Long-Term effects of Environment on Seismic Performance of Dez Concrete Arch Dam

In the first part of this paper, the degradation of the mechanical properties of the mass concrete of the Dez concrete...

Besides the effect of water, some unexpected external loads, like severe earthquake loads, can cause the degradation of strength and integrity of old concrete arch dams.
Consequently, it can be outlined that the weakening of aged concrete arch dams may have resulted from two main factors: 1.
Time variant external loading, and
Three different approaches have been persuaded until today to address and contribute the effects of these two different origin types of loading in the analysis of aged concrete arch dams: 1.
The first method studies the changes in the characteristics of transmitted and received waves which travel through the thickness of the arch dam. This nondestructive test method is used for estimating the strength and elastic properties of mass concrete and for locating and characterizing voids and cracks within the structure Bond et al. [16,17].

2.
Development of mathematical models which quantify and measure the aging effects in structural analysis is the second method [5,6,9,15,18,20].

3.
In the third group, named as diagnosis approaches, the damage diagnosis methods have been implemented for identification of degraded strength parameters such as elastic modulus of the dam Wittmann [2]; Maier et al. [21]; Fedele et al. [22]; Garbowski et al. [23].

Dynamic vibration by vibrodynes and measurements
through accelerometers and identification of young modulus distributions based on modal analysis in linear dynamics Salawu 1997 [27], and

5.
Hydrostatic loading attributable to fast reduction in water surface in the reservoir, measurement of deformations by instruments of the dam such as pendulums, collimators and/ or interferometric radar and statical overall inverse analysis of elastic moduli through a linear finite element model (FEM) or nonlinear FEM if vertical block relative movements are considered Ardito et al. [28]; Ardito and Cocchetti [29]; Fedele et al. [22]. The Dez concrete arch dam is located in an aggressive condition from the environmental point of view based on the study of Naik (1985) [30]. According to this study, the worst environmental condition of concrete is occurred when the weather is hot and contains high humidity. He described this situation quantitatively and specifically mentioned that at an air temperature of 122 °F and relative humidity of 100%, concrete becomes weak both in compression and tension. He added more that this is a critical condition for which the maximum load for a concrete structural member should be re-computed. Holding this issue in mind, it is interesting to note that the ambient temperature in the site location of the Dez dam reaches to 50 °C (122 °F) in the summer. Remembering this circumstance, on the other hand, the upstream face of the Dez dam at the same time is exposed dominantly to the reservoir water and therefore it is rational to suppose that some portions of the upstream face of the dam are completely saturated.
So, it is no surprise if the environmental condition of the Dez dam in some days of the summer is classified as an aggressive condition.
Downie [31] performed a comprehensive study on the effects of heat and moisture transport within the concrete on its mechanical properties. He concluded that higher temperature and degrees of This process leads to an increase in porosity of the concrete and consequently to decrease of the integrity and strength of the concrete Ekstrom [12].

Part I: Transversely isotropic elastic degradation
As it was mentioned in the previous research, the behavior of the dam and its abutments are still elastic based on the observations from the instruments located in the dam and supports besides to the available geological and geotechnical report of the dam at construction time Labibzadeh et. al. [39].  It should be emphasized here that; the authors of this paper like to Fedele et. al [22], believes that the degradation of concrete Considering Figure 1, the constitutive law for the long-term deterioration of Dez concrete can be stated as a relation (1): In the above relation, denotes the Young's modulus along the x-axis (axis of elastic symmetry) and indicates the corresponding elastic parameter in the plane of isotropy e.g. Y-Z plane herein. is Poisson's ratio, characterizing the transverse strain reduction in plane of isotropy (Y-Z) due to tensile stress in a direction normal to it (X). represents also Poissin's ratio but in the plane of isotropy.
stands for the shear modulus for planes normal to plane of isotropy.

Methodology
According to equation (1), in this study, five independent constants of the compliance matrix; C; were considered in a general form to be the unknowns and extensive trials have been made to identify them through a thermal inverse analysis algorithm described in detail in labibzadeh, et al. [39]. The dam was subdivided into nine individually homogeneous zones in the thickness direction and into six similar sections along the height of the dam.
To each of these sub-regions, the above mentioned five unknowns In relations 2 to 4, is the stiffness matrix; denotes the corresponding nodal force vector contains the effects of gravity, hydrostatic and thermal actions; is the strain-displacement matrix; indicates the transversely isotropic elastic fourth tensor and is the volume of each sub-divisions of the dam. Eq. (5) It should be noted here that the recorded displacements are limited to specific regions of the dam where the inverse pendulums are located. For the other regions, rational interpolation and extrapolation schemes have been followed to obtain the required unavailable data. Then, a traditional discrepancy function J was formulated as a quadratic form of obtained residuals as follows: where denotes the identity matrix. The solution is defined as a set of the variables { } p which minimizes the function J.

Long-Term deterioration: heterogeneously and orthotropically
After performing sensitivity analyses on the material parameters, it was revealed that the function J did not alter through the variation of the thermal expansion coefficient so this parameter was considered as a constant and equal to the value which obtained before from the previous study of the authors; thermal expansion coefficient= 1/˚C Labibzadeh et al. [39]. However, it was also pointed out that the magnitude of error function J changes noticeably when the Poisson's ratios change. This is in contrast to the results of Oliveira et al. [40] and Garbowski et al. [23]. In the following, the obtained results of this study have been outlined in Table 1    In the above tables, the word 'zone' points to the subdivisions numbered in Figure 2 and, are defined based on the Eq. 7 as below: In Table 1 and stand for the out-of-plane and in-plane elastic modulus respectively. As it is seen in that table, for each Figure 6 are selected in such a way that the level of the reservoir is the same for these days but there is the maximum difference between the temperatures recorded by thermometers for them labibzadeh et al. [39]. 1 J , 2 J , 3 J and error function J in Table 1 are those parameters that defined in eqs. (8) and (9). The same parameters have been used in Tables 2 & 3. In Table 2, and HV v refer to the Poisson's ratios at out-of-plane and in-plane respectively see Figure 1. The last independent material parameter as defined by eq. (1) is the which denotes the out-of-plane shear modulus of the dam and used in Table 3. It is worth mentioning that the above tables have been shown in this paper in an order agrees with the order that inverse parameter identifications were performed in this attempt. Hence, the optimum or minimum of error function J can be found in the last table Table 3. This value (5.085E-07) is ten times smaller than the corresponding value obtained before by the authors Labibzadeh et al. [39], e.g. 1.37 E-06 based on the assumption of homogeneity and isotropy. Therefore, the question was asked in the beginning of this article now can be replied; the long-term deterioration process of concrete of the Dez dam is both heterogeneous and anisotropic.

Part II: Seismic Response of the Strength Degraded Dam
As it was demonstrated in the first part of this study, the strength of the Dez dam has been reduced during its service life.
In this part, in order to evaluate the seismic behavior of the dam in its current condition, it was simulated against to an earthquake excitation. For this study, the horizontal and vertical acceleration records of Tabas earthquake have been used. These records are shown in Figure    The element types used for FE simulation of the dam-reservoirfoundation system have been outlined in Table 4. The length of the reservoir was considered as three times of the height of the dam in the above-mentioned FE simulation. Hence, the seismic waves travel to the far end of the reservoir are completely damped. To show the influence of long-term effects of the Environment as well as reservoir interaction on the response of the dam three different systems have been considered.
• System A: The dam with degradation strength.
• System B: The dam without degradation strength.
• System C: results of the dam with Hariri and Mirzabozorg's [41] assumptions.
The following response quantities for these systems have been compared: • Accelerations of the dam.
• Displacements at the crest of the dam.
• Envelope of max principal stress.
• Maximum crest displacement envelops.  Figure 12 shows different reservoir levels.

Volume 4 -Issue 1 Copyrights @ Mojtaba Labibzadeh, et al. Tr Civil Eng & Arch
In spite of changing of the depth of the reservoir, modal periods of the dam-reservoir-foundation system obtained in the current study by the assumption of strength degradation are smaller than the corresponding values obtained by Hariri and Mirzabozorg [41].
The measuring line for Figure 17-19 was shown in Figure 16.   By changing the reservoir depth, different dam responses have been calculated. Figure 17 shows non-concurrent envelopes of displacement along the height of the crown cantilever of the dam extracted from Hariri and Mirzabozorg [41], with and without strength degradation assumptions in various performance levels.
In the considered systems and the depths of reservoir, the amounts obtained by Hariri and Mirzabozorg [41] have the smallest displacements and the dam with strength degradation have the largest displacements. Figure 18 represents non-concurrent velocity envelope along the height of the central cantilever.
The quantitative comparisons among the peak values of different response quantities for Hariri and Mirzabozorg [41] and the current model with strength degradation show Table 5 that the displacements, velocities, and accelerations get changed significantly with the consideration of strength degradation ( Figure   19).

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For convenience of the readers in better investigating of the change in the seismic resistance of the Dez dam, the envelope of the non-concurrent maximum and minimum principal stresses on the upstream and downstream faces of the dam have been compared with the results obtained by Hariri and Mirzabozorg [41] in Figure   20 through 27. It should be mentioned that these researchers did not consider any degradation for the mass concrete of the dam. As it can be seen from Figure 20-23, current study shows considerable reduction in the compressive regions (blue colored) of the dam due to ageing effects.

Conclusion
In this paper, subsequent to the previous attempt done by the authors on the Dez dam Labibzadeh et al. [39] and based on that, an effective thermo-elastic inverse analysis has been implemented for in-detail elastic property identification of this dam after a long time being passed from its operation time. In this new work, the property of age-related degradation of the dam was investigated from the heterogeneity as well as anisotropy point of views. By reviewing the obtained results, it was revealed that the ongoing deterioration of the concrete material of the Dez dam is a heterogeneous and orthotropic process. Heterogeneity is due to the difference in the environmental conditions circumvented the dam as well as the change of hydrostatic and gravity loads along the height of the dam and anisotropy because of the shape of the dam and the state of stresses resulted from the permanent external loading exposed on the dam. Furthermore, the effects of this degradation were