# Effect of Micropiles on Clean Sand Liquefaction Risk Based on CPT and SPT
## 2 Material and Methods
### CPT-Based Simplifeid Liquefaction Assessment (Site I)  
At site I, CPT, as the most reliable site tool for soil liquefaction characterization ([PERSON] and [PERSON], 2014), was used. In this regard, the cyclic resistance of the soil against the liquefaction (CRR) was compared to the seismic-based cyclic shear stress (CSR). The factor of safety for predicting the risk of liquefaction  
Figure 2: Single bar reinforced micropile after the first phase of pressure grouting using a sleeve pipe. triggering (FS) is defined as the ratio of CRR to CSR [31]. Liquefaction is triggered if the FS value is more than 1. The CSR value is presented in Equation (1). \[\text{CSR}_{\sigma^{\prime}_{\text{v0}},\text{ M}_{\text{W}}}=0.65\frac{\tau_{ \text{cyc}}}{\sigma^{\prime}_{\text{v0}}}=0.65\frac{a_{\text{max}}}{g}\ \frac{\sigma_{\text{v0}}}{\sigma^{\prime}_{\text{v0}}}\text{t}_{\text{d}}( \text{z},\text{M}_{\text{W}}) \tag{1}\]  
where \(\tau_{\text{cyc}}\) is the maximum seismic induced shear stress, \(\sigma^{\prime}_{\text{v0}}\) and \(\sigma_{\text{v0}}\) are the vertical effective and total stress at the specified depth, \(a_{\text{max}}\) is the peak horizontal ground acceleration, and \(r_{\text{d}}\) is the shear stress reduction coefficient, which is the function of the specified depth of soil layers (z) and moment magnitude (M\({}_{\text{W}}\)) [47]. In Equation (1), CSR and \(a_{\text{max}}\) are not functions of developed excess pore pressure during the seismic loadings. Empirical curves to evaluate the resistance capacity of soil against the liquefaction were developed using the CPT case history database of clean sands in the site I. The database was collected from sites with the earthquake history, noting if liquefaction was triggered or not. In these deterministic empirical curves, the CRR quantities were correlated to laboratory test indices. The curves act as boundary lines by separating the case histories to determine if liquefaction occurs or not. All available case history data were revised to reference effective stress \(\sigma^{\prime}_{\text{v0}}=1\) atm and moment magnitude M\({}_{\text{W}}=7.5\) to present a single graph to determine the liquefaction manifestation. The measured CPT penetration resistance values were corrected to include the effect of fines contents (FC) and overburden stress. For the correction, the available data were categorized in different bins of existing soils (clean sand, sandy silts, and silty sands) and compared to the equivalent clean sand cone penetration resistance (q\({}_{\text{c1 NCs}}\)). The resulting graph to evaluate CPT-based liquefaction determination is presented as q\({}_{\text{c1 NCs}}\) versus CSR\({}_{\sigma^{\prime}_{\text{v0-1}}M_{\text{W}}=7.5}\) in the following sections. Table 1 presents the soil profile and liquefaction risk assessment using the Boulanger and Idriss 2014 method [31]. Following this method, a new recommended magnitude scaling factor (MSF) and an updated procedure for including the effect of fines contents (FC) is used in the calculating procedure. Adjustments by the \(r_{\text{d}}\) coefficient for various depths of soil layers are included in the calculations. In Table 1, parameters such as q\({}_{\text{c1 NCs}}\), CRR, and FS indicate soil improvement against liquefaction after jet grouting using micropiles. Figure 3 illustrates the effect of jet grouting on the improvement of the q\({}_{\text{c1 NCs}}\) parameter in clean sands. In this figure, the values of q\({}_{\text{c1 NCs}}\) at different depths for five boreholes are presented for the soil profile containing only SP clean sand soil. Similar depth values are related to different borehole numbers, as specified in Table 1. The average rate of increase for the q\({}_{\text{c1 NCs}}\) values in the clean sand was 38%. The highest increase rate of the q\({}_{\text{c1 NCs}}\) was measured as 82% at a 3 m depth related to the borehole BH-I-5. Figure 4 displays q\({}_{\text{c1 NCs}}\) measurements before and after grouting in soil layers including SP-SC, SP-SM, SC, and SM.