The Behavior of Aged Concrete Gravity Dam under the Effect of Isotropic Degradation Caused by Hygro- Chemo-Mechanical Actions

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1 International Journal of Engineering Studies ISSN Volume 1, Number 2 (29), pp Research India Publications The Behavior of Aged Concrete Gravity Dam under the Effect of Isotropic Degradation Caused by Hygro- Chemo-Mechanical Actions A. Burman 1, D. Maity 2 and S. Sreedeep 3 1 Lecturer, Dept. of Civil Engineeing, BIT Mesra, Ranchi, India 2 Associate Professor, Dept. of Civil Engineeing, IIT Kharagpur, India 3 Assistant Professor, Dept. of Civil Engineeing, IIT Guwahati, India Abstract The degradation of concrete due to various hygro-chemo-mechanical actions are inevitable for structures whose purpose is to retain water during their service lives. Because of constant contact with water, the strength of the concrete gets reduced as the micro-pores of concrete structures get penetrated by the water, frost and various other harmful materials. In order to ascertain the behaviour of such structures at a later stage after its construction, it is necessary to determine the degraded strength of the concrete. A curve fitting analysis is carried out to predict the behavior of concrete at a later stage of its life based on some already published experimental results showing the gain of compressive strength of concrete with age. The predicted strength is further used to determine the effect of degradation of concrete by applying the model to determine the behavior of Koyna gravity dam after its construction. Keywords: Aged concrete behavior; Isotropic degradation; Hygro-chemomechanical actions; Curve fitting analysis; Koyna gravity dam. Introdction Some structures such as concrete gravity dam, water tanks, well foundations etc. have to retain water throughout their lifetime. The leaching of water saturates the numerous pores of concretes. This phenomenon induces stresses in the concrete, which depends on the degree of saturation reduces the strength of the concrete. At the macro-level, this effect is manifested as a loss of elastic stiffness. Apart from this, structural deformations may occur due to inhomogenous material characteristics and the nonuniform moisture distribution due to asymmetry in the geometrical configuration of

2 16 A. Burman, D. Maity and S. Sreedeep the structure. The shrinkage of concrete due to moisture effect may further induce micro-cracks as the local strength of the material may get exceeded. For such a structure, the strength of the material will be largely different from that at the time of construction. Therefore, it is important to estimate the strength of the concrete at a later stage after construction because the structure may be hit by an earthquake long after it has been constructed. At that moment, the response of the structure will be significantly different from what it would have if the earthquake had hit just after the construction was over. In the present paper, a model for depicting the reduced concrete strength due to ageing process has been suggested. The suggested model is a variation of an already existing model for describing the ageing behaviour of concrete. The result of this alternative model has been found to match the results of the existing model very closely. Since the scope of the present work is to predict the behaviour of concrete ageing, a number of relevant literatures are reviewed and presented in brief. Byfors (198) stated that the hydration is the primary cause of ageing of concrete, which at micro level appears to change the mechanical properties of the concrete. Bazant s (1994) study of hydration of concrete at micro-level reveals that it is a change in concentration of non-ageing constituents like hardened cement gel constituting of tri and bicalcium silicate hydrates. Ulm and Coussy (1995) explored the theory of reactive porous media for modelling of concrete at early ages. The model accounts explicitly for hydration of cement by considering the thermodynamic imbalance between the chemical constituents. The intrinsic relation between heat generation, ageing and autogeneous shrinkage is derived. Niu et al. (1995) developed a finite element modelling procedure for describing the thermo-mechanical damage of early-age concrete in the construction of large dam. The stress deformation analysis procedure includes temperature-induced, creep-induced and autogeneous deformations. A failure criterion for each failure mode was developed along with constitutive relationships for pre-failure and post-failure states during loading and unloading conditions. Bazant et al. (1997) proposed a new physical theory and constitutive model considering effects of long term ageing and drying on concrete creep. This theory is an improvement over the solidification theory in which ageing is modelled by volume growth. Cervera et al. (1999, 2a, b) proposed a thermo-chemical model to simulate the hydration and ageing process of concrete considering creep and damage in a roller compacted concrete dam. The evolution of temperature, elastic moduli, compressive and tensile stress distribution inside the dam can be predicted in terms of ageing degree at any time during the construction process and also during the first years following the completion of the dam. This procedure can be applied to understand the effect of some major variables such as the placing temperature, the starting date and the placing speed on the construction process. In the long term, ageing of concrete is affected by the concentration of various constituents in the concrete matrix, chemical reactions such as calcium leaching or alkali-silica reaction, moisture transport and loading due to submergence in water. According to Cervera et al. (2b), the consideration of creep is significant if the stress analysis includes simulation of construction process. The model describes the behavior of early age concrete.

3 The Behavior of Aged Concrete Gravity Dam 17 Lindvall (21) determined the service life of concrete structures mathematically that was dependent on material properties, construction process and environmental effect. The prediction of deterioration of concrete was based on theories of transport in porous materials and empirical models, which were based on observations from structures. Bangert et al. (23) evaluated the long-term material degradation in concrete structures due to a chemically induced degradation processes and calcium leaching. Steffens et al. (23) introduced an ageing approach to determine the degradation of concrete structures considering water effect on Alkali-Silica Reaction (ASR). A comprehensive mechanical model was proposed for the material swelling with a hydro-chemo-mechanical approach, to study structural effects of ASR. The model adopts a two-stage mechanism for the swelling kinetics, consisting of (i) the formation of an amorphous gel for which a characteristic time of reaction is identified and (ii) the quantity of water interacting with the gel. The ageing effect on the material degradation and structural response is validated with experimental results. Mazzotti and Savoia (23) presented a creep-damage model for concrete under uniaxial compression, which takes into account both nonlinear creep and damage growth with time. Creep strain is modeled extending solidification theory in the nonlinear range. Nonlinear creep strains are evaluated as a function of damage index, which is calibrated from experimental results. It is also assumed that most of creep strain does not produce damage, so that only a fraction of creep strain contributes to damage evolution with time. This assumption is based on the experimental evidence that, at low stress levels, strain due to creep can be large (even larger than that corresponding to peak stress for short term loading), without any significant damage of concrete. Gogoi and Maity (27) investigated the degradation of strength of an aging concrete gravity dam adjacent to a reservoir in conjunction with the effects of sediment layers in the fluid-structure interaction analysis. A new parameter called degradation index is introduced to account for the extent of isotropic degradation occurring in the concrete due to various hygro-chemo-mechanical actions. The degradation index within the elastic limit is derived considering environmental factors due to exposure to water, mechanical loading and chemical reaction. In their work, the gain in compressive strength of concrete is obtained from experimental data published by Washa et al. (1989) of fifty years of compressive strength of concrete by curvefitting procedures. In the present paper, the same fifty years of concrete compressive strength is represented by a new curve by carrying out least square analysis on the experimental data. The new curve is used to determine the isotropic degradation index suggested by Gogoi and Maity (27). Thus, the phenomena of concrete degradation with age as well as the gain of concrete compressive strength are combined in the present model. The constitutive relationships for degraded concrete has been suggested for plane strain condition and applied to the analysis of Koyna gravity dam subjected Koyna (1967) earthquake accelerations. The results obtained from the present model have been compared with the published results (Gogoi and Maity, 27) with satisfactory agreement.

4 18 A. Burman, D. Maity and S. Sreedeep Modeling of Aged Concrete The state of stress and strain within Hook s law can be expressed as { σ} = [ D]{} ε (1) In the above equation, {σ} T = { σ x, σ y, τ xy } and {ε} T = {ε x, ε y, γ xy } are the vectors of stress and strain respectively, and [D] is the constitutive matrix under plane strain condition defined as ( 1 μ) μ [ ] ( ) ( )( ) ( ) E D = d μ 1 μ (2) 1+ μ 1 2μ 1 2μ 2 for a material with elastic modulus E d and Poisson s ratio μ. The concept of degradation of concrete strength is based on the reduction of the net area capable of supporting stresses. The loss of rigidity of the material follows as a consequence of material degradation due to various environmental and loading conditions. Adopting an analogy given by Ghrib & Tinawi (1995) to measure the extent of damage in concrete, the orthotropic degradation index can be determined as d n Ωi Ωi Ωi d gi = 1 = 1 (3) Ωi Ωi d Here, Ω i = tributary area of the surface in direction i; and Ω i = area affected by degradation. In a scale of to 1, the orthotropic degradation index, d gi = indicates no degradation and d gi = 1 indicates completely degraded material. The index i = 1,2 corresponds with the Cartesian axes x and y in two-dimensional case. The effective plane strain material matrix can be expressed as 2 ( 1 μ) Λ 1 μλ1 Λ2 E [ ] ( ) ( )( ) ( ) ( ) d 2 D d = μλ1 Λ2 1 μ Λ + 2 (4) 1 μ 1 2μ μ Λ Λ Λ + Λ 1 2 / 1 2 where Λ 1 = (1 - d g1 ) and Λ 2 = (1 - d g2 ). In the above equation, E d is the elastic modulus of the material without degradation. If d g1 = d g2 = d g, the isotropic degradation model is expressed as 2 [ Dd ] = ( 1 d g ) [ D] (5) where [D d ] and [D] are the constitutive matrices of the degraded and un-degraded model respectively. Equation (5) was used by Gogoi and Maity (27) to determine the degraded strength of concrete due to various hygro-chemo-mechanical actions. Evaluation of degradation elastic modulus E n The compressive strength of concrete is expected to decrease with age due to chemical and mechanical material degradation. But it is also a known fact that concrete gains compressive strength with age. In the present work, an attempt was made to simulate the concrete strength considering both of these above-mentioned factors.

5 The Behavior of Aged Concrete Gravity Dam 19 Following the work of Gogoi and Maity (27), the relation between degraded elastic modulus due to porosity of concrete, E n and the elastic modulus of concrete considering strength gain at a particular age, E can be considered to be E n = (1-d g )E. Using the dimensionless value of total porosity obtained by multiplying the scalar degradation variable, as reaction extent, the variation of degradation with respect to time can be given as E n t a τa ( 1 φ) E = (6) In the above expression, τ a is the characteristic age for which the structure is designed and t a is the time corresponding to which the degraded elastic modulus E n is determined. The symbol φ stands for total porosity of concrete which can be further expressed as the sum of initial porosity, φ the porosity due to matrix dissolution, φ c and the apparent mechanical porosity, φ m. φ = φ + φ c + φ m (7) Bangert et al. (23) and Kuhl et al. (24) have outlined the detailed procedure to calculate mechanically induced porosity φ m. The apparent mechanically induced porosity, φ m considers the influence of mechanically induced micro-pores and microcracks on the macroscopic material properties of the porous material. It is obtained as [ φ φ c ] d m φ m = 1 (8) where d m is the scalar degradation parameter. The strain based exponential degradation function as proposed by Gogoi and Maity (27) is given as κ [ ( βm [ κ κ d = 1 α + α ]) m as m m e ] (9) κ Where κ = Value of strain at initial threshold degradation given by f t /E κ = Internal variable defining the current damage threshold depending on the loading history Here f t = Static tensile strength of concrete E = Elastic modulus of undegraded concrete before the imposition of any type of mechanical loading. Equation (9) may be used to find out the value of d m at any age, which again varies with κ caused by the mechanical loading history. When there will be no degradation due to mechanical loading, the value of κ may be considered equal to κ (i.e. κ =κ ). Also, in case of no degradation caused by mechanical loading, φ m is also considered to be zero (i.e. φ m = ). Bangert et al. (23) outlined the procedure to calculate the values of the mechanical parameter α m and β m. In eq. (9), the value of a s is considered to lie between 1. and. indicating complete and no degradation (Simo and Ju, 1987) respectively. Gain of Compressive Strength With Age It is a known fact that concrete gains compressive strength with age. This phenomenon is predicted by a curve fitting on 5 years of compressive strength data

6 11 A. Burman, D. Maity and S. Sreedeep published by Washa et al. (1989). The compressive strength test results of various concrete specimens of different proportions were published in the referred literature. These specimens were cured for 28 days and then placed in outdoors, which was on level ground in an open location. All the specimens were kept in open so that they were subjected to change in severe weather conditions of 25 cycles of freezing and thawing each winter, annual precipitation including snowfall of about.813 cm and air temperature variation between -32. C and 35. C. Gogoi and Maity (27) sought to carry out a least square curve fitting analysis on the set of compressive strength data published by Washa et al. (1989). In engineering problems, an experiment produces a set of data points (x 1, y 1 ),., (x n, y n ), where the abscissas {x k } are distinct. It is often our objective to relate these data with the help of a mathematical function. While choosing the particular mathematical function for the curve fitting of the experimental data sets, the physical behaviour of the system should be kept in mind i.e. the mathematical function should be comprised of physically meaningful parameters. In the present case, we seek to suggest a mathematical function involving the time in years and the compressive strength of concrete. While expressing these experimental data by a mathematical function of the form y = f(x), some errors are inevitable which may originate from the test conditions of the experiments as well as human or any other errors which can not be accounted for. Therefore, the actual value f(x k ) (Mathews 21) satisfies f(x k ) = y k + e k (1) where e k is the measured error. Some of the methods that can determine how far the curve y ls = f(x) lies from the data are: { y } Maximum error: E ( f ) = max f ( x ) k 1 k N 1 N E = 1 f f N k= 1 Average error: ( ) ( ) Root-meansquare error: E 2 1 N = N k x k y k ( f ) f ( ) k = 1 x k y k The best fitting line is found by minimizing one of the quantities in eq.(13). Amongst, all the three choices given in equation (11), E 2 (f) is preferred most of the times because of computational convenience. The least squares line is the line that minimizes the root-mean-square error E 2 (f) and is given as y ls = f(x) = Ax + B (12) In the above equation, A and B can be determined from N sets of experimental data as follows: A = N N N xk yk k = 1 1 N xk k = (11) yk xk k = 1 k =, B = A (13) N N

7 The Behavior of Aged Concrete Gravity Dam 111 For the present work, the fifty years of compressive strength data set corresponds to a concrete specimen of mixed proportion 1:2.51:5.34 (cement : sand : gravel by weight) with water cement ratio of.49. Here, the following forms are considered for curve fitting: I. y A ( x) + B II. III. IV. = ln y = C e A y = C x A ln x y = C xe A ln x (14) In the above expression, C = e B and D = -A. Data linearization is carried out by transforming points (x k, y k ) in the xy plane by the operation (X k, Y k ) = (ln(x k ), ln(y k )) in the XY plane for curve II and curve III. In case of curve IV, the transformation operation carried out is (X k, Y k ) = (ln(x k ), ln( y k xk )) in the XY plane. Then the least squares line is fitted to the points {(X k, Y k )} to give the predicted results. The predicted results using the above expressions (eq. 14) are plotted in Fig Compressive strength (Mpa) Expemental data (Washa et al. 1989) Curve I Curve II Curve III Curve IV Time (years) Figure 1: Curve fitting of experimental data. The curve I (i.e. y = A ln ( x) + B ) has been used by Gogoi and Maity (27) with excellent result. According to Washa et al. (1989), the specimen showed an increase in compressive strength roughly proportional to the logarithm of age during the first 1 years and small variation thereafter. Therefore, curve III seems to be the most logical choice to fit the experimental data. However, it is observed from Fig. 1, that curve I also shows excellent agreement with the experimental data of fifty years of concrete compressive strength. Gogoi and Maity (27) proposed an equation to predict the gain of concrete compressive strength with the passage of time (in terms of years) as below: f t = 3.57ln t (15) () () 33 f f ( t) = 43.47t.8ln t ( t) = 43.47e (16).8 f ( t) = 43.47te.92 ln t (17) (18)

8 112 A. Burman, D. Maity and S. Sreedeep The values of compressive strength obtained are in SI units and t a is age of concrete in years. Eq. (15) was obtained by Maity and Gogoi (27) by carrying out least square analysis using a curve of the form y = A ln ( x) + B. Equation (18) has been obtained by carrying out a least square analysis using a curve of the form Aln x y = C e with the necessary transformation of the coordinates as mentioned before. In this case, the values of C and A obtained are and.8 respectively. Equation (17) has been obtained by carrying out a least square analysis using a curve of the A form y = C x with the necessary transformation of the coordinates as mentioned before. In this case also, the values of C and A obtained are and.8 respectively. Equation (18) has been obtained by carrying out a least square analysis A ln x using a curve of the form y = C xe with the necessary transformation of the coordinates as mentioned before. In this case also, the values of C and A obtained are and.92 respectively. From Fig. 1, it can be noticed that the results obtained from eq. (16), eq. (17) and eq. (18) are all similar and these results agree quite well with the experimental data as well as the results obtained from eq. (17) proposed by Gogoi and Maity (27). Further, it may be noticed that eq. (16) and eq. (17) are not unique but alternative to each other considering the transformation of coordinates to be carried out. Since the results obtained from eq. (16), eq. (17) and eq. (18) are almost identical, eq. (17) (as shown by curve III in Fig. 1) is chosen for all the further analyses carried out in this work. This choice is done keeping in mind the ease of use of an equation. In the present analysis, both eq. (17) and the equation suggested by Gogoi and Maity (i.e. eq. (15)) have been used to predict the gain of concrete strength with age and the obtained results are compared. The value of static elastic modulus of concrete in SI units (Neville and Brooks, 1987) is obtained from E = 4733 f () t (19) After calculating the static elastic modulus of concrete E, the degraded elastic modulus of concrete (E n ) due to various hygro-chemo-mechanical effects may be obtained from eq. (8). Having obtained the value of E n, the value of degradation index is given by eq. (2) (Gogoi and Maity, 27). En d = 1 (2) E g The value of d g is used in the constitutive relationship given by eq. (4) to describe the behavior of a concrete gravity dam (analyzed under plane strain assumption). In Fig. 2, the variation of degradation index with age is plotted. The degradation index d g is calculated from eq. (2) as a function of elastic modulus of concrete considering the strength gain at a particular age E. E is determined from eq. (19) which may be approximated by eq. (15) (suggested by Gogoi and Maity, 27) and eq. (17) proposed in the present work. From Fig. 2, it may be observed that the degradation index values obtained for different HCM design life (i.e. 5 years and 1 years respectively) match very closely with each other. It is also observed that the degradation of the concrete is less if the HCM design life ( τ a ) is considered to be less compared to the situation when τ a value is more.

9 The Behavior of Aged Concrete Gravity Dam 113 Degradation index Design life = 5 yrs, Gogoi and Maity (27) Design life = 5 yrs, Present analysis design life = 1 yrs, Gogoi and Maity (27) Design life = 1 yrs, Present analysis Age (yrs) Figure 2: variation of degradation index with age of concrete for different HCM design life. Numerical Results and Discussions In the present work, the Young s modulus of concrete at a later stage after construction of the structure is determined by using both eq. (15) (Gogoi and Maity, 27) and eq. (17) suggested in the present analysis are used to analyze the behaviour of Koyna gravity dam against Koyna (1967) earthquake accelerations under the assumption of plane strain condition. The foundation material of the dam is assumed to be hard rock. Therefore, the base of the dam is considered to be fixed at the ground. Geometry of Koyna Gravity Dam The geometry of the dam body is shown in Fig. 3. The height of the dam is 13. m and the width of the base is 7. m. The discretization of the dam body used for analysis purpose is also shown in Fig. 2. The dam is analyzed against reservoir empty condition subjected horizontal component of Koyna earthquake (1967) acceleration data. The behaviour of the dam is observed at the crest point at different ages after the construction. Figure 2: Geometry and discretization of koyna gravity dam.

10 114 A. Burman, D. Maity and S. Sreedeep Material Properties As per Gogoi and Maity (27), the Young s modulus of dam body is assumed to be 3.15e+1 N/m 2. The Poisson s ratio is taken to be.235 and the mass density is assumed to be kg/m 3. The damping of the structure is considered to be 3%. The dam is analyzed against empty reservoir condition because our objective to asses the performance the degradation model (eq. 4) by using eq. (15) to find out the value of degraded elastic modulus. Element Selection The dam is discretized with a two dimensional eight nodded isoparametric finite element. This element is chosen over the lower order four nodded because it provides more accurate results due to the quadratic variation of displacement profiles within the element body (Bathe, 1996). Selection of an Optimum Mesh Size To check the convergence of the results obtained for various mesh grading, the model shown in Fig. 3 has been chosen for the extensive analysis using finite element technique. The dimension and the material properties of the dam in the present case are same as listed before. The dam is discretized with 8-noded quadratic elements as shown in Fig. 3 and is analyzed using plain strain formulation. A concentrated horizontal load of 1 kn is applied at the crest of the structure and the static analysis is carried out considering the bottom nodes of the dam to be fixed. Also, the eigen value analysis is carried out to observe the convergence of natural frequencies and time periods. The structure is discretized with different mesh grading and the convergences of results for the time periods and the crest displacements obtained for different discretizations are presented in Table 1. It is observed from the results that the solution converges sufficiently for a discretization of 6 4. Analysis of Koyna Gravity Dam Against Koyna Earthquake Acceleration In the present analysis, the proposed concrete degradation model (eq. 6) has been used to determine the behavior of Koyna gravity dam against Koyna earthquake (1967) acceleration. The geometry of the dam is shown in Fig. 1 and the material properties of the dam are as stated before. Koyna gravity dam is further analyzed using the model proposed by Gogoi and Maity (27) given by eq. (4) and both the results are compared. Equation (19) is used to predict the value of elastic modulus E as a function of compressive strength of concrete considering the gain with age. The concrete compressive strength is determined from eq. (17) proposed in the present work. Also, the elastic modulus E is further calculated by using eq. (15) (proposed by Gogoi and Maity, 27) to determine the compressive strength of concrete at any age. Both the results are compared in Fig. 3. It is observed that the value of the elastic modulus E is slightly higher when eq (17) is used to predict the value of concrete compressive strength at any age. The value of the material parameter a s has been taken equal to.57 as considered by Gogoi and Maity (27) in their work.

11 The Behavior of Aged Concrete Gravity Dam 115 Table 1: Convergence of time periods and horizontal crest displacement of the Koyna dam. Dam With Mesh Size Time Period (sec) Horizontal Crest Displacement (m) due to 1 kn horizontal load N v N h Mode 1 Mode 2 u v Next, the variation of degraded elastic modulus with age is observed. The elastic modulus of concrete (E d ) considering the strength gain with age is obtained from eq. (19). Having obtained the value of E d, the degraded elastic modulus E n is calculated from eq. (6). The variation of elastic modulus of concrete considering hygro-chemomechanical effects with design life of 1 years is plotted in Fig. 4. The degraded elastic modulus is found out as a function of the elastic modulus considering the gain of strength with age which is further obtained using both eq. (15) and eq. (17). In Fig. 5, the variation of the degraded elastic modulus with the material parameter a s is also plotted. In case of hygro-chemo-mechnically induced degradation, the total porosity φ of concrete is expressed as the summation of initial porosityφ, chemically induced porosity φ c and mechanically induced porosity φm according to eq. (7). The values of φ and φc are considered to be.2 (Gogoi and Maity, 27; Kuhl et al., 24). Following eq. (8), the value of mechanically induced porosity φ m is expressed as a function of scalar degradation parameter dm which may be calculated from eq. (9). In eq. (9), the values of material parameters α m, βm, φ and κ are considered to be.9, 4 1,.2 and respectively (Kuhl et al., 24). The value of φ c may be considered between. and.2 in the presence of chemical degradation due to silt deposition on the upstream face of the dam. The maximum allowable range of values for d m should lie between 1. and. indicating complete and no degradation of concrete respectively. The value of the material parameter a s has been varied from.4 to 1. for a HCM (hygro-chemo-mechanical) design life of 1 years. The variation

12 116 A. Burman, D. Maity and S. Sreedeep of elastic modulus with different values a s has been plotted in Fig. 5. The elastic modulus has been calculated by using eq. (15) and eq. (17) and values of elastic modulus have been compared. The elastic modulus values obtained from the present analysis using eq. (17) to predict the value E d are found to match closely with the values of elastic modulus obtained by Gogoi and Maity (27) by using eq. (15). It is also noticed that the values of elastic modulus obtained by using eq. (17) is slightly on the higher side of that obtained sing eq. (15). It is observed that considering a s =1. reduces the value of elastic modulus of concrete to a very low value which is practically incorrect. Having observed the effects of the different values of the material parameter a s, the value of has been fixed at.57 for further analyses (Gogoi and Maity, 27). Elastic modulus considering gain of compressive strength (Mpa) present analysis Gogoi and Maity (27) as= Age of concrete (years) Figure 4: The variation of elastic modulus of concrete with age considering the effect of compressive strength gain. Elastic modulus of concrete (M pa) Age of concrete (years) as = 1. (Gogoi and Maity, 27) as = 1. (Present analysis) as =.6 (Gogoi and Maity, 27) as =.6 (Present analysis) as =.5 (Gogoi and Maity, 27) as =.5 (Present analysis) as =.4 (Gogoi and maity, 27) as =.4 (Present analysis) No degradation (Gogoi and Maity, 27) No degradation (Present analysis) Figure 5: Variation of elastic modulus of concrete with age (Design life = 1 years).

13 The Behavior of Aged Concrete Gravity Dam 117 Next, the behavior of the Koyna gravity dam under the influence of ageing effects caused by various hygro-chemo-mechanical actions is observed. The Young s modulus is calculated by using eq. (19) which is a function of the concrete compressive strength f () t to be determined at the particular age of the concrete structure. The compressive strength of the concrete at any age after construction is determined by eq. (17) as suggested in the present paper. The comparisons of the horizontal crest displacement of the structure after 25 years after construction and 75 years of construction respectively when the HCM design life of concrete is considered to be 1 yrs under reservoir empty condition. The results are shown in Fig. (6). The maximum and minimum values of the horizontal crest displacements obtained from the present analysis observed are 6.14 cm and cm respectively after 25 years of construction. After 75 years of construction, the similar values were obtained to be 7.17 cm and cm respectively. Therefore, it is observed that the displacement increases after 75 years of construction because degradation of concrete is more in that case. Horizontal crest disp. (m) After 25 yrs of construction After 75 yrs of construction Time (sec) Figure 6: Comparison of horizontal crest displacement vs. age under empty reservoir condition after 25 and 75 years of construction (HCM design life = 1 yrs). Major principal stress (Mpa) 9 After 25 yrs of construction 8 After 75 yrs of construction Time (sec) Figure 7: Comparison of major principal stress vs time at point O under empty reservoir condition after 25 and 75 years of construction (HCM design life = 1 years).

14 118 A. Burman, D. Maity and S. Sreedeep Similar analyses are carried out in order to compare the values of major principal stresses occurring at point O (as shown in Fig. 2) after 25 years and 75 years of construction respectively under the empty reservoir condition. The HCM design life of concrete is considered to be equal to 1 years. It is observed that the maximum value of the major principal stress obtained after 25 years of construction is 7.59 Mpa and whereas that obtained after 75 years of construction is 2.93 Mpa. The major principal stress vales have decreased at the age of 75 years after construction because the stiffness of the material reduces by a large amount due high degradation experienced at a later stage of its life. Fig. 8 shows the variation of minor principal stress vs. time at the point O as shown in Fig. 3. The value of minimum minor principal stress obtained after 25 years of construction is Mpa whereas that value is obtained as Mpa after 75 years of construction. In this case also, the value of the minor principal stress was observed to decrease at a later stage of its life because the material loses its stiffness due to high amount of degradation. Minor principal stress (Mpa) After 25 yrs of construction After 75 yrs of construction Time (sec) Figure 8: Comparison of minor principal stress vs time at point O under empty reservoir condition after 25 and 75 years of construction (HCM design life = 1 years) Next, the behavior of Koyna gravity dam under the effect of Koyna earthquake acceleration is observed after 25 years and 75 years of its construction considering the HCM design life of concrete to be 5 years. The degradation index values at 25 years and 75 years are calculated using the eq. (17) suggested for the calculation of compressive strength proposed in the present work. Fig. 9 shows the comparison of horizontal crest displacement computed in both the cases. The maximum and minimum values of horizontal crest displacements observed after 25 years are 5.73 cm and cm respectively. Also, the corresponding values after 75 years of construction are 7.11 cm and cm respectively. Therefore, displacements at a later stage of the structure s life is found to increase because the stiffness of the structure reduces with increasing degradation with the passage of time.

15 The Behavior of Aged Concrete Gravity Dam 119 Horizontal crest disp (m) after 25 yrs of construction after 75 yrs of construction Time (sec) Figure 9: Comparison of horizontal crest displacement vs. age under empty reservoir condition after 25 and 75 years of construction (HCM design life = 5 yrs). Similarly, the variation of major and minor principal stresses vs. time is also observed for point O (shown in Fig. 3) for both the cases i.e. when the compressive strength is calculated from eq. (17). Fig. 1 shows the variation of major principal stress vs. time at point O when the HCM design life is 5 years. The maximum values of major principal stresses observed at point O after 25 years and 75 years after construction are 5.88 Mpa and 3.34 Mpa respectively. The principal stress values decreases at a later stage of the life of the structure because of the reduction of its stiffness due to higher degradation experienced with time. Fig. 11 shows the variation of minor principal stress vs. time at point O of concrete gravity dam (shown in Fig. 3) for both types of analyses. The minimum value of the minor principal stress observed at point O is Mpa after 25 years after construction whereas the minimum value of minor principal stress observed at point O is Mpa after 75 years of construction of the dam. Same reasoning of lower stiffness with higher age is responsible for yielding of lower value of minor principal stress at point O. Major principal stress (Mpa) After 25 yrs of construction After 75 yrs of construction Time (sec) Figure 1: Comparison of major principal stress vs time at poin O under empty reservoir condition after 25 and 75 years of construction (HCM design life = 5 years).

16 12 A. Burman, D. Maity and S. Sreedeep Minor principal stress (Mpa) After 25 yrs of construction After 75 yrs of construction Time (sec) Figure 11: Comparison of major principal stress vs time at poin O under empty reservoir condition after 25 and 75 years of construction (HCM design life = 5 years). Conclusion In the present work, the effect of degradation of concrete due to various hygro-chemomechanical effects has been investigated on Koyna gravity dam subjected to Koyna earthquake acceleration. Based on the test results of fifty years of concrete compressive strength, a least square curve fitting analysis has been carried out. From the curve fitting analysis, a new equation was obtained to predict the gain of concrete compressive strength with time and the results were used to compute the degradation index of concrete responsible concrete degradation due to various hygro-chemomechanical analysis. The degraded elastic modulus of concrete is used in the material constitutive matrix to determine the behavior of Koyna gravity dam against Koyna earthquake (1967) acceleration. The equation used in the present analysis to predict the concrete compressive strength at any age is slightly on the higher side when compared to values obtained by using eq. (15) suggested by Gogoi and Maity (27). Therefore, degradation index predicted by the present method is slightly lower than that suggested by Gogoi and Maity (27). Based on the concrete compressive strength predicted by the newly proposed curve (eq. 17), the elastic modulus of concrete at various stages of its life is determined. This elastic modulus is used to determine the response of Koyna gravity dam under Koyna earthquake acceleration considering reservoir empty condition. The graphs showing the variation of horizontal crest displacements, major and minor principal stresses after 25 years and 75 years of construction suggest that the displacements increase whereas the major and minor principal stress reduces with passage of time. This phenomenon is attributed to loss of stiffness of the structure with increasing degradation experienced with higher age.

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