After the great 1906 San Francisco earthquake, in 1910, Harry Fielding Reid published the article "The Mechanics of the Earthquake". From an investigation of the deformation of the ground surface which accompanied the 1906 earthquake and the seismological data from USGS Reid expounded explicitly the correlation between the faults and the shallow earthquake. He put forward firstly the elastic rebound model to explain the mechanical mechanism of the earthquake. The model consists of three basic points:
1)The earthquake originates from the fault movement; 2)The movement leads to the inhomogeneous elastic deformation on both sides of fault, accumulating vast amounts of energy; 3)Part of the elastic energy is released in the earthquake.
Brace(1966)proposed that the physical mechanism of elastic rebound should be explained with jerky sliding motion or stick-slip which is well-known in engineering. The introduction of the stick-slip concept combines the physical interpretation of the earthquakes between the shallow and deep source one and converts the research of deformation into the problem of friction, thus, resulting in a great upsurge in the study of friction in the 1970s to 90s. Twelve years later, Byerlee published the research paper-Friction of rock(1978), regarded as the Byerlee's Law, that is, when the normal stress σn is smaller than 2kb, the shear stress τ=0.85σn approximately; when σn is larger than 2kb, τ=0.5+0.65σn.
Unfortunately, although Byerlee's paper referred to the variation of data for many times, the empirical formula of his own did not give the range of variation, so the reader could not calculate or evaluate its reliability. Furthermore, in the friction constitutive relation expressed by a piecewise function, the cut-off point is set at 2kb, of which there have been no explanations about its physical meaning or statistical basis so far. In Byerlee's frame, stick-slip is assimilated as a spring-block model. Fault displacement is set for the rigid block friction movement and deformation is set for spring extension. The spring extension is imputed optionally to the mechanical frame deformation of loading machine.
The friction constitutive relation can be described only by one constant and the stress field along the fault plane be gotten directly with projection transformation of loading force. This simplified mechanical model is so exciting that it seems to be paving the understanding avenue in the process of earthquake. Only after a year when Byerlee published the paper about rock friction, a mathematical model was deduced based on the simplified assumptions(Dieterich, 1979), and soon it was further simplified as the so-called velocity-dependence equation:τ[μ0+(a-b)ln (V/V0)]σ
Where, τ is shear stress and σ is effective normal stress; a and b represent the material properties; V is sliding velocity, where V0 is the reference velocity, and μ0 is steady-state friction coefficient when V=V0. For a specified fault, the sliding friction behavior or the instability depends only on the plus or minus of(a-b)
.But if μ0 is not constant, the situation will become very complicated. The experimental results show that the numerical scale(a-b)is often on the parts per thousand(0.001～0.004). Then even the same rocks in different conditions or different sliding stages the variation of friction coefficient is also on decimal point first(such as granite: 0.5～0.7, gabbro: 0.2～0.7). Therefore, if the variation of friction coefficient μ0 is taken into account, the contribution or effect of (a-b) to the friction angle changes is almost negligible.
In addition, the stress σ and τ on fault surface are taken from the axial projection. The projection must assume the rock slide block is rigid. It means along the slip surface of rock without any deformation. This has violated the elastic rebound model in essence described by the basic facts and does not conform to earthquake field investigation results.
Actual measurements have proved there is a complex deformation mode on smooth fault slip zone. Different parts of the fault have different deformation processes. Even the average stress state of the near fault parts is different from both in the direction and the value projected with loading force. Other experimental results show that, during the stick-slip, fault is not only to complete a simple smooth one-way movement, but experiences complicated multi-times and multi-point tremors to release the energy accumulated in the fault zone. These new experimental results agree with the basic model proposed from Reid by earthquake field investigation in 100 years ago.
Back to the classic is to change the research direction back to reality of earthquake, this is the right way of the future.
