MAXSURF | MOSES | SACS | OpenWindPower - Soil Liquefaction

Introduction

Soil liquefaction may occur when offshore foundations are subjected to seismic loading. The following equations are used to modify the P-Y and T-Z curves to simulate the effects of soil liquefaction.

Soil Liquefaction

The soil behavior is first classified using the soil behavior index:

$I_c = \sqrt{(3.47-logQ)^2+(1.22+logF)^2}$

Q and F are the normalized tip and sleeve friction ratios:

$Q = \frac{(q_c-\sigma_{vo})(P_a/\sigma^\prime_{vo})^n}{P_a}$

$F = \frac{f_s}{q_c-\sigma_{vo}}\times100\%$

Where $f_s$ is the sleeve friction, $q_c$ is the cone tip resistance, $\sigma_{vo}$ is the overburden pressure, $\sigma^\prime_{vo}$ is the effective overburden pressure, $P_a$ is the atmospheric pressure, and $n$ is the soil type exponent.

The soil type exponent varies between 0.5 in sands and 1.0 in clays. In SACS, the following values are used:

$n = \left \{ \begin{array}{ll} 1.0 & \text{if soil type CLAY or unknown} \\ 0.7 & \text{if soul type is SILT} \\ 0.5 & \text{if soil type is SAND} \end{array}\right.$

If the soil type is not specified, SACS will determine $n$ based upon the relationship between $I_c$ and $n$ .

The normalized dimensionless core penetration test can then be calculated:

$q_{c1N} = \frac{C_Q*q_c}{P_a}$

Where $C_q$ is the overburden stress concentration factor:

$C_Q = \left(\frac{PA}{\sigma^\prime_{vo}}\right)^n \leq 1.7$

The clean sand normalized core penetration resistance is then calculated;

$(q_{c1N})_{cs} = q_{c1N}K_c$

Where $K_c$ is the clean sand normalization factor:

$K_c = \left \{ \begin{array}{lr} 1.0 & I_c \leq 1.64 \\ -0.403I_c^4 + 5.581I_c^3 -21.63I_c^2+33.75I_c-17.88 & I_c > 1.64\\ \end{array}\right.$

They cyclic resistance ratio, $CRR_{7.5}$ , can then be calculated:

where

$\alpha_{v}$ is the user-defined vertical shift of the CRR curve and $\alpha_h$ is the user-defined horizontal shift of the CRR curve.

The cyclic stress ratio can be calculated as:

$CSR = 0.65\frac{a_{max}}{g}\frac{\sigma_{vo}}{\sigma^\prime_{vo}}r_d$

where

$a_{max}$ is the peak ground acceleration, $g$ is the acceleration of gravity and $r_d$ is the stress reduction factor calculated as:

$r_d = \left \{ \begin{array}{lr} 1.0 - 0.00233z & z < 30 ft \\ 1.174 - 0.00813z & 75 ft \geq z > 30 ft \\ \end{array}\right.$

The factor of safety can then be calculated:

$FS = (CRR_{7.5}/CSR) MSF$

Where $MSF$ is the magnitude scaling factor, expressed as:

$MSF = \frac{10^{2.24}}{M_w^{2.56}}$

Where $M_w$ is the earthquake magnitude.

If the factor of safety is less than 1, then soil liquefaction occurs in the soil layer and the following modifications are applied to the p-y, t-z, and q-z curves.

The corrected standard penetration resistance is calculated using the following equation:

$(N_1)_{60cs} = [3.242(q_{c1N})_{cs}^{0.264}-7.209]^2$

And the soil liquefaction reduction factor is then determined using the Average Brandenburg curve:

$m_p = 4E-4 (N_1)_{60cs}^2 + 1E-3 (N_1)_{60cs} +5E-2$

$m_p$ may be modified with the liquefaction multiplier factor $\alpha_{m_p}$

The p-y, t-z, and q-z curves are then modified by the $m_p$ factor:

$P^\prime = P m_p$

$T^\prime = T m_p$

$Q^\prime = Q m_p$

n calculation algorithm

First calculate $I_c$ with n = 1.

$n = \left \{ \begin{array}{lr} 0.5 & I_c \leq 2.6 \\ 1.0 & I_c > 2.6\\ \end{array}\right.$

If $n = 1.0$ then soil type is considered to be CLAY and there is no liquefaction.

If $n = 0.5$ then recalculate $Q$ and $I_c$

$n = \left \{ \begin{array}{lr} 0.5 & I_c > 2.6 \\ 0.7 & I_c \leq 2.6\\ \end{array}\right.$

If $n = 0.5$ soil type is SAND. If $n=0.7$ soil type is SILT then recalculate $Q$ and $I_c$ .