MIGUEL RODRIGUES, SERGIO OLIVEIRA, JOSE NUNO LIMA & JORGE PROENCA


Table 1. Adjustment functions used in each term of the regression equation Table 1 displays the use of exponential functions to represent the HP elastic effect, where


a is the regression coefficient, h is the reservoir water level and cf is a shape coefficient for the exponential function. One should note that FEM results can be used to better define the


exponential function shape that characterizes the elastic response to the HP variation (for example, in Figure 7 top left graph, the thin grey curve represents the HP elastic effect computed by the FEM as a result derived from a combination of exponential functions). The HP creep effect is obtained as a superposition response to a sequence of constant load “steps” (equivalent to a discretization of the water level variation in constant intervals): creep coefficients are applied to the elastic displacement values calculated for each constant water level step. The viscoelastic response is equal to the superposition of the creep effect computed for each step (Figure 6a). The creep effect estimation for the water level variation is given by the following equation:


(2)


where we have a sum over the p water level discretization steps (from j = 1 to p) as presented in Figure 6a, being ϕ(t,tj


′) the creep coefficient at time t for the hydrostatic load step at time instant tj′. 156 DAM ENGINEERING Vol XXXI Issue 3


Page 1  |  Page 2  |  Page 3  |  Page 4  |  Page 5  |  Page 6  |  Page 7  |  Page 8  |  Page 9  |  Page 10  |  Page 11  |  Page 12  |  Page 13  |  Page 14  |  Page 15  |  Page 16  |  Page 17  |  Page 18  |  Page 19  |  Page 20  |  Page 21  |  Page 22  |  Page 23  |  Page 24  |  Page 25  |  Page 26  |  Page 27  |  Page 28  |  Page 29  |  Page 30  |  Page 31  |  Page 32  |  Page 33  |  Page 34  |  Page 35  |  Page 36  |  Page 37  |  Page 38  |  Page 39  |  Page 40  |  Page 41  |  Page 42  |  Page 43  |  Page 44  |  Page 45  |  Page 46  |  Page 47  |  Page 48  |  Page 49  |  Page 50  |  Page 51  |  Page 52  |  Page 53  |  Page 54  |  Page 55  |  Page 56  |  Page 57  |  Page 58  |  Page 59  |  Page 60  |  Page 61  |  Page 62  |  Page 63  |  Page 64  |  Page 65  |  Page 66  |  Page 67  |  Page 68  |  Page 69  |  Page 70  |  Page 71  |  Page 72  |  Page 73  |  Page 74  |  Page 75  |  Page 76  |  Page 77  |  Page 78  |  Page 79  |  Page 80  |  Page 81  |  Page 82  |  Page 83  |  Page 84  |  Page 85  |  Page 86  |  Page 87  |  Page 88  |  Page 89  |  Page 90  |  Page 91  |  Page 92  |  Page 93  |  Page 94  |  Page 95