In seismic prone areas, earthquakes happen more than just main shocks which are happen with sequences of shocks include of different intensity of aftershocks. In technical documents, these kinds of several earthquakes are called mainshock-aftershock ground motions. In this study, seismic behavior of RC frame under mainshock-aftershock with different ratios of maximum acceleration of aftershock to maximum acceleration of mainshock was evaluated. In this paper, nonlinear time-history analysis of frame were performed under mainshock-aftershock sequences and then the residual interstory drift ratio for comparing response of frame under seismic sequences was evaluated. The results show that, residual interstory drift ratio of frame, related to intensity of aftershocks to mainshock and enhance of intensity of aftershock due to increase residual interstory drift ratio of frame. Although, growth of residual interstory drift ratio of top stories more significant than below stories of frame.
Parameter | Unit | Layer No. 1 | Layer No. 1 |
Internal friction angle (CU) | Deg. | 29 | 33 |
Cohesion (CU) | Kg/cm2 | 0.15 | 0.45 |
Density | Kg/cm3 | 18.5 | 20 |
Poisson ratio of unloading/reloading | Kg/cm2 | 0.2 | 0.2 |
Secant deformation modulus | Kg/cm2 | 550 | 900 |
Power of stress level of stiffness | 0.5 | 0.5 | |
Stiffness unloading | Kg/cm2 | 1650 | 2700 |
Specimen | Tensile Strength (MPa) | Fracture Toughness (MPa√m) |
Limestone | 3.74 | 1.23 |
Sandstone | 7.14 | 1.63 |
Tuff | 16.36 | 2.17 |
Lithic Tuff | 4.34 | 1.01 |
Andesite | 13.25 | 1.86 |
Travertine | 8.27 | 1.14 |
One of the effective parameters in the dynamic behavior of reinforced soil walls is the fundamental vibration frequency. In this paper, analytical expressions for the first three natural frequencies of a geosynthetic reinforced soil wall are obtained in the 3D domain, using plate vibration theory and the energy method. The interaction between reinforced soil and the wall is also considered by modeling the soil and the reinforcement as axial springs. The in-depth transverse vibration mode-shapes, which were impossible to analyze via 2D modeling, are also analyzed by employing plate vibration theory. Different behaviors of soil and reinforcements in tension and compression are also considered for the first time in a 3D analytical investigation to achieve a more realistic result. The effect of different parameters on the natural frequencies of geosynthetic reinforced soil walls are investigated, including the soil to reinforcement stiffness ratio, reinforcement to wall stiffness ratio, reinforcement length, backfill width and length to height ratio of the wall, using the proposed analytical expressions. Finally, the results obtained from the analytical expressions proposed are compared with results from the finite element software Abaqus and other researchers’ results, showing that the proposed method has high accuracy. The proposed method will be a beginning of the 3D analytical modeling of reinforced soil walls.
In cases such as explosion, fire, deep drilling and geothermal energy extraction, rocks are exposed to high temperatures influencing the rock toughness. Thus, the aim of this study is to investigate the effect of temperature on the fracture toughness of the rocks. In this study, the effect of temperature on the mode I fracture toughness is investigated. To this end, three-point bending tests were performed on semicircular specimens of four types of natural rocks including sandstone, limestone, tuff, andesite, and a series of concrete specimens to determine the fracture toughness. The specimens were first heated to 100, 200, 300, 500 and 700 °C. After reaching the desired temperatures, the specimens were cooled. A series of tests was performed on the specimens at ambient temperature (25 °C). The heating rate in the electric furnace was 15 °C/min in accordance with the temperature rise in fires. Petrographic studies and X-ray diffraction analysis (XRD) were performed to identify the composition of the rocks. Furthermore, the effective porosity and the weight loss of heated specimens were determined to study the behavior of rocks. Comparison of the test results indicated the higher impact of temperature on the fracture toughness of fine-grained rocks. In addition, the fracture toughness decreased by increasing the effective porosity and decreasing the weight loss. According to the results, the mode I fracture toughness of sandstone, tuff, limestone, andesite and concrete specimens underwent a heating-cooling cycle up to 700 °C respectively decreased 45, 17, 44 and 9.5 and 37 percent compared with that of unheated specimens.
Deformation Modulus (MPa) | Peak Friction Angle (deg.) | Cohesion (kPa) |
USCS | Depth (m) |
Sample |
50-60 | 39 | 30-35 | GW-GM | 5 | Moderately Cemented Soil (M.C. Soil) |
75-85 | 41 | 50-60 | SP-SC | 10 | |
85-90 | 41 | 50-60 | GW-GC | 15 | |
95-105 | 41 | 50-60 | GW-GC | 20 | |
60-70 | 39 | 35-40 | GW-GM | 5 | Highly Cemented Soil (H.C. Soil) |
75-85 | 39 | 50-60 | GW-GC | 10 | |
110-120 | 42 | 65-75 | GW-GC | 15 | |
125-140 | 41 | 110-120 | GC | 20 |
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