analysis

The height of Xiluodu arch dam is 278m，crest elevation is 610m，annual average temperature is 21.7℃，annual amplitude of air temperature is 9.25℃，joint closure temperature of elevation above 560m is 16℃，joint closure temperature of elevation below 560m is 13℃，upstream normal water level is 600m，corresponding downstream water level is 378m，water depth of constant temperature strata is 140m，concretes thermal diffusivity is 1.68m²/month.

Fig.3 Finite element mesh of Xiluodu arch dam

The temperature load and temperature stress of temperature drop in mid-January are calculated by standard methods and finite element method.In which the time of calculating temperature field by finite element method is 50 years，the temperature tends to be stable 20 years later，and this paper takes the temperature in mid-January of 49 years as the temperature corresponding to temperature-drop.

The finite element mesh of Xiluodu arch is shown in Fig.3，the temperature load of operation period in mid-January at 590m elevation and 400m elevation are shown in Fig.4.

Fig.4 Temperature load in mid-January at different elevation

From the above results we can see that：①in the upper dam，because dam thickness is small and temperature gradient change is big at upstream and downstream surface，the difference between the results obtained by standard method and finite element method is big in the whole cross-section，the influence of non-linear temperature difference almost affects entire cross-section；②In the lower dam，because dam thickness is big，temperature amplitude of upstream dam surface is small or even zero，temperature amplitude of downstream dam surface is big，the difference between the results obtained by standard method and finite element method is small near upstream surface and in dam interior but big near downstream surface.The influence of non-linear temperature difference only affects the region near downstream surface.

5 Conclusion

（1）This paper takes free plate as an example，has calculated the temperature field of temperature rise in mid-July by analytical method，finite element method，standard method，the results obtained by finite element method and analytic method are basically same，explains the rationality of using written program to carry on finite element analysis.

（2）This paper takes Xiluodu arch dam as an example，the dam temperature load and temperature stress of temperature drop in mid-January has been calculated by using finite element method and standard method.The influence of non-linear temperature difference is big in the whole cross-section of upper dam and near downstream surface of lower dam.

（3）Using finite element method to calculate temperature load of arch dam，can consider the influence of non-linear temperature difference，the result matches practical case.Along with the computer level’s development，in the practical application，finite element method can be used to calculate temperature load of arch dam.

References

［1］SL 282—2003.Design specification for concrete arch dam.Beijing：China Water&Power Press，2003.

［2］Yang Bo，Zhu Bofang.Analysis of autogenous thermal stress in operating period in Arch dams.Water Resources and Hydropower Technology，2003，34：24-26.

［3］Zhu Bofang.Thermal stresses and temperature control of mass concrete.Beijing：China Electric Power Press，1999.

本文发表于2013年。