5. From the three-phase composite model, the effective bulk K and shear modulus G of concrete can be estimated by the fo

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5 From The Three Phase Composite Model The Effective Bulk K And Shear Modulus G Of Concrete Can Be Estimated By The Fo 1 (48.78 KiB) Viewed 42 times

5. From the three-phase composite model, the effective bulk K and shear modulus G of concrete can be estimated by the following Hashin bounds. The three phases are labeled as the subscript p. a (aggregate), i, respectively. V V 3 V.K K- /) 38. 1 + Ki+ 4G/3 V, V. 2 V.G. +0.4V. 2.5G G- G G K, +4G/3 G+ 1 + K+ 4G/3+20 + ** K+46,13 ' * = V,K, Kit 6 + a) C = v.C + Page 1 of 2 Here t, is the ratio of interface thickness to equivalent radius of spherical inclusions, the subscripts (+) and (-) indicate the upper and lower bound, respectively. One may also use the logarithmic mixture rule, as follows, to estimate effective Young's modulus of concrete. log E. = V., log E, +V, log E, + V, log E; From the Hashin bounds, please use reasonable material parameters for concrete to calculate the bounds for effective Young's modulus and Poisson's ratio. Please discuss the validity of the logarithmic rule along with the Hashin bounds.