As also stated elsewhere above, the liquefaction analysis was conducted for three likely-to-recur scenario earthquakes of magnitudes *M*_{w}7.8, *M*_{w}8.0, and *M*_{w}8.4 considering peak ground acceleration (PGA) of 0.18 g, 0.30 g and 0.36 g respectively using existing standards and frequently used analysis and computation methods.

The PGAs and earthquake magnitudes were taken from three standard seismic hazard assessments conducted for the Kathmandu Valley. JICA (2002) reported a PGA of 0.3 g for the scenario earthquake of *M*_{w}8.0 with a 10% probability of exceedance in 50 years (i.e., return period of 475 years) in the Kathmandu Valley. A PGA of 0.18 g was observed in the valley during the *M*_{w}7.8, 2015 Gorkha Earthquake. After the 2015 Gorkha Earthquake, NBC (2020) has recommended an earthquake of *M*_{w}8.4 with a PGA of 0.36 g for the Kathmandu Valley. All these recommended scenarios were used in the analysis of liquefaction susceptibility in terms of factor of safety (FOS), liquefaction potential index (LPI) and probability of ground failure (*P*_{G}). These parameters were obtained using standard procedures as described in the below sections. The obtained result data were interpolated in ArcGIS using inverse distance weighting (IDW) method and presented as spatial zonation maps in terms of the FOS, LPI and *P*_{G}. Moreover, graphical and statistical visualizations were prepared using OriginPro. Finally, the target SPT-N values (*N*_{improved}) at potentially liquefiable areas were assessed using back analysis to ascertain no liquefaction during the aforementioned three scenario earthquakes.

### Determination of the factor of safety (FOS) against liquefaction

Several methods based on cone penetration test (CPT), shear wave velocity and cyclic loading test (Bolton Seed et al. 1985; Robertson and Wride 1998; Onder Cetin et al. 2004; Moss et al. 2006; Idriss and Boulanger 2008) are used to do accurate liquefaction potential assessment. However, as the CPT, shear wave velocity test, and cyclic loading test are not commonly practiced in Nepal, the liquefaction potential assessment in the valley largely relies on borehole data with SPT-N. In this regard, a method developed by Idriss and Boulanger (2008) is adopted in this study to perform an analysis of the factor of safety (FOS) against liquefaction. Idriss and Boulanger (2008) method is further modified and verified with the liquefaction cases during earthquakes. Additionally, the Iwasaki et al. (1982) method is adopted to compute liquefaction potential index (LPI) at the target locations.

Idriss and Boulanger (2008) use the SPT-N data and geotechnical properties of the soil layers to predict the FOS against the liquefaction for each layer. The cyclic resistance ratio (CRR) of the soils is specified in the system, and the stress (loading) produced in the field as a result of a design earthquake that results in liquefaction is defined as the cyclic stress ratio (CSR). Equation 1 is used to determine the factor of safety against liquefaction:

$$FOS=\frac{{CRR}_{7.5}}{CSR}MSF\bullet {K}_{\sigma }$$

(1)

where *CRR*_{7.5} is the cyclic resistance ratio calibrated for the earthquake of *M*_{w}7.5; *MSF* is the magnitude scaling factor that accounts for the effects of shaking duration, and *K*_{σ} is a factor for the presence of sustained static shear stresses, such as may exist beneath foundations or within slopes.

*MSF* and *K*_{σ} were calculated using Eqs. 2 and 3

$$MSF=6.9{e}^{-\frac{{M}_{w}}{4}}-0.058 (\le 1.8)$$

(2)

$${K}_{\sigma }=1-{C}_{\sigma }ln\left(\frac{{\sigma }_{v}^{^{\prime}}}{{P}_{a}}\right)\le 1.1$$

(3)

where

$${C}_{\sigma }=\frac{1}{18.9-2.55\sqrt{{\left({N}_{1}\right)}_{60cs}}}\le 0.3$$

(4)

The SPT-N value derived from the field investigation was used to calculate the CRR, while Eq. 5 was used to correct the raw SPT-N value.

$${\left({N}_{1}\right)}_{60}=N{C}_{N}{C}_{E}{C}_{B}{C}_{R}{C}_{S}$$

(5)

where *(N*_{1}*)*_{60} is the SPT-N normalised to an overburden pressure of 101 kPa (i.e., atmospheric pressure) with a hammer efficiency of 60%. *N* is the measured SPT blow count. *C*_{N} is the correction factor for overburden stress. *C*_{B} is the correction factor for borehole diameter. *C*_{E} is the correction factor for the hammer energy ratio. *C*_{R} is the correction factor for rod length. *C*_{S} is the correction factor for samplers with and without liners.

The *CRR*_{7.5} is calculated using Eq. 6.

$$\begin{aligned}{CRR}_{7.5}&=exp\left(\frac{{\left({N}_{1}\right)}_{60cs}}{14.1}+{\left(\frac{{\left({N}_{1}\right)}_{60cs}}{126}\right)}^{2}\right.\\ &\quad \left. -{\left(\frac{{\left({N}_{1}\right)}_{60cs}}{23.6}\right)}^{3}+{\left(\frac{{\left({N}_{1}\right)}_{60cs}}{25.4}\right)}^{4}-2.8\right)\end{aligned}$$

(6)

where *(N*_{1}*)*_{60cs} is an equivalent clean-sand SPT blow count.

Equations 7 and 8 are used to calculate (*N*_{1})_{60cs}:

$${\left({N}_{1}\right)}_{60cs}={\left({N}_{1}\right)}_{60}+\Delta {\left({N}_{1}\right)}_{60}$$

(7)

$$\Delta {\left({N}_{1}\right)}_{60}=exp\left(1.63+\frac{9.7}{FC+0.01}-{\left(\frac{15.7}{FC+0.01}\right)}^{2}\right)$$

(8)

where *FC* is the fines content in the soils obtained from sieve analysis of the borehole or split-spoon samples.

The *CSR* is calculated by using Eq. 9.

$$CSR = 0.65\frac{{\tau_{max} }}{{\sigma_{vc}^{\prime } }} = 0.65\frac{{\sigma_{vc} }}{{\sigma_{vc}^{\prime } }}\frac{{a_{max} }}{g}r_{d}$$

(9)

where *a*_{max} is the peak horizontal ground acceleration (PGA) at the ground surface, *g* is the gravitational acceleration, *σ*_{vc} and \(\sigma_{vc}^{\prime }\) are the total overburden stress and effective overburden stress, respectively, and *r*_{d} is the stress reduction factor as given in Eq. 10.

$$\begin{aligned}{r}_{d}&=exp\left[-1.012-1.126sin\left(\frac{z}{11.73}+5.133\right)\right.\\ &\quad \left. +{M}_{w}\left(0.106+0.118sin\left(\frac{z}{11.28}+5.142\right)\right)\right]\end{aligned}$$

(10)

where *z* is the depth of the soil layer in meters.

### Estimation of the liquefaction potential index (LPI)

The FOS in Eq. 1 above does not help to obtain precise information on the severity of the potential ground deformation at a given depth while the liquefaction potential index (LPI) introduced by Iwasaki et al. (1982) considers the effect of the liquefiable soil layer's width, depth, and FOS assuming that the severity of liquefaction is proportional to the thickness of the liquefied layer, its proximity to the ground surface, and the extent to which the FOS is less than 1. The LPI is estimated by using Eq. 11 for the top 20 m or less soil profile (Iwasaki et al. 1982).

$$LPI={\int }_{0}^{z}F\left(z\right)W\left(z\right)dz$$

(11)

where *z* = depth of layer; *F(z)* = function of FOS against liquefaction and is defined as:

$$F\left( z \right) = {1}\quad {\text{for}}\;\;{\text{FOS}} \le 1$$

(12)

$$F\left( z \right) = {0}\quad {\text{for}}\;\;{\text{FOS}} > 1$$

(13)

*W*(*z*) is a depth-weighting factor defined as:

$$W\left( z \right) = 10 - 0.5z.$$

(14)

Based on the LPI value, the liquefaction sensitivity can be divided into four groups: very low, low, high, and very high.

### Estimation of the probability of ground failure (PG)

For quantitative evaluation, the liquefaction-induced probability of ground failure (*P*_{G}) was estimated using Eq. 15 (Li et al. 2006).

$$P_{{\text{G}}} = \frac{1}{{1 + e^{4.71 - 0.71*LPI} }}$$

(15)

where *LPI* is the liquefaction potential index as in Eq. 11.

### Improved SPT-N values

The *N*_{improved} is calculated to provide desired SPT-N after ground improvement ensuring no liquefaction condition. Improved SPT-N values were determined for all liquefiable sites using calculations for desired FOS. Correlations in Eqs. 5, 6, 7, 8, and 9 are used to determine the amount of in-situ soil strength change needed to avoid liquefaction at previously defined liquefiable locations. In case any soil stratum is found to be liquefiable for a known value of CSR, the \({CRR}_{7.5}^{improved}\) is calculated using Eq. 16 as follows.

$${CRR}_{7.5}^{improved}=CSR\times FOS$$

(16)

Then, *(N*_{1}*)*_{60cs} is evaluated using Eq. 6, and Eqs. 7, 8, and 5 are subsequently used to obtain the final targeted SPT-N (i.e. *N*_{improved}) value. The obtained *N*_{improved} values ensure no potential liquefaction with suitable methods of ground improvement needed at liquefaction-prone sites. These values are supposed to prove highly evidential in planning and estimating the cost of ground improvement.