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R(z,N)is reached to 1 or more, the initial liquefaction occurs.
Typical example
To show the basic ideal and principle of the method proposed in this paper, as a complete
example, we give a concrete evaluation of liquefaction of subsoil under a strip footing with the
width of 2b Q , which rest on the ground surface of an isotropic homogeneous semi-space.
According to the cone model theory, Men et al gave the stress distribution of the each zone in
subsoil, as follows
Zone I r f =
§
°>-^7
( 12 )
w a mf
a. =±- z+zA 2g
Zone II ( 13 )
Zone III
If r — W*VJ
( 14 )
where i d , a are the total dynamic shear stress and total compression stress, respectively. r s ,
is the additional dynamic shear stress due to existing building, w is the vertical static load
undertaken by the footing, and A is the area of footing, zj, ZQ are tne a P ex ne ig nt of shear
cone and compression cone ^respectively, p is the volume weight of soil, p, is the buoyancy
volume weight of soil, a mdx is the peak acceleration of ground, g is the acceleration of gravity.
Using the above formulas, the equivalent cyclic shear stress amplitude and the vertical
compression stress of each point with arbitrary depth in each zone can be calculated respectively.
Then, the equivalent cyclic shear strain can be determined in terms of nonlinear constitutive
relationship (9). Finally, the pore water pressure produced under a definite cyclic shear loading
value in different zones of subsoil can be evaluated.