Numerical Assessment of the Loading Factors Affecting Liquefaction-Induced Failure

This paper presents parametric studies that assess the role of loading factors (i.e., number of cycles, frequency, and amplitude) on liquefaction-induced failure by performing numerical simulations. Most of the existing literature considers the effects of the soil properties on the development of excess pore pressure with few research endeavours focusing on the effects of the input motion itself. Numerical simulations are performed herein, via the advanced software platform OpenSees, to generate several finite element models that consider non-linear development of pore pressure inside the soil. Several sinusoidal inputs were considered to study the effects of the various loading factors and compare the responses. The main findings arise from evaluating the effects of several input motion parameters (number of cycles, frequency, and amplitude) on soil liquefaction through numerical simulations. This research study, based on state-of-the-art knowledge, may be applied to assess future seismic events and to update or propose new code provisions for soil liquefaction.


Background
Soil liquefaction is a complex phenomenon associated with pore water pressure development and the corresponding reduction in volume during undrained loading that may result in several additional failure mechanisms, such as lateral spreading, slope failure, excessive settlement, and bridge and building foundation failure, as described by several researchers [1][2][3][4][5][6][7].
Historically, liquefaction effects have been observed and documented in many earthquakes all over the world. In particular, liquefaction-induced effects observed during field reconnaissance from the 1964 Niigata, 1990 Luzon, 2010-2011 Canterbury, and 2011 Tohoku earthquakes have been shown to depend on many input parameters such as shaking intensity, duration, and frequency [8][9][10] as well as material and geometric factors such as relative density, fines content, soil thickness, building weight and width. Many relationships between liquefaction resistance and soil parameters have been proposed [11][12][13][14][15][16][17][18][19][20]. Among them, Ref. [13] applied SPT results to a second-moment statistical analysis as a development of the empirical procedure introduced by Robertson and Wride [18].
In addition, these approaches assess liquefaction-induced settlement with semi-empirical procedures that predict post-liquefaction, one-dimensional, consolidation settlement for free-field conditions [8][9][10]. Other contributions (i.e., [21,22]) investigated post-liquefaction free-field settlements by considering the cyclic stress ratio and soil relative density to estimate a volumetric strain. In particular, Ref. [21] considered that this procedure is affected by a potential error ranging from 25-50% and stated that liquefaction conditions are more complex than accounted for in their prediction.
In addition, Ref. [23] proposed an expression for the maximum earthquake-induced shear stress that considers both peak ground acceleration (PGA) and peak ground velocity and rough set theory to calculate the weights of factors for soil liquefaction.
In this context, liquefaction has been studied primarily through two different approaches: (1) laboratory tests, and (2) site observations of past earthquakes. Only a few contributions [47][48][49][50][51][52][53][54][55] proposed advanced numerical simulations that assess liquefaction potential. This paper targets this gap through focused numerical simulations that study the factors that affect liquefaction, specifically concentrating on those connected with the input motion characteristics. Several parametric studies are proposed to evaluate the influence of various factors (duration, amplitude, and frequency) that define the input motions. The soil layers were taken from the profile previously analyzed in [50], and free-field conditions are applied in order to focus on the effects of liquefaction on the soil. The main novelties of the proposed methodology consist in (1) performing parametric studies with advanced numerical simulations as an alternative to the more common approaches (i.e., experimental investigations and site observations) generally adopted in literature, (2) concentrating on the loading factors themselves while most other research endeavours focused on the effects of soil parameters on the liquefaction potential, and thus the liquefaction-induced damage scenarios, and (3) that the outcomes may be considered for revisions or proposals of new code provisions that may account for loading factors in the assessments of liquefaction potential.
The paper is divided into four sections. Section 2 describes the case study by focusing on (1) the performed numerical model, (2) the constitutive materials used to model the soil layers, and (3) the non-linear analyses that have been performed. Section 3 describes the three parametric studies that have been performed to assess the role of (1) the number of cycles, (2) the frequency, and (3) the amplitude. Finally, the results are compared with the existing literature.

Case Study
Numerical liquefaction analyses require complex computational approaches. The following sections describe the numerical assumptions, algorithms, and non-linear procedures that were performed with the finite element interface OpenSeesPL [56], an opensource platform (soilquake.net/openseespl/ accessed on 13 January 2022).

Numerical Model
The complete 3D numerical model of the free-field soil profile consists of a layered 38 m deep series of materials, with a 3D mesh ( Figure 1) that was calibrated via a convergence study between several meshes with an increasing number of nodes and elements (Table 1). Mesh 2 is used herein, as it is an efficient and effective compromise between computational time and accuracy as derived from performing 25 cycles of the sinusoidal input motion described below (frequency: 1 Hz; amplitude: 0.2 g) as compared to the relative error of the maximum longitudinal displacement at the surface with respect to mesh 3. It consists of a 100 × 100 × 38 m mesh, comprised of 27,540 20-node BrickUP elements [56,57] and 29,826 nodes. Each BrickUP element is constructed with 20 nodes describing the solid translational degrees of freedom and 8 nodes (at the corners) that represent the fluid pressure. For each node, the first, second, and third degrees of freedom (DOF) represent solid displacement (u), and DOF 4 describes fluid pressure (p), which are recorded using the Node Recorder [50][51][52] at the corresponding integration points. The dimensions of the element increase from the centre of the model to the lateral boundaries, in order to guarantee convergence and avoid problems of instability.

Numerical Model
The complete 3D numerical model of the free-field soil profile consists of a layered 38 m deep series of materials, with a 3D mesh ( Figure 1) that was calibrated via a convergence study between several meshes with an increasing number of nodes and elements (Table 1). Mesh 2 is used herein, as it is an efficient and effective compromise between computational time and accuracy as derived from performing 25 cycles of the sinusoidal input motion described below (frequency: 1 Hz; amplitude: 0.2 g) as compared to the relative error of the maximum longitudinal displacement at the surface with respect to mesh 3. It consists of a 100 × 100 × 38 m mesh, comprised of 27540 20-node BrickUP elements [56,57] and 29826 nodes. Each BrickUP element is constructed with 20 nodes describing the solid translational degrees of freedom and 8 nodes (at the corners) that represent the fluid pressure. For each node, the first, second, and third degrees of freedom (DOF) represent solid displacement (u), and DOF 4 describes fluid pressure (p), which are recorded using the Node Recorder [50][51][52] at the corresponding integration points. The dimensions of the element increase from the centre of the model to the lateral boundaries, in order to guarantee convergence and avoid problems of instability.
In order to reproduce the infinite domain of the real soil, lateral boundaries were modelled with the penalty method to reproduce transmitting boundary conditions. A tolerance of 10 −4 was chosen as a compromise; it is large enough to ensure strong constraint conditions without introducing instability problems [50][51][52]. Base boundaries (depth of 38 m) are considered elastic to allow wave filtering. The vertical direction for both the base and lateral boundaries was constrained. The longitudinal and transversal directions were unconstrained for the lateral boundaries (shear deformations) and constrained at the base of the mesh. The mesh was defined by considering the previous contributions and its performance was verified by comparing the accelerations at the top of the mesh with the free field. The water level was located at depth of 4 m below the surface, as the water profile was governed by a nearby canal.  In order to reproduce the infinite domain of the real soil, lateral boundaries were modelled with the penalty method to reproduce transmitting boundary conditions. A tolerance of 10 −4 was chosen as a compromise; it is large enough to ensure strong constraint conditions without introducing instability problems [50][51][52]. Base boundaries (depth of 38 m) are considered elastic to allow wave filtering. The vertical direction for both the base and lateral boundaries was constrained. The longitudinal and transversal directions were unconstrained for the lateral boundaries (shear deformations) and constrained at the base of the mesh. The mesh was defined by considering the previous contributions and its performance was verified by comparing the accelerations at the top of the mesh with the free field. The water level was located at depth of 4 m below the surface, as the water profile was governed by a nearby canal.

Soil Materials
In order to model a realistic case study, the characteristics of the soil layers were derived from the representative values in [58]. The considered layers are representative of the typical riverbank subsoil of the studied area. The layers were modelled herein with three cohesionless soil units (S1, S2, and S3, as described in Table 2) and a clayey soil, C. Such assumptions were necessary to implement a feasible numerical model inside OpenSeesPL. The soil materials were modelled following the u-p formulation (u is the displacement of the soil skeleton and p is the pore pressure) [59]. Several assumptions were applied: (1) small deformations and rotations; (2) the soil and water densities remain constant in both time and space; (3) porosity was considered homogeneous and constant with time; (4) incompressibility of the soil grains; and (5) equal accelerations for the soil and water [41]. The sand layers (named S1, S2, S3) were defined with the PressureDependMultiYield model (PDMY) [49,50], based on the multi-yield-surface plasticity framework by [60]. This model reproduces the mechanism of cycle-by-cycle permanent shear strain accumulation in clean sands ( Figure 2). The model was calibrated to the response of Nevada sand (at a relative density of approximately 40%) and under situations of liquefaction and lateral spreading [49]. The PDMY model applied conical-shaped yield surfaces with the common apex at the origin of principal stress space and describes the volumetric dilatation and contraction (under shear deformations) with a non-associative flow rule ( Figure 2). Table 2 shows the adopted parameters: low-strain shear modulus and friction angle, shear wave velocities, permeability and the parameters that control the contraction (c1), dilatancy (d1 and d2), and the level of liquefaction-induced yield strain (l1, l2, and l3). Figure 3 shows the backbone curves for all the selected sand models. In particular, contraction and dilatancy parameters define the rate of shear-induced volumetric decrease (contraction) or increase (dilatancy). Larger values correspond to faster rates, with a more detailed discussion found in [48].        Backbone curves S1 S2 S3 Figure 3. Backbone curves for soils S1, S2, and S3.
Material properties of the clay soil (called soil C) were defined with the PressureInde-pendMultiYield (PIMY) model [56,57] and consist of a non-linear hysteretic material based on a Von Mises multi-surface kinematic plasticity and an associate flow rule ( Figure 4). This model captures both monotonic and hysteretic elastoplastic cyclic response by assuming that the shear behaviour is insensitive to confining stress. Plasticity is exhibited in the deviatoric stress-strain response and the volumetric response is linear-elastic. Table 3 shows the values used for this material, and Figure 5 shows the backbone curves for the C model. The number of yield surfaces is equal to 20 for all soil models.

Non-Linear Analyses
The highly non-linear analyses were divided into four subsequent sub-steps in order to solve the convergence issues by separating the various sources of numerical instability. The first two steps consider the loading of the soil mesh, and linear properties (weight, shear, and bulk moduli) were considered: step (1) the weight of the soil only (with no water) was applied; step (2) the water was introduced. In step 3 the properties were changed from elastic to plastic by applying 25 load steps to reach convergence. Step 4 consisted of the dynamic analysis itself, and the NewtonLineSearch algorithm [57] was used. Numerical damping was applied to avoid high frequency components that can cause instability, since the system has a large degree-of-freedom and nonlinear material behaviour. The Newmark transient integrator (γ = 0.6 and β = 0.3) was used. In addition, energy dissipation at low deformation levels was considered by applying Rayleigh

Non-Linear Analyses
The highly non-linear analyses were divided into four subsequent sub-steps in order to solve the convergence issues by separating the various sources of numerical instability. The first two steps consider the loading of the soil mesh, and linear properties (weight, shear, and bulk moduli) were considered: step (1) the weight of the soil only (with no water) was applied; step (2) the water was introduced. In step 3 the properties were changed from elastic to plastic by applying 25 load steps to reach convergence.
Step 4 consisted of the dynamic analysis itself, and the NewtonLineSearch algorithm [57] was used. Numerical damping was applied to avoid high frequency components that can cause instability, since the system has a large degree-of-freedom and nonlinear material behaviour. The Newmark transient integrator (γ = 0.6 and β = 0.3) was used. In addition, energy dissipation at low deformation levels was considered by applying Rayleigh damping as calculated in [61,62]. The damping was set up equal to 2% and proportional to stiffness and mass (at 1 and 6 Hz), corresponding to mass-proportional and stiffness proportional coefficients of 0.12542 and 0.00090946, respectively.

Parametric Studies
Several input motions were selected by varying the characteristics of the loading factors (intensity, duration, and frequency) as detailed in Tables 4-6, in order to study the effects of various input motions on liquefaction-induced effects on the soil. Three parametric studies have been performed.  (1) PS1: the objective is to assess the role of the number of cycles of the input motion on the liquefaction-induced effects. The number of cycles of a sinusoidal motion (1 Hz frequency and 0.2 g amplitude) were considered: 25, 20, 10, and 5 as described in Table 4. (2) PS2: the objective is to assess the role of the frequency of the input motion. The frequency of a sinusoidal motion (35 s duration and 1 g amplitude) has been varied: 1 Hz, 2 Hz, 3 Hz, 4 Hz, and 5 Hz as shown in Table 5 (3) PS3: the objective is to assess the role of the amplitude. The amplitude of a sinusoidal motion (1 Hz frequency and 35 s duration) has been varied: 0.04 g, 0.08 g, 0.14 g, and 0.20 g as illustrated in Table 6.

Results and Discussion
As previously discussed, liquefaction analyses require complex computational formulations. In particular, the steady state of deformation defined as the locus point describing the relationship between the void ratio and the effective confining pressure is useful for identifying the conditions under which a particular soil may or may not be susceptible to liquefaction [63]. In order to discuss the results presented below, the pore pressure ratio (r u ) is considered herein. The definition of r u considers the pore pressure as a fraction of the vertical stress, as described in [11]. In particular, an r u value approaching 1 is generally considered to correspond to the onset of liquefaction. Although, in most practical cases, soils supporting infrastructure will likely fail prior to an r u of 1 as the effective stress, and thus the shear capacity of the soil, is greatly reduced.

Number of Cycles
As shown in [63], the effects of liquefaction-induced failures (such as lateral spreading) develop incrementally during the period of earthquake shaking and the number of shaking cycles required to produce said failure depends largely on the shear amplitude and soil density. Therefore, liquefaction failure may occur in only a few cycles in a loose soil subjected to large cyclic shear, while many cycles are needed for a dense soil. Historical earthquake records (i.e., Loma Prieta in 1989, Northridge in 1994, and Kobe in 1995) showed that there are many factors (and thus uncertainties) other than magnitude that are connected to duration [64].
Herein the importance of the number of cycles is assessed by performing several analyses with a different number of cycles and consequently duration (Table 4). Figure 6 shows the results for the parametric study, where the horizontal line represents r u = 1 and is assumed to be the point at which liquefaction occurs. If the number of cycles is less than 10 (input duration: 10 s), liquefaction does not occur. When the input motion is extended to 20 and 25 cycles (20 s and 25 s, respectively), the maximum r u reaches significant values . This finding demonstrates that the longer the duration of an input motion of sufficient amplitude occurs, the higher the pore water pressure that accumulates inside the soil, confirming what is presented in [65], where the influence of duration on liquefaction potential was described as the possibility that pore water pressure may accumulate and thus liquefaction becomes more likely. In addition, [64] considered the duration of the shaking as proportional to the earthquake magnitude. Figure 7 represents the time histories of shear strain for 25 cycles (PS1- 25), showing that the increase in the deformation with time depends on the number of cycles. The linear trend observed aligns with data found in many centrifuge tests, e.g., [66,67].
Herein the importance of the number of cycles is assessed by performing several analyses with a different number of cycles and consequently duration (Table 4). Figure 6 shows the results for the parametric study, where the horizontal line represents ru = 1 and is assumed to be the point at which liquefaction occurs. If the number of cycles is less than 10 (input duration: 10 s), liquefaction does not occur. When the input motion is extended to 20 and 25 cycles (20 s and 25 s, respectively), the maximum ru reaches significant values of 1.51 and 1.61, for PS1-20 and PS1-25, respectively, as taken from a location 5 m deep in the centre of the mesh (i.e., 1 m below the water table). This finding demonstrates that the longer the duration of an input motion of sufficient amplitude occurs, the higher the pore water pressure that accumulates inside the soil, confirming what is presented in [65], where the influence of duration on liquefaction potential was described as the possibility that pore water pressure may accumulate and thus liquefaction becomes more likely. In addition, [64] considered the duration of the shaking as proportional to the earthquake magnitude. Figure 7 represents the time histories of shear strain for 25 cycles (PS1-25), showing that the increase in the deformation with time depends on the number of cycles. The linear trend observed aligns with data found in many centrifuge tests, e.g., [66,67].

Frequency
Frequency is the second factor that has been assessed via numerical modelling, keeping the number of cycles and acceleration the same (25 and 0.2 g, respectively), but changing the frequency from 1 Hz to 5 Hz. The influence of frequency on ru is shown in Figure  8

Frequency
Frequency is the second factor that has been assessed via numerical modelling, keeping the number of cycles and acceleration the same (25 and 0.2 g, respectively), but changing the frequency from 1 Hz to 5 Hz. The influence of frequency on r u is shown in Figure 8, which indicates that: (1) the development of pore pressure does not depend on the frequency for the range of 2-5 Hz; in fact the various trends are almost superposed on each other; (2) for 4 Hz and 5 Hz, the soil deposit does not liquefy completely because the performed number of cycles (25) does not subject the model to a significant duration, after which soil liquefaction may occur (the maximum r u values are 0.91 and 0.87, respectively, for 4 and 5 Hz); (3) for 3 Hz, liquefaction is observed at 8 s and the maximum value of r u is 1.04; (4) for frequencies 3 Hz, 2 Hz, and 1 Hz, r u reaches the maximum values of 1.05, 1.19, and 1.61, for PS2-3, PS2-2, and PS2-1, respectively; and (5) for 1 Hz, pore pressure increases slower than for the other frequencies, showing that there is a value of frequency at which pore pressures begin to increase at a higher rate. Figure 9 shows the time histories of shear strain for the most significant cases (PS2-1; PS2-2; PS2-3) in order to assess the role of frequency in the development of the pore pressure. The results confirm what was found in [38], where three series of tests varying the frequency of base shaking were carried out to demonstrate that the frequency of base shaking at which the sand starts to liquefy depends on the density of sand.

Amplitude
The original input motion characterized by a 0.20 g acceleration amplitude at a frequency of 1 Hz and 25 cycles, corresponding to 25 s, was then reduced in amplitude in order to study the effects of the maximum acceleration on the liquefaction-induced effects.

Amplitude
The original input motion characterized by a 0.20 g acceleration amplitude at a frequency of 1 Hz and 25 cycles, corresponding to 25 s, was then reduced in amplitude in order to study the effects of the maximum acceleration on the liquefaction-induced effects. From Figure 10, it is clearly observed that the soil response is substantially affected by the

Amplitude
The original input motion characterized by a 0.20 g acceleration amplitude at a frequency of 1 Hz and 25 cycles, corresponding to 25 s, was then reduced in amplitude in order to study the effects of the maximum acceleration on the liquefaction-induced effects. From Figure 10, it is clearly observed that the soil response is substantially affected by the variations in acceleration amplitude. For all the acceleration amplitudes less than 0.14 g, there were increases in r u without reaching the point at which liquefaction is considered to occur (maximum r u values: 0.86 and 0.75, respectively, for 0.08 g and 0.06 g), since their curves do not reach r u = 1. For an amplitude of 0.14 g, the buildup of pore pressure is slower than that for 0.20 g, and r u reaches a maximum value of 1.35 for PS3-014, compared with 1.61 for PS3-020. It is important to consider that the time to reach liquefaction (r u = 1) decreases as the amplitude increases, as shown in [38], which demonstrated the same outcome by performing shaking table tests. In particular, the authors concluded that acceleration amplitude is the most important cyclic loading parameter that controls liquefaction: the higher the acceleration, the smaller the number of cycles needed for liquefaction with higher pore water pressure developed at any stage. This finding is important because changes in the amplitude of the input motions can cause modifications in the generation of pore water pressure, demonstrating that liquefaction depends on the level of shear strength in the soil deposit. In particular, the amount of deformation (and thus the liquefaction-induced effects) depends on the difference between the soil shear strength and shear stress required for equilibrium [55]. Figure 11 compares the time histories of the shear stress for the most significant case studies (PS3-020, PS3-014, PS3-006), demonstrating that the amplitude is fundamental in the increase in the deformations inside the soil deposit. For case study PS3-014, Figure 10 shows a downward spike in pore pressure just after 2 s, which is manifested as a negative strain in Figure 11 at the same time. Similar results are often observed in centrifuge tests [65,66]. outcome by performing shaking table tests. In particular, the authors concluded that acceleration amplitude is the most important cyclic loading parameter that controls liquefaction: the higher the acceleration, the smaller the number of cycles needed for liquefaction with higher pore water pressure developed at any stage. This finding is important because changes in the amplitude of the input motions can cause modifications in the generation of pore water pressure, demonstrating that liquefaction depends on the level of shear strength in the soil deposit. In particular, the amount of deformation (and thus the liquefaction-induced effects) depends on the difference between the soil shear strength and shear stress required for equilibrium [55]. Figure 11 compares the time histories of the shear stress for the most significant case studies (PS3-020, PS3-014, PS3-006), demonstrating that the amplitude is fundamental in the increase in the deformations inside the soil deposit. For case study PS3-014, Figure 10 shows a downward spike in pore pressure just after 2 s, which is manifested as a negative strain in Figure 11 at the same time. Similar results are often observed in centrifuge tests [65,66].

Conclusions
The paper investigates the effects of loading factors on the development of pore pressure and consequently on the liquefaction-induced effects on a soil deposit. Three parametric studies have been performed that consider the number of cycles, frequency, and duration of the input motions, and several numerical models have been compared, with specific findings as summarized below: 1. The number of cycles has a profound impact on the pore water pressure generated, with longer duration sinusoidal input motions resulting in higher pressures. Further, a larger number of cycles increases the deformation of the soil and thus the shear strain accumulation. 2. The role of frequency may be significant in the development of pore pressure; however, this effect is non-linear and depends on the displacement of the input motion as well as the soil characteristics. In the parametric study performed here, there was a threshold frequency where the rate of pore pressure generation increased with frequency (i.e., from 1 to 2 Hz) as well as an observed trend in which the magnitude of the maximum ru decreased with frequency. 3. The soil response is substantially affected by variations in the acceleration amplitude.
For all the acceleration amplitudes less than 0.14 g, there were increases in ru without reaching the point at which liquefaction is considered to occur (maximum ru values: 0.86 and 0.75, respectively, for 0.08 g and 0.06 g), since their curves do not reach ru = 1. For an amplitude of 0.14 g, the buildup of pore pressure is slower than that for 0.20 g and ru reaches a maximum value of 1.35 for PS3-014, compared with 1.61 for PS3-020. It is important to note that the time to reach liquefaction (ru = 1) decreases as the amplitude increases.
The results have been discussed by considering the existing literature, and the effects of the loading factors have been analysed on a free-field model of a realistic soil deposit. In particular, the novelty of the work consists in proposing numerical models to represent the most common experimental studies. These two approaches (experiments and numerical simulations) may be used together to support and advance modelling as whole. The advanced non-linear analyses described in this paper have been performed with the state-

Conclusions
The paper investigates the effects of loading factors on the development of pore pressure and consequently on the liquefaction-induced effects on a soil deposit. Three parametric studies have been performed that consider the number of cycles, frequency, and duration of the input motions, and several numerical models have been compared, with specific findings as summarized below: 1.
The number of cycles has a profound impact on the pore water pressure generated, with longer duration sinusoidal input motions resulting in higher pressures. Further, a larger number of cycles increases the deformation of the soil and thus the shear strain accumulation.

2.
The role of frequency may be significant in the development of pore pressure; however, this effect is non-linear and depends on the displacement of the input motion as well as the soil characteristics. In the parametric study performed here, there was a threshold frequency where the rate of pore pressure generation increased with frequency (i.e., from 1 to 2 Hz) as well as an observed trend in which the magnitude of the maximum r u decreased with frequency.

3.
The soil response is substantially affected by variations in the acceleration amplitude. For all the acceleration amplitudes less than 0.14 g, there were increases in r u without reaching the point at which liquefaction is considered to occur (maximum r u values: 0.86 and 0.75, respectively, for 0.08 g and 0.06 g), since their curves do not reach r u = 1.
For an amplitude of 0.14 g, the buildup of pore pressure is slower than that for 0.20 g and r u reaches a maximum value of 1.35 for PS3-014, compared with 1.61 for PS3-020. It is important to note that the time to reach liquefaction (r u = 1) decreases as the amplitude increases.
The results have been discussed by considering the existing literature, and the effects of the loading factors have been analysed on a free-field model of a realistic soil deposit. In particular, the novelty of the work consists in proposing numerical models to represent the most common experimental studies. These two approaches (experiments and numerical simulations) may be used together to support and advance modelling as whole. The advanced non-linear analyses described in this paper have been performed with the state-of-the-art 3D finite elements OpenSeesPL that may consider the mechanisms of cycle mobility inside the soil that has been previously shown in the laboratory tests. The numerical models have been described in order to detail the various assumptions that have been considered to allow the study of the various performances in terms of pore pressure development inside the soil deposit. The most significant results have been discussed in terms of shear strain relationships. Overall, the paper demonstrates that soil liquefaction may significantly depend on the loading factors, and they need to be accounted for design purposes. Although the findings are limited to the performed conditions, they may potentially be useful to propose code provisions. To this end, further parametric numerical studies on the response of other soil deposits will be performed.