A new yield function for geomaterials. - Ingegneria - Università degli ...
A new yield function for geomaterials. - Ingegneria - Università degli ...
A new yield function for geomaterials. - Ingegneria - Università degli ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
On a <strong>yield</strong> <strong>function</strong> 273<br />
Table 1. Yield criteria obtained as special cases of (6)-(9), r = fc/ft and fc and ft are the<br />
uniaxial strengths in compression and tension, respectively.<br />
Criterion Meridian <strong>function</strong> f(p) Deviatoric <strong>function</strong> g(θ)<br />
von Mises<br />
Drucker-Prager<br />
Tresca<br />
mod. Tresca<br />
Coulomb-Mohr<br />
α =1, m =2,<br />
M = 2ft<br />
, c = pc −→ ∞<br />
pc<br />
α =0, M =<br />
3(r − 1)<br />
√ 2(r +1) ,<br />
c = 2fc<br />
, pc = fc m −→ ∞<br />
3(r − 1)<br />
as <strong>for</strong> von Mises,<br />
√<br />
except that<br />
3ft<br />
M =<br />
pc<br />
as <strong>for</strong> Drucker-Prager, except that<br />
M = 3√3(r − 1)<br />
2 √ 2(r +1)<br />
as <strong>for</strong> Drucker-Prager, except that<br />
M = 3 r cos β π<br />
<br />
π<br />
π<br />
− − cos β 6 3<br />
6<br />
√<br />
2(r +1)<br />
c = fc<br />
<br />
π π<br />
π<br />
cos β − +cosβ 6 3<br />
6 <br />
π<br />
− 3cosβ<br />
3r cos β π<br />
6<br />
− π<br />
3<br />
6<br />
β =1, γ =0<br />
as <strong>for</strong> von Mises<br />
β =1, γ −→ 1<br />
as <strong>for</strong> Tresca<br />
β = 6<br />
π tan−1<br />
√<br />
3<br />
2r +1 ,<br />
γ −→ 1<br />
mod. Cam-clay m =2,α=1,c=0 as <strong>for</strong> von Mises<br />
The Mohr-Coulomb limit merits a special mention. In fact, if the following values<br />
of the parameters are selected<br />
α =0, c = fc<br />
<br />
π π<br />
π<br />
cos β 6 − 3 +cosβ6 3r cos β π<br />
<br />
π<br />
π ,<br />
6 − 3 − 3cosβ6 M = 3 r cos β π<br />
<br />
(14)<br />
π<br />
π<br />
6 − 3 − cos β 6<br />
√ ,<br />
2(r +1)