13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- E AKc 2 fracture E = , (6) where A is the total fractured area along the fault plane (m2), cK is the rock fracture toughness with the unit MPa m1/2, and E is the rock elastic modulus (MPa). If E = 20,000 MPa, cK = 1 MPa m1/2, and A = 6.39 ×109 m2 (=426 km × 15 km), then, Efracture = 3.2 ×10 11 Joule. So, Efracture (3.2 ×10 11 Joule) is far less than the ES (8.9×10 16 Joule). Thirdly, the specific heat capacity frozen pc for completely frozen soil can be determined with the following equation: 0 0 1 w c w c c ice p soil p frozen p + + = , (7) where soil pc is the specific heat capacity for soil and is equal to 800 Joule/(kg °C), ice pc is the specific heat capacity for ice and is equal to 2060 Joule/(kg °C), and 0w is the water (ice) content in the complete frozen soil. Normally, frozen pc is between 800 and 2060 Joule/(kg °C). The temperature increase TΔ of the frozen soil has the following relation with its mass soil M and the heat increase QΔ : soil frozen pc M Q T Δ Δ = , (8) Assuming, 0w is 15% and its degree of saturation 100%, then frozen pc 964 Joule/(kg °C) and the unit weight of the frozen soil is about 2209 kg/m3. Assuming, for a total frozen soil along the ruptured zone, its thickness is 20 m, its length 426 km and its width 100 m. Its total mass is 1.9×1012 kg. It might have the temperature from –1°C to –20°C. The heats for the total frozen soil temperature increases 1°C and 20°C are 1.8×1015 Joules and 3.6×1016 Joules, respectively. The frozen soil has a total of 2.4×1011 kg ice. As the latent heat of ice is 3.34×105 Joule/kg, the total latent heat required for melting all the ice at 0°C in all the permafrost soil into liquid water is 8.2×1016 Joules. As a result, the total heat required for melting all the frozen soil is between 8.3×1016 Joules and 11.8×1016, which is similar to the released radiated seismic strain energy ES 8.9×10 16 Joule. Furthermore, if ES is perhaps only about 0.01 to 0.1 of the total released energy ET [5], there would be enough heat energy to melt and thaw the entire frozen soils along the surface ruptured zone. But, no melting or thawing phenomena were observed in the 140 site photographs [17]. The theoretical results and field observations can demonstrate that the elastic rebound theory is incorrect. 5. The Gas Cause of Earthquakes A further question may be asked: what type of loading can rapidly crack the crustal fault for tens to hundreds km long and tens km deep, generates the strong seismic waves, but does not produce heat? One most possible and feasibility loading is the rapid expansion and migration of highly compressed natural gas from deep crustal traps via tectonic fault channel. This is the internal loading associated with the gas hypothesis for cause of earthquakes [6-10]. The hypothesis can be briefly described below. An earth quaking is an adiabatic process of interaction between rapid upward expansion and migration of compressed natural gas and its surrounding crustal rocks and ground soils. The natural gas is produced in core and/or mantle and gradually accumulated in the traps below crustal fault rocks. It escapes from its traps in deep fault zones of the lower crustal rocks. Because of the
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