Thermal and structural analysis of RCC double-curvature arch dam.

Abdulrazeg, Aeid Ali ; Noorzaei, Jamaloddin ; Jaafar, Mohamed Saleh 等

Introduction

The RCC technology has being applied in gravity arch dams in the late of 1980s. The first RCC arch dam was constructed in the world is Kenllpoort dam, which was completed in S. Africa in 1988 (Qiuhua 2003). Up to the end of 2003, the number of RCC arch dams completed or under construction is 14. The construction technology of a RCC arch dam is very similar to that of a RCC gravity dam. The main differences between arch RCC dam and gravity RCC dam are that arch dam has a wider surface and lesser thickness, accordingly different thermal and stress response.

Xie et al. (2005) and Zhang et al. (2009) used a three-dimensional finite element relocating mesh method to simulate construction process and compute temperature field. In their work, many factors have also been considered, such as thermal adiabatic rise of temperature with age, the process of placement by layer, creep, work suspension in summer and the change of air temperature. However, the studies were limited for thermal analysis only. In addition, further studies to select the proper relocating age of concrete are essential. Penghui et al. (2007) determined creep values for thermal analysis of Dahuashui RCC arch dam, applied time and stress dependent coefficient, in a multi-term expression, whereby certain constants were apparently derived through experimental study to an accuracy of six decimal places. In the presented work, the variation of the RCC mechanical properties with time has not been considered and fixed values were used during the analysis.

Shuping et al. (1999) performed an emulation analysis of two RCC arch dams using three dimensional finite elements. It has been found that, the thermal stresses were too high for the construction plan without contraction joints. However, the authors ignored the effect of dam foundation interaction. In 2003, a similar study was conducted by Nilipour (2003). It was concluded that, at the same elevation higher temperature rise was experienced in the core of the dam in applying conventional method as compared with RCC method. However, higher tensile stress occurs in the model using conventional method in the early age of concrete. Whereas, maximum tensile stress in RCC model occurs later due to operation loads comparatively with a lower value, hence post-cooling is not necessary in RCC construction method. However, in these investigations a simplified relation for stress-strain relationship has been used which will overestimate the stress of the dam (Crichton et al. 1999).

It is of particular significance to observe that, most of the studies that address the stress analysis of RCC dams have considered the time dependent deformation such as creep very approximately or neglected it all together (Araujo, Awruch 1998; Agullo, Aguado 1995; Saetta et al. 1995; Malkawi et al. 2003; Noorzaei et al. 2006; Zhiqi 2007). However, creep has a significant influence on the stress values of the concrete blocks, especially in early ages (Santurjian, Kolarow 1995). Moreover, there was a concern that RCC acts in the same manner as conventional concrete and various models developed for the conventional concrete are applied for RCC without any form of verification. Furthermore, the material laws for concrete, mainly based on the age of concrete and very limited study, considered the temperature effect on the mechanical properties of the concrete (Luna, Wu 2000; Cervera et al. 2000).

Consistent cracking criterion is also necessary for an exact evaluation of the dam behavior. Most of the previous researchers who investigated dam concrete mainly focused on the uniaxial compressive strength and tensile strength, so their studies did not provide information on the behavior of dam concrete under bi-axial or tri-axial stress states (Wang, Song 2008).

1. Motivation of the present work

The present investigation is a continuation of the authors' previous work (Bayagoob et al. 2010) and presenting a numerical implementation using three-dimensional finite element method to simulate the construction process of RCC arch dams. The primary objectives of the present research work:

--This paper presents a new comprehensive numerical procedure to simulate the construction process of arch RCC dams. It takes into account the more relevant features of the behavior of concrete such as hydration, ageing, thermal and creep effect;

--To apply the proposed model to an actual arch RCC dam to demonstrate the efficiency of the model.

2. Computation of thermal field

The Numerical solution scheme used in this study is based on the Taylor-Galerkin approach. Upon applying this approach, the following system of differential equations is obtained (Bayagoob et al. 2010):

[[[K.sub.t]].sup.(e)][{T}.sup.(e)] - [[C].sup.e] [{[partial derivative]T/[partial derivative]t}.sup.(e)] = [{F}.sup.(e)], (1)

where: [[C].sup.e] is the capacitance matrix; [[K.sub.t]] is the heat stiffness matrix; {F} is the total load heat vector due to hydration and convection actions.

The finite difference approximation was used to solve Eqn (1) in the time domain numerically. This solution (after assembly of the stiffness matrices) is given by (Sergerlind 1984):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)

where: [{T}.sub.b] and [{[F.sub.t]}.sub.b] are {T} and {[F.sub.t]} at time (b) and [{T}.sub.a] and [{Ft}.sub.a] are {T} and {[F.sub.t]} at time (a); [theta] is a scalar (0 [less than or equal to] [theta] [less than or equal to] 1) which is equal to 2/3 in the Galerkin method. Then Eqn (2) takes the following general form:

[[A.sub.G]]{[DELTA]T} = [[F.sub.G]], (3)

where:

[[A.sub.G]] = 1/[DELTA]t [C] + 2/3[[K.sub.t]] (a-4)

and

{[F.sub.G]} = 1/2([{[F.sub.t]}.sub.a] + 2[{[F.sub.t]}.sub.b] - 3[[K.sub.t]][{T}.sub.a]), (b-4)

where: {[DELTA]T} represents the temperature changes at the nodal points with respect to time At which is used for evaluation of temperatures at the new time stage using the following expression:

[{T}.sub.b] = [{T}.sub.a] + 2/3 {[DELTA]T}. (c-4)

3. Constitutive theories for aging viscoelastic materials

Time dependent behavior of concrete is described by the theory of viscoelasticity for aging materials. The sum of elastic {[[epsilon].sub.e]} and creep {[[epsilon].sub.c]} strain is replaced by the viscoelastic strain {[[epsilon].sub.ve]} as follows:

{[[epsilon].sub.ve]} = {[[epsilon].sub.e]} + {[[epsilon].sub.c]}. (5)

According to the viscoelastic theory, the strain at time t caused by constant stress a applied at time [theta] is given by:

[epsilon](t, [theta]) = J(t, [theta])[sigma]. (6)

According to Boltzmann's principal of superposition of strains, which was modified by Neville (Neville et al. 1983) to include the effect of aging of concrete, the summation of the strain history due to all stress increments [DELTA][sigma]([theta]) before time (t) is expressed as (Atrushi 2003):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (7)

where: t is current time (measured from casting of concrete); [theta] is concrete age at loading;[deLTA][sigma]([theta]) is stress increment applied at [theta]; [epsilon](t) is total strain and J(t, [theta]) is creep compliance.

If the stress varies continuously, Eqn (7) could be expressed as (Du, Liu 1994):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (8)

3.1. Creep compliance of RCC material

The exponential model of creep has been attractive from the computation point of view, because it can avoid storing the whole stress history and made the implementation feasible comparing with other models (Abdulrazeg et al. 2010).

The creep functions may be expressed with Dirichlet series (Wu, Luna 2001) as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (9)

where: J (t, [theta]) is creep functions; [[mu].sub.[gamma]]([theta]) is function of one variable, called the reduced times; [theta] is the loading age in days, [y.sub.[gamma]]([theta]) is experimental function.

Neglecting temperature effects, a specific form of the compliance function is often used (Du, Liu 1994):

J(t, [theta]) = C(t, [theta]) + 1/E(t), (10)

where C (t, [theta]) is creep compliance, it can be expressed as,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (11)

where [[alpha].sub.[gamma]], [[beta].sub.[gamma]], [[delta].sub.[gamma]], D, [S.sub.[gamma]] are constants determined from the experimental data.

E(t) is elastic modulus, and the model which developed by (Conrad et al. 2003), has been used in this study. This model expresses the variation of the elastic modulus of RCC material with time:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (12)

where [E.sub.c] is the final elastic modulus, a and b are model parameters.

4. Proposed models of creep and elastic with temperature effect

Bazant introduced the concept of the degree of hydration to include the temperature influence (Bazant et al. 2004). Term of equivalent age [[theta].sub.e], which represents the hydration period for which the same degree of hydration is reached at a current temperature as that one reached during the actual time (t) at a reference temperature. The concrete age, [theta] will be replaced by equivalent age [[theta].sub.e] in the exponential model Eqn (9):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (13)

where [beta](i) is a function of current temperature and expressed as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (a-13)

where: T (t) is a current temperature, Tr = 20[degrees]C; [[PI].sub.h] is function of hydration degree = 2700 K. To consider the temperature effect on the creep compliance, a function [y.sub.[gamma]](t) is introduced as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (14)

where [[psi].sub.[tau]](t) is a function of current temperature and expressed as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (a-14)

where [[PI].sub.[alpha]] is function of activation energy of creep = 5000 K.

Using the introduced term of equivalent age [[tau].sub.e], which represents the hydration period, the concrete age, [tau] will be replaced with this equivalent age [[tau].sub.e] in the above elastic modulus Eqn (12). So modified model includes the aging and temperature effects on the elastic modulus (Abdulrazeg et al. 2010a).

5. Creep at variable temperature

For changing temperature conditions while the concrete is under load, an additional creep component, the so-called transient thermal creep, which develops at the time of a temperature increase, should be considered (Bosnjak 2000). Transient thermal creep is interdependence between temperature response and mechanical response, and based on that the thermal strain rate should be made depending on the current stress state (Thelandersson 1987):

[DELTA][[epsilon].sub.T] = [alpha][DELTA]T (1 + [xi] [sigma]/[f.sub.c]), (15)

where: [DELTA][[epsilon].sub.T] is thermal strain increment; [sigma] current stress; [f.sub.c] is uniaxial compressive strength at reference temperature; [DELTA]T is temperature change; [xi] model parameter and [alpha] coefficient of thermal expansion.

Jonasson (1994) applied Eqn (15) to young concrete and further modified the Eqn (13) and expressed as:

[DELTA][[epsilon].sub.T] = [alpha][DELTA]T(1 + [xi] [sigma]/[f.sub.t] sign[DELTA]T), (16)

where: [f.sub.t] is the tensile strength at reference temperature and [xi] range between (0.1-0.7) the best value for [xi] fitted to the test results was 0.27 (Hedlund 1996).

6. The formulation of RCC creep with temperature effects

To predict the response of the concrete in the early period of construction, a step-by-step method is necessary. At the beginning of each time step, deformation due to thermal variation (hydration and environment) and creep during the current time interval are imposed. This imposed incremental strain on any point at ith time interval is defined as:

[DELTA][[epsilon].sub.n] = [DELTA][[epsilon].sup.e.sub.n] + [DELTA][[epsilon].sup.c.sub.n] + [DELTA][[epsilon].sup.T.sub.n] + [DELTA][[epsilon].sup.Trcr.sub.n], (17)

where [DELTA][[epsilon].sup.e.sub.n], [DELTA][[epsilon].sup.c.sub.n], [DELTA][[epsilon].sup.T.sub.n], [DELTA][[epsilon].sup.Trcr.sub.n] refer to elastic, creep, temperature and transient thermal creep strain increment column vectors, respectively.

Wu and Luna 2001 introduced the numerical procedure for creep strain in mass concrete structure with temperature effects by modifying the exponential algorithm for concrete and the final formula for the incremental in strain (Eqn (17)) are presented below.

Let the total time interval [[t.sub.0], t] be subdivided into N steps, for the step [[t.sub.i-1], [t.sub.i]], the creep strain increment column vector within step [[t.sub.n-1], [t.sub.i]] may be generalized as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (18)

where:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; (a-18)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]l (b-18)

qn = [3.summation over ([gamma]=1)] [[phi].sub.[gamma]n][h.sub.[gamma]n]; (c-18)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; (d-18)

[Y.sub.n] = [S.sub.n] [n.summation over (j=1)] [[psi].sub.Tj][[DELTA].sub.Tj]; (e-18)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; (f-18)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (g-18)

The corresponding stress increment can be obtained:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; (19)

where: [[D.sub.n]] is the elastic matrix for plane strain problem at the "th time interval. The full details of the mathematical derivation are given in the previous work, the authors (Abdulrazeg et al. 2010).

7. Crack analysis

The crack development in RCC dam due to deferent loads acting on the dam during the construction or the operation stages such as thermal load, gravity, hydrostatic load and creep, in a given time interval depends on the development of mechanical properties, especially elastic modulus and tensile strength. Making reliable crack prediction assessment involves advanced modelling of the time and temperature dependent behaviour of the properties.

7.1. Cracking criteria of RCC gravity dam under triaxial stress states

In order to check the safety of the dam against cracking under Triaxial Stress States a new mathematical model has been developed during the present study to predict the crack development in RCC dam during the construction and operation stages. The respective failure criteria for mass concrete in principal stress space and octahedron stress space which proposed by (Wang, Song 2008) is adopted in the developed model.

The cracking criterion suggested by Wang and Song (2008) is a function of octahedral shear stress [[tau].sub.oct] and octahedral normal stress [[tau].sub.oct]

[[sigma].sub.oct] = ([[sigma].sub.1] + [[sigma].sub.2] + [[sigma].sub.3]/3); (a-20)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (20)

Let [[sigma].sub.1], [[sigma].sub.2] and [[sigma].sub.3] denote the tensile stress, intermediate stress and compressive stress at failure under triaxial C-C-T, respectively. The values of [[sigma].sub.oct]/fc and [[tau].sub.oct]/fc will be regressed in a parabolic formula as follows (Wang, Song 2008):

[[tau].sub.oct]/fc = 0.0655 - 0.9097 [[sigma].sub.oct]/fc -0.08936[([[sigma].sub.oct]/fc).sup.2]. (21)

This formula to be compatible with RCC construction sequence further modified as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (22)

In triaxial tension [[sigma].sub.1] < [[sigma].sub.2] < [[sigma].sub.3] < 0.00 the triaxial tensile strength is equal to uniaxial tensile strength [f.sub.t](t). In tension-compression--compression (T-C-C), [[sigma].sub.1] > 0.00, and [[sigma].sub.2] < [[sigma].sub.3] < 0.00, the maximum strength is given by Eqn (22).

The variation in the compressive strength with time is calculated according to (ACI 1995), which relates the elastic modulus to the compressive strength as:

E(t) = 4750[square root of [f.sub.c](t)], (23)

where E(t) is the elastic modulus, which is time and temperature dependent Eqn (10). The tensile strength of RCC material is evaluated using the model that developed by (Zdiri et al. 2008):

[f.sub.t] = 0.214 [f.sup.0.69.sub.c]. (24)

Taking into account this criterion, cracking on an element begins where the relation [[psi].sub.cr] drop below the allowable value. The following expression is defining the crack index (Abdulrazeg et al. 2010b):

[[psi].sub.cr] = [[tau].sub.oct][(t).sup.ult]/[[tau].sub.oct](t), (25)

it can be verified that when [[psi].sub.cr] > 1.0 the element is not cracked, and cracking occurs when [[psi].sub.cr] < 1.0.

Finally, the allowable octahedral shear stress will be determined using Eqn (22) and based on that the crack safety factor is generated by Eqn (25). If safety coefficient of crack is greater than one, the element will be considered safe against crack. But if the coefficient is less than one, crack will develop in the dam body.

7.2. Gradient cracking criteria

Design specification for concrete arch dam (Abdulrazeg 2012) demands that the tensile stress should be controlled by the following equation:

[epsilon]T [less than or equal to] [[epsilon].sub.p]/[K.sub.f]; (26)

[[epsilon].sub.T] = [DELTA]T x [alpha], (27)

where: [[epsilon].sub.T] is tensile strain of concrete which caused by temperature difference [DELTA]T; [alpha] is thermal expansion coefficient; [[epsilon].sub.p] is ultimate tensile strain of concrete; and [K.sub.f] is safety coefficient and range from 1.3-1.8 (SL282-2003). The laboratory test reported by Dunstan (1981) showed that a typical value of the tensile strain capacity is 80 [micro]mm.

8. Development of finite element code

In previous discussion, the formulation in Sections 2 (temperature), Sections 6 (creep) and Sections 7 (crack analysis) are implemented in the present research program (Abdulrazeg 2012). Based on that, a three-dimensional finite element program was developed and the following are the features of the finite element code.

1) Simulation of sequence of construction for both gravity and arch RCC dam;

2) Thermal analysis;

3) Structural analysis with or without creep effect;

4) Combined thermal and structural analysis with or without creep effect;

5) Crack safety evaluation.

The desired outcome of the modified code with respect to both two and three-dimensional finite element method are:

--Spatial distribution of temperature and its evolution with time;

--The stress distribution during and following the dam construction;

--Assessment of the crack occurrence either at short or long term.

The developed finite element program is written in FORTRAN language and can work under power station environment. The flowchart shown in Figure 1 represents the architecture of the program. The main program calls 36 main subroutines, each main subroutine calls another sub-subroutines and the code is about 7198 lines (Abdulrazeg 2012):

1) Divided the structure into stages according to construction schedule;

2) Divided each stage into several times;

3) Perform the thermal analysis, if only the temperature field analysis is desired, then the program moves to the next time step;

4) Perform stress analysis, and in case the creep is taken into consideration, the computational procedures in Section 6 will be preformed;

5) Performing crack prediction using the procedures in Section 7.

9. Analysis of actual RCC arch dam

The Karun III has been taken as a case study for the purpose of verification of the developed code. The Karun III dam is a hydroelectric dam on the Karun River in the province of Khuzestan, Iran. The dam is unsymmetrical double curvature type, 205 m high from the foundation. Its foundation width is 29.5 m. The arch dam design is an ideal one for a dam built in a narrow, rocky gorge to hold back water in a reservoir. Table 1 shows the main characteristics of the dam. Figure 2 shows original view and plan view of Karun III arch dam. The construction of the dam was started on 1995 and was put in operation 2005 (Karun III technical report 1995). The dam was originally designed as conventional concrete arch dam. In this study, RCC technology has been ascertained as an alternative method to reduce the cost of the project.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The dam site is generally hot and occasionally humid. Summertime temperatures routinely exceed 50[degrees]C. Khuzestan province is known as one of the hottest state in the world.

9.1. Material properties and site conditions

The material properties for the RCC and the rock foundation are tabulated in Table 2. These values were chosen based on values reported in the literature for RCC materials which are used in arch RCC dam (Xie, Chen 2005). The creep experimental data which were reported in the literature by (Zhang 1995) for RCC material have been adopted in the present study; these data are tabulated in the Table 3. In addition, the average monthly air temperatures at the project site are plotted in Figure 3 according to NASA organization (www.Eosweb.larc.nasa.gov/sse/ RETScreen). The average annual wind speed which is 4.0 m/s recorded at the site.

[FIGURE 3 OMITTED]

9.2. Construction schedule

In this study, the construction schedule of 205.0 m height RCC arch dam is proposed. The construction of the dam is planned according to a similar project was reported in the literature (Xie, Chen 2005), to be realistic, the construction schedule is adjusted based on the corresponding geometry of the adopted project. However, during the high temperature of the summer time, the construction will be stopped during July, August and September. Table 4 shows the proposed construction schedule of the dam.

9.3. Finite element modeling of RCC arch dam

The three-dimensional finite element model of the block foundation and dam body is shown in Figure 4. The finite element of the dam body is generated according to the construction Schedule which was given in Table 4. Twenty node isoparametric element is used for propose of discretization of the dam body and foundation block. 2880 isoparametric elements are used to model the foundation block and 560 elements to model the dam body, over all 17627 nodes have been used to define the coordinate of the finite element mesh of the entire system.

[FIGURE 4 OMITTED]

9.4. Simulation of the initial conditions

The temperature distribution in the rock foundation and the RCC placing temperature are the two initial conditions considered in the analysis. In this case of study, the main annual temperature recorded near the project site is 25.6[degrees]C it was assigned first to the all nodes of the block foundation as an initial condition. Then heat transfer between the atmospheric temperature and the block foundation was performed for a period of two years using the average monthly temperature (Ishakawa 1991). The RCC placing temperature is taken as the environmental temperature at the casting time but not permitted to exceed 30[degrees]C.

10. Results and discussion

10.1. Temperature distribution of Karun III RCC arch dam

According to the proposed schedule which given in Table 4, the thermal analysis is performed. The construction was started on March 1995 and completed in October 2000. However, the construction process was stopped every year for three months to avoid the work in very hot weather at the construction site during the summer period (July, August and September).

Temperature distribution in the body of the arch dam at the end of construction for the crown cantilever of the central section and different levels of the dam (20 m, 75 m, and 95 m) are shown in Figures 5 and 6 respectively. Higher temperatures zones are observed at the lower elevation levels near the abutments as shown in Figure 6. This can be anticipated to the higher thickness at these locations which provide high insulating property compared to the upper levels where the dam thickness decreased progressively.

In addition, high temperature concentration was observed at the upper elevation levels (150 m and 195 m) of the dam that because, the hydration process is still high in this part. However, the temperature at the lower part of the dam is 42[degrees]C and it reduced to the air temperature at the boundary condition.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

10.1.1. Gradient cracking control standard

According to the methodology described in Section 7.2, allowable gradient strain is determined and compared with a computed strain based on the predicted temperature obtained from finite element analysis. The maximum internal temperature is 42.0[degrees]C (determined from the plots). The minimum temperature is 12.0[degrees]C (based on the annual temperature cycle) taken from Figure 3. The coefficient of thermal expansion is given in Table 2. The calculated induced strain based on Eqn (27) is 166.8 umm, which exceeded the allowable strain (Eqn (26)). This could be controlled by determining the proper spacing of the RCC blocks.

10.2. Stress analysis of Karun III RCC arch dam

A viscoelastic mathematical model which involves ageing and temperature effects (presented in Section 6) is adopted for the stress analysis. First, the thermal analysis is performed for each time step. Then the degree of equivalent hydration period is determined. Based on this degree the mechanical properties such as elastic modulus (Eqn (12)) and creep compliance (Eqn (11)) are calculated. Finally, the crack safety factor will be determined for each time step (Fig. 1).

Figure 7 shows the principal stress contours or (MPa) in the dam body, the result indicates that, the tensile stresses developed mainly at the dam bottom and the abutment boundaries, because of the contact between two dissimilar materials. In addition, the tensile stress has been observed at the upstream side (1.6 MPa) due to arch action combined with the restraint against environmental thermal variation, which doesn't exceed the limit according to U. S. crops of engineering (ACI. EM 1110-2, 2006).

On the other hand, compressive stress contours are developed at the downstream side due to the arch action and gradually decreased in the direction of boundaries.

[FIGURE 7 OMITTED]

Figure 8 shows contour plots for the evolution of the intermediate principal stress [[sigma].sub.2] (MPa). It can notice that, tensile stresses developed at the same locations of the principal stress [[sigma].sub.1] with smaller values. In addition, high compressive stresses zones are observed at some level at the downstream side (75.0 and 150.0 m).

[FIGURE 8 OMITTED]

Figure 9 shows the distribution of the minimum principal stress 03. High compressive stress zones concentrated at the upper part of the upstream dam side which gradually decreased in the direction of abutment sides. Generally, the compressive stresses developed in the dam body during the construction are not exceeding the allowable compressive strength specified by ACI 207 (1999).

[FIGURE 9 OMITTED]

10.3. Crack analysis and safety evaluation

Simultaneously during the stress analysis the crack safety factor will be calculated using the procedure described in Section 7.1 at each Gaussian point. The safety factor against cracking in any point of a generic finite element is determined using Eqn (25).

An attempt is made to draw the crack safety factor at level of 105.0 m along the dam width for different construction levels as shown in Figure 10. Observing Figure 10, it is verified that the crack safety factor along the section for different construction height at that particular lift is greater than the allowable limit. Thus, it is considered to be safe against the crack development. However, near the abutments of the dam, the crack safety factor is dropped below the limit which coincides with higher tensile stress zone (Fig. 7f). Hence, special attention must be given to locations during the design of the dam.

[FIGURE 10 OMITTED]

Conclusion and remarks

The capability of the developed system for thermal and structural analysis of RCC arch dam has been demonstrated through analyzing 205.0 height Karun III arch dam located in Iran. In this study, RCC technology has been as ascertained as an alternative method. The analysis was carried out during the construction stages only.

Based on the limitations and assumptions used in the present study, the following points can be drawn:

--The finite element code developed in this study is capable of simulating the structural response of arch RCC dams efficiently. This is clearly shown from the reasonable stresses distributions obtained;

--Higher temperature zones are formed at the center part of the dam, especially at the thicker places near the abutments which gradually decreased in values to reach the air temperature at the boundaries. The requirements of strength and crack resistance are greater in high Zone, because of the adiabatic temperature is high in this zone;

--High Tensile stresses have been observed at the dam bottom and the abutment boundaries in the upstream side section due to the restriction from the abutment and foundation rock. This is because of low temperature, ranging from dam foundation to abutment and there is no transverse joint in RCC arch dam. Engineers should pay special attention to this zone. Moreover, the tensile stress has been observed at the upstream side due to arch action combined with the restraint against environmental thermal variation;

--High compressive stress zones concentrated at the upper part of the upstream dam side which gradually decreased in the direction of abutment sides.

doi: 10.3846/13923730.2013.801897

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Aeid Ali ABDULRAZEG completed his PhD study at the Universiti of Putra Malaysia. He is currently lecturer at the civil engineering department of Omar Al Mukhtar University. His main area of interest is the finite element analysis of complex structures.

Jamaloddin NOORZAEI completed his PhD study at the University of Roorkee, India. His research interests include computational techniques in civil engineering applications especially those related to structural engineering, soil- structure interaction and earthquake engineering. He was Professor and Head of the Structural Engineering Research group at the Universiti Putra Malaysia (UPM).

Mohamed Saleh JAAFAR obtained his PhD from the University of Sheffield. Currently Professor and Deputy Vice Chancellor of Universiti of Putra Malaysia. His research interests include concrete and prestressed concrete structures, high performance concrete and structural conditions assessment.

Parvin KHANEHZAEI obtained her MSc degree from the Universiti of Putra Malaysia. She is currently a PhD candidate at the same University. Her main area of interest is soil-structure interaction and structural engineering.

Thamer Ahmed MOHAMED completed his PhD study at the Universiti Putra Malaysia, Malaysia. Currently Professor of the Faculty of Engineering UPM, Malaysia. His research interests include hydraulic and hydrologic modeling, sediment transport, urban drainage, groundwater modeling.

Aeid Ali ABDULRAZEG (a), Jamaloddin NOORZAEI (b,c), Mohamed Saleh JAAFAR (b), Parvin KHANEHZAEI (b), Thamer Ahmed MOHAMED (b)

(a) Civil Engineering Department, Omar Al Mukhtar University, El-Beida, Libya

(b) Civil Engineering Department Universiti Putra Malaysia, 43400 UPM- Serdang, Malaysia

(c) Institute of advance Technology, Universiti Putra Malaysia, 43400 UPM- Serdang, Malaysia

Received 08 Dec 2011; accepted 20 Feb 2012

Corresponding author: Aeid Ali Abdulrazeg

E-mail: aied@omu.edu.ly

Table 1. Main characteristics of Karun III concrete arch dam

Characteristic                            Quantity

Maximum height above foundation            205.0 m
Crest width                                 5.5 m
Base width                                 29.5 m
Crest length                               462.0 m
Placed concrete                      1300000.0 [m.sup.3]
Reservoir normal capacity          2,970,000,000 [m.sup.3]

Table 2. Thermal and mechanical properties for
Karun III concrete arch dam

Characteristic                               RCC      Rock

Cement (Kg/[m.sup.3])                        90
Fly ash (Kg/[m.sup.3])                       110
Coefficient of thermal expansion           3.04E-6   4.2E-6
Thermal conductivity(KJ/m h [degrees]C)     8.314     10.0
Specific heat (J/(kg. K))                   1080      1500
Elastic Modulus (MPa)                       18200    24000

Table 3. Creep data for RCC and CMC materials (Zhang 1995)

Material       [[alpha].   [[beta].sub.i]   [[delta].sub.i]     D
                sub.i]

CVC        1    0.35494        0.4836           0.35361       0.835
           2    3.7335         -0.186           0.01248
           3    2.5644         0.1378           0.03264
RCC        1    0.05886       0.38362            1.356        4.2808
           2    7.4729        -11.115           0.08919
           3    5.2079         7.9619          0.078675

Table 4. Construction schedule of
Karun III RCC Arch Dam

Time of pouring    Height of
(D-M-Y)           casting (m)

3/1/1995              1.2
3/30/1995             3.0
4/20/1995             6.0
5/14/1995             9.0
9/7/1995             12.0
10/1/1995            15.0
10/25/1995           18.0
11/18/1995           21.0
12/11/1995           24.0
1/5/1996             27.0
1/29/1996            30.0
2/22/1996            33.0
3/16/1996            36.0
4/2/1996             39.0
4/21/1996            42.0
5/26/1996            45.0
9/21/1996            48.0
10/14/1996           51.0
11/8/1996            54.0
12/1/1996            57.0
12/25/1996           60.0
1/19/1997            63.0
2/12/1997            66.0
3/5/1997             69.0
3/29/1997            72.0
4/23/1997            75.0
9/16/1997            78.0
10/10/1997           81.0
11/3/1997            84.0
12/27/1997           87.0
1/20/1998            90.0
2/16/1998            93.0
3/9/1998             96.0
4/3/1998             99.0
5/27/1998            102.0
6/10/1998            105.0
7/1/1998             108.0
10/1/1998            111.0
10/21/1998           114.0
11/10/1998           117.0
11/30/1998           120.0
12/20/1998           123.0
1/10/1999            126.0
1/30/1999            129.0
2/20/1999            132.0
3/10/1999            135.0
3/30/1999            138.0
4/21/1999            141.0
5/11/1999            144.0
5/29/1999            147.0
6/20/1999            150.0
7/10/1999            153.0
10/1/1999            156.0
10/20/1999           159.0
11/10/1999           162.0
11/29/1999           165.0
12/20/1999           168.0
1/11/2000            171.0
1/29/2000            174.0
2/21/2000            177.0
3/11/2000            180.0
3/30/2000            183.0
4/19/2000            186.0
5/11/2000            189.0
5/30/2000            192.0
6/19/2000            195.0
7/10/2000            198.0
10/1/2000            201.0
10/21/2000           205.0