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مکانیک::
فشار اصطکاکی
Johnson and Jackson (1987) proposed a critical state solid frictional pressure that allows for a slight compressibility with very limited particle concentration change (Makkawi and Ocone 2005).
The Johnson and Jackson correlation for frictional pressure can be written as
Note that pc is the critical state frictional pressure and many studies assumed the critical state frictional pressure is equal to solid frictional pressure pf (Nikolopoulos et al. 2012; Abbasi and Arastoopour 2011; Tsuo and Gidaspow 1990), although clearly it is not an accurate assumption.
Srivastava and Sundaresan (2003) modified the Schaeffer expression for the frictional stress and also the Johnson and Jackson (1987) expression for the frictional pressure (see Eq. 2.108), to approximately account for strain rate fluctu- ations and slow relaxation of the assembly to the yield surface following Savage's (1998) argument of existence of fluctuations in the strain rate, even in purely quasi- static flow.
It is worth mentioning that decreasing the value of n in the compactness branch will cause more deviation from the critical state frictional pressure.
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