This paper presents the exact and complete fundamental singular solutions for the boundary value problem of a n-layered elastic solid of either transverse isotropy or isotropy subject to body force vector at the interior of the solid. The layer number n is an arbitrary nonnegative integer. The mathematical theory of linear elasticity is one of the most classical field theories in mechanics and physics. It was developed and established by many well-known scientists and mathematicians over 200 years from 1638 to 1838. For more than 150 years from 1838 to present, one of the remaining key tasks in classical elasticity has been the mathematical derivation and formulation of exact solutions for various boundary value problems of interesting in science and engineering. However, exact solutions and/or fundamental singular solutions in closed form are still very limited in literature. The boundary-value problems of classical elasticity in n-layered and graded solids are also one of the classical problems challenging many researchers. Since 1984, the author has analytically and rigorously examined the solutions of such classical problems using the classical mathematical tools such as Fourier integral transforms. In particular, he has derived the exact and complete fundamental singular solutions for elasticity of either isotropic or transversely isotropic layered solids subject to concentrated loadings. The solutions in n-layered or graded solids can be calculated with any controlled accuracy in association with classical numerical integration techniques. Findings of this solution formulation are further used in the companion paper for mathematical verification of the solutions and further applications for exact and complete solutions of other problems in elasticity, elastodynamics, poroelasticty and thermoelasticity. The mathematical formulations and solutions have been named by other researchers as Yue’s approach, Yue’s treatment, Yue’s method and Yue’s solution.

This paper presents a detailed and rigorous mathematical verification of Yue’s approach, Yue’s treatment, Yue’s method and Yue’s solution in the companion paper for the classical theory of elasticity in n-layered solid. It involves three levels of the mathematical verifications. The first level is to show that Yue’s solution can be automatically and uniformly degenerated into these classical solutions in closed-form such as Kelvin’s, Boussinesq’s, Mindlin’s and bi-material’s solutions when the material properties and boundary conditions are the same. This mathematical verification also gives and serves a clear and concrete understanding on the mathematical properties and singularities of Yue’s solution in n-layered solids. The second level is to analytically and rigorously show the convergence and singularity of the solution and the satisfaction of the solution to the governing partial differential equations, the interface conditions, the external boundary conditions and the body force loading conditions. This verification also provides the easy and executable means and results for the solutions in n-layered or graded solids to be calculated with any controlled accuracy in association with classical numerical integration techniques. The third level is to demonstrate the applicability and suitability of Yue’s approach, Yue’s treatment, Yue’s method and Yue’s solution to uniformly and systematically derive and formulate exact and complete solutions for other boundary-value problems, mixed-boundary value problems, and initial-boundary value problems in layered solids in the frameworks of classical elasticity, boundary element methods, elastodynamics, Biot’s theory of poroelasticity and thermoelasticity. All of such applications are substantiated by peer-reviewed journal publications made by the author and his collaborators over the past 30 years.

As a novel structural control strategy, tuned mass damper (TMD) inspired passive and semi-active smart building isolation systems are suggested to reduce structural response and thus mitigate structural damage due to earthquake excitations. The isolated structure’s upper stories can be utilized as a large scaled TMD, and the isolation layer, as a core design point, between the separated upper and lower stories entails the insertion of rubber bearings and (i) viscous dampers (passive) or (ii) resettable devices (semi-active). The seismic performance of the suggested isolation systems are investigated for 12-story reinforced concrete moment resisting frames modeled as “10+ 2” stories and “8+ 4” stories. Passive viscous damper or semi-active resettable devices are parametrically evaluated through the optimal design principle of a large mass ratio TMD. Statistical performance metrics are presented for 30 earthquake records from the three suites of the SAC project. Based on nonlinear structural models, including P-delta effects and modified Takeda hysteresis, the inelastic time history analyses are conducted to compute the seismic performances across a wide range of seismic hazard intensities. Results show that semi-active smart building isolation systems can effectively manage seismic response for multi-degree-of freedom (MDOF) systems across a broader range of ground motions in comparison to uncontrolled case and passive solution.

Based on the performance results of the previously suggested smart building isolation systems (1st companion paper), this following study verifies the control effects of the systems from the view point of energy dissipation and damage level metrics. Several different model cases of the strategically isolated multi-story building structures utilizing passive dampers and semi-active resettable devices are analyzed and the energy-based target indices are compared. Performance comparisons are conducted on statistically calculated story/structural hysteretic energy and story/structural damage demands over realistic suites of earthquake ground motion records, representing seismic excitations of specific return period probability. Again, the semi-active solutions show significant promise for applications of resettable device, offering advantages over passive systems in the consistent damage reductions. The specific results of this study include the identification of differences in the mechanisms by which smart building isolation systems remove energy, based on the differences in the devices used. Less variability is also seen for the semi-active isolation systems, indicating an increased robustness.

The present paper deals with the numerical analysis of tall reinforced concrete chimneys with piled raft foundation subjected to along-wind loads considering the flexibility of soil. The analysis was carried out using finite element method on the basis of direct method of soil-structure interaction (SSI). The linear elastic material behavior was assumed for chimney, piled raft and soil. Four different material properties of soil stratum were selected in order to study the effect of SSI. The chimney elevation and the thickness of raft of piled raft foundation were also varied for the parametric study. The chimneys were assumed to be located in terrain category 2 and subjected to a maximum wind speed of 50 m/s as per IS:875 (Part 3)-1987. The along-wind loads were computed according to IS:4998 (Part 1)-1992. The base moments of chimney evaluated from the SSI analysis were compared with those obtained as per IS:4998 (Part 1)-1992. The tangential and radial bending moments of raft of piled raft foundation were evaluated through SSI analysis and compared with those obtained from conventional analysis as per IS:11089-1984, assuming rigidity at the base of the raft foundation. The settlements of raft of piled raft foundation, deflection of pile and moments of the pile due to interaction with different soil stratum were also evaluated. From the analysis, considerable reduction in the base moment of chimney due to the effect of SSI is observed. Higher radial moments and lower tangential moments were obtained for lower elevation chimneys with piled raft resting on loose sand when compared with conventional analysis results. The effect of SSI in the response of the pile is more significant when the structure-foundation system interacts with loose sand.

This paper presents a combined experimental and numerical study on the damage and performance of a soft-hard-soft (SHS) multi-layer cement based composite subjected to blast loading which can be used for protective structures and infrastructures to resist extreme loadings, and the composite consists of three layers of construction materials including asphalt concrete (AC) on the top, high strength concrete (HSC) in the middle, and engineered cementitious composites (ECC) at the bottom. To better characterize the material properties under dynamic loading, interface properties of the composite were investigated through direct shear test and also used to validate the interface model. Strain rate effects of the asphalt concrete were also studied and both compressive and tensile dynamic increase factor (DIF) curves were improved based on split Hopkinson pressure bar (SHPB) test. A full-scale field blast test investigated the blast behavior of the composite materials. The numerical model was established by taking into account the strain rate effect of all concrete materials. Furthermore, the interface properties were also considered into the model. The numerical simulation using nonlinear finite element software LS-DYNA agrees closely with the experimental data. Both the numerical and field blast test indicated that the SHS composite exhibited high resistance against blast loading.