3. Description

The POST_LIQUEFACTION command makes it possible to calculate the value of a criterion evaluating the liquefaction zones in a geotechnical structure, modelled by a saturated porous medium. Four formulas are available to calculate this criterion:

• DP_SIGV_REF: the criterion is based on the values at any material point of the interstitial pressure \({p}_{h}\) at time \(t\), of the pore pressure at the reference time \({t}_{\mathrm{réf}}\), of the component of the effective stress field \({\sigma }_{v}^{\mathrm{eff}}\) at the reference moment, according to the direction of gravity, associated with the weight of the earth. It is accepted that when the value of the criterion exceeds 0.8, a risk of local liquefaction is deduced: consult for example document DGPR, « Seismic risk and safety of hydraulic structures », final version of October 2014. His expression is as follows, at moment \(t\) and point \(x\):

\[\]

: label: EQ-None

{r} _ {u} (t,mathrm {x}) =frac {{p}} _ {h} (t,mathrm {x}) — {p} _ {h} ({t} _ {t} _ {mathit {ref}} _ {mathit {ref}} _ {v} _ {v} _ {v} _ {v} _ {v} _ {v} _ {mathit {ref}}} _ {v} _ {v} _ {mathit {ref}}} _ {v} _ {v} _ {mathit {ref}}} _ {v} _ {v} _ {mathit {ref}}} {mathit {ref}}} {mathit {ref}}} {mathit {ref}}}}} ({t} _ {mathit {ref}}},mathrm {x})}

• DP_SIGM_REF: the criterion is calculated from the values at any material point of the interstitial pressure \({p}_{h}\) at the time \(t\), the interstitial pressure at the reference time \({t}_{\mathit{réf}}\) and the average effective stress \({\mathrm{\sigma }}_{m}^{\mathit{eff}}\) at the reference time at the reference time. His expression is as follows, at moment \(t\) and point \(x\):

\[\]

: label: EQ-None

{r} _ {u} (t,mathrm {x}) =frac {{p}} _ {h} (t,mathrm {x}) — {p} _ {h} ({t} _ {t} _ {mathit {ref}}) {mathit {ref}}} {mathit {ref}}} _ {m} _ {m} _ {m} _ {m} _ {m} _ {m} _ {m} _ {mathit {ref}}} _ {m} _ {m} _ {m} _ {mathit {ref}}} _ {m} _ {m} _ {m} _ {mathit {ref}}} _ {m} _ {m} _ {m} _ {mathit {ref}}} _}} ({t} _ {mathit {ref}}},mathrm {x})}

with the mean stress defined by

\[\]

: label: EQ-None

{mathrm {sigma}} _ {m} ^ {mathit {eff}}} ({t} _ {mathit {ref}},mathrm {x}) =frac {({mathrm {sigma}} ^ {mathit {sigma}}} _ {mathrm {sigma}}} _ {mathrm {sigma}}} _ {mathrm {sigma}}} _ {mathrm {sigma}}} _ {mathrm {sigma}}} _ {mathrm {sigma}}} _ {mathrm {sigma}}} _ {mathrm {sigma}}} _ {mathit {ref}}},mathrm {x}) + {mathrm {sigma}}} _ {mathit {yy}}} ^ {mathit {eff}} ({t} _ {mathit {ref}}},mathrm {x}}) + {mathrm {x}}) + {mathrm {x}}) + {mathrm {x}}) + {mathrm {x}}) + {mathrm {sigma}}} _ {mathit {zz}} ^ {mathit {eff}}},mathrm {x}) + {mathrm {x}) + {mathrm {x}}) + {mathrm {x}}) + {mathrm {x}} {mathit {ref}},mathrm {x}))} {3}

• DP: it is a difference in interstitial pressure \({p}_{h}\) between an instant \(t\) and a reference time \({t}_{\mathit{réf}}\). His expression is as follows, at moment \(t\) and point \(\mathrm{x}\):

\[\]

: label: EQ-None

{r} _ {u} (t,mathrm {x}) = {p} _ {x}) = {p} _ {x}) — {p} _ {h} ({t} _ {mathit {x}}) = {p} _ {mathit {ref}}},mathrm {x})

• P_ SIGM: the criterion is calculated from the interstitial pressure \({p}_{h}\) and the mean effective stress at time \(t\). His expression is as follows, at moment \(t\) and point \(x\):

\[\]

: label: EQ-None

{r} _ {u} (t,mathrm {x}) =frac {{p} _ {h} (t,mathrm {x})} {{mathrm {sigma}}} _ {m}} _ {m}}} _ {m}} ^ {m} ^ {mathit {eff}}} (t,mathrm {x})}

with the mean stress defined by

\[\]

: label: EQ-None

{mathrm {sigma}} _ {m}} ^ {mathit {eff}} (t,mathrm {x}) =frac {({mathrm {sigma}}} _ {mathit {xx}}} ^ {mathit {xx}}} ^ {mathit {eff}}} ^ {mathit {eff}}} ^ {mathit {eff}}} (t,mathrm {x}}) + {mathrm {sigma}}} _ {sigma}} _ {sigma}} _ {sigma}} _ {sigma}} _ {sigma}} mathit {yy}} ^ {mathit {eff}} (t,mathrm {x}}) + {mathrm {sigma}} _ {mathit {zz}}} ^ {mathit {eff}}} (t,mathrm {x}})} {3}

This post-treatment calculation is independent of the mechanical behavior model of the porous medium in question. Note that only one formula can be associated with the order. If the user wants to calculate several criteria, he must use the command several times. The zzzz403a test case [V1.01.403] illustrates an implementation of the command on a fictional case and the documentation [U2.04.09] shows the liquefaction calculations.