Effect of Nonlinear Constitutive Models on Seismic Site Response of Soft Reclaimed Soil Deposits

Abstract

This study investigates the impact of nonlinear constitutive models on one-dimensional seismic site response analysis (SRA) for soft, reclaimed soil deposits in Saemangeum, South Korea. Two widely used models, MKZ and GQ/H, were applied to three representative soil profiles using the DEEPSOIL program. Ground motions were scaled to bedrock peak ground accelerations (PGAs) corresponding to annual return periods (ARPs) of 1000, 2400, and 4800 years. Seismic response metrics include the ratio of GQ/H to MKZ shear strain, effective PGA (EPGA), and short- and long-term amplification factors (F_a and F_v). The results highlight the critical role of the site-to-motion period ratio (T_g/T_m) in controlling seismic behavior. Compared to the MKZ, the GQ/H model, which features strength correction and improved stiffness retention, predicts lower shear strains and higher surface spectral accelerations, particularly under strong shaking and shallow conditions. Model differences are most pronounced at low T_g/T_m values, where MKZ tends to underestimate amplification and overestimate strain due to its limited ability to reflect site-specific shear strength. Relative to code-based amplification factors, the GQ/H model yields lower short-term estimates, reflecting the disparity between stiff inland reference sites and the soft reclaimed conditions at Saemangeum. These findings emphasize the need for strength-calibrated constitutive models to improve the accuracy of site-specific seismic hazard assessments.

1. Introduction

Local site conditions play a critical role in modifying seismic wave propagation, significantly affecting both the intensity and frequency of ground shaking [1,2,3]. Even neighboring locations can experience markedly different levels of seismic demand due to site-specific effects [4,5]. To account for this, modern seismic design codes incorporate site amplification factors based on soil classification schemes [6,7,8].

Reclaimed ground, often composed of loosely deposited and relatively unconsolidated materials, tends to be less stable than naturally sedimented inland soils [9,10]. With the increasing development of major infrastructure on reclaimed land, particularly in coastal regions, assessing the seismic resilience of these areas has become a pressing engineering concern.

Although South Korea is generally categorized as a region of low to moderate seismicity [11,12], recent moderate-to-strong earthquakes in Gyeongju, as reported by Kim et al. [13] and Pohang, Woo et al. [14], have sparked increased interest in site-specific seismic hazard assessment. Prior studies have extensively examined inland soil profiles across the Korean Peninsula to quantify site amplification effects and inform seismic risk [11,12,15,16,17]. However, studies focused explicitly on reclaimed soils remain limited.

Yang et al. [10] evaluated nonlinear site effects on a reclaimed island using field and numerical data, reporting significant amplification under strong motion due to the nonlinear behavior of reclaimed soils. Noda et al. [9] analyzed seismic response in artificial reclaimed ground, emphasizing the risks of post-earthquake settlement. Choi [18] investigated the seismic stability of road embankments on reclaimed land, highlighting their susceptibility to dynamic instability. It was reported that reclaimed soils are highly susceptible to seismic instability, emphasizing the need for targeted mitigation strategies. Adewoyin et al. [19] conducted integrated geotechnical investigations near coastal reclaimed areas, stressing the need for reliable seismic evaluation. Seo and Won [20] used earthquake records from Pohang to show that reclaimed sites exhibit short-term spectral amplification, necessitating tailored seismic design. Similarly, Antomopoulos et al. [21] found that nonlinear soil behavior significantly affects the seismic performance of port structures on reclaimed land. Won et al. [22] investigated the seismic amplification characteristics of soft reclaimed ground using 1D nonlinear ground response analysis with spectrally matched input motions, identifying notable short-term de-amplification and proposing modified site-specific amplification factors that highlight the distinct seismic behavior of reclaimed soils compared to code-based assumptions. Beyond free-field ground response analyses, numerous studies [23,24,25,26,27] have explored the soil–structure interaction effects of coastal structures on reclaimed ground, highlighting the critical influence of site amplification and the unique dynamic characteristics of reclaimed profiles.

Despite this growing body of work, many studies overlook the pronounced nonlinear behavior of the soft soil layers typically found in reclaimed profiles. These layers can experience large shear strains (3–10%) during seismic events [28]. At the same time, conventional modulus reduction and damping curves are generally calibrated for strains below 0.1%, which makes them insufficient for accurately capturing the high-strain response.

This study aims to investigate the influence of constitutive model selection on the seismic response of soft reclaimed soils with shallow bedrock using one-dimensional (1D) site response analysis (SRA) via the DEEPSOIL program [29]. Specifically, we compare the Modified Kondner-Zelasko (MKZ) model [30] and the General Quadratic/Hyperbolic (GQ/H) model (GQ/H) [31] models, which represent soil nonlinearity through distinct backbone curve formulations. Accurate SRA is essential for seismic design and is sensitive to the selected constitutive model.

Three (03) representative soil profiles were selected from Saemangeum reclaimed land, a major land reclamation project initiated in 1991 on Korea’s west coast. The project, protected by the world’s longest sea wall (34 km), covers approximately 400 km² and is intended for multi-sector development, including agriculture, urbanization, industry, and renewable energy [32,33,34]. Model parameters for each soil layer were calibrated using the Modulus Reduction and Damping Curve Fitting (MRDF) method based on reference G/G_max and damping (D) values. Nonlinear 1D SRA was performed using a suite of scaled input motions to assess model sensitivity. The results, including surface response spectra, shear strain distributions, and spectral accelerations, were compared to evaluate the differential impact of the MKZ and GQ/H models on seismic amplification behavior in soft reclaimed soils.

2. Soil Profiles

This study employed Suspension P-S Logging (SPS) test data from three representative soil profiles located in the reclaimed waterfront area of Saemangeum, South Korea. The stratigraphy at these sites comprises a sequence of reclaimed fill, alluvial soils, weathered rock, and soft rock. All three profiles fall under site class S₄, according to the Korean seismic design standard MOLIT [35], and exhibit shear wave velocity (V_s) profiles characteristic of soft ground conditions.

The site period T_g for the selected profiles ranges from 0.60 to 0.87 s, with bedrock depths (H) between 35.0 and 48.5 m. The bedrock horizon was defined following MOLIT criteria, where V_s > 760 m/s marks the seismic bedrock. The average shear wave velocity in the upper 30 m (V_s30), used in site classification, further confirms the soft soil nature of the profiles (ranging from 186 to 215 m/s). Figure 1 illustrates the V_s profiles, along with the corresponding stratigraphic layers, classified according to the Unified Soil Classification System (USCS). The legend is as follows: SM—Silty Sand; CL—Low-Plasticity Clay; ML—Low-Plasticity Silt; SP—Poorly Graded Sand; WR—Weathered Rock; and SR—Soft Rock.

To characterize soil strength, the Mohr–Coulomb failure criterion [36] was used to define the shear strength parameters as input parameters for the GQ/H constitutive model. The internal friction angle (φ) for each soil layer was estimated using the empirical correlation between corrected SPT blow count N₆₀ and φ, as proposed by Wolff [37].

Table 1. Summary of selected profiles.

Profile	H (m)	Vs,soil (m/s)	Tg (s)	Vs30 (m/s)	MOLIT (2018) [35]
P1	35	232	0.60	215	S4
P2	39	215	0.70	199
P3	48.5	220	0.87	186

summarizes the key characteristics of the soil profiles.

3. Input Ground Motions

Three earthquake ground motions were selected for this study to represent a range of spectral characteristics and to examine the effect of shear strength correction on seismic site response. Two of the records, Gyeongju and Pohang, were obtained from recent inland earthquakes in South Korea and sourced from the Korean Institute of Geoscience and Mineral Resources (KIGAM) database [38]. The third, a Parkfield earthquake record, was selected from the NGA-West2 database [39] providing a broader spectral representation with different source mechanisms.

The selected records were chosen to cover a range of mean spectral periods (Tₘ) from 0.146 to 0.473 s, allowing for the analysis of period-dependent amplification behavior. Figure 2 illustrates the acceleration response spectra of the input ground motions scaled to a bedrock peak ground acceleration (PGA) of 0.11, 0.16, and 0.21 g, which corresponds to 1000-, 2400-, and 4800-year annual return periods (ARPs).

All motions were linearly scaled to three intensity levels, 0.11 g, 0.16 g, and 0.21 g, reflecting seismic hazard levels derived from the Probabilistic Seismic Hazard Assessment (PSHA) maps of South Korea. These PGA values correspond to ARPs of 1000, 2400, and 4800 years, respectively, and were taken from the National Emergency Management Agency, NEMA [40].

Table 2. Summary of input ground motions.

Sr No.	Name	Magnitude	Mechanism	Rrup (km)	Tm (s)
EQ1	Gyeongju	5.54	Strike slip	13	0.146
EQ2	Pohang	5.4	Strike slip	30	0.473
EQ3	Park field	6.2	Reverse	42	0.411

summarizes the key parameters of the selected ground motions, including magnitude, rupture mechanism, closest distance to rupture (R_rup), and mean period (T_m).

4. One-Dimensional (1D) Site Response Analysis

In this study, a 1D nonlinear SRA was performed using DEEPSOIL to evaluate the seismic behavior of soft reclaimed ground. Two widely used constitutive models, the Modified Kondner–Zelasko (MKZ) and General Quadratic/Hyperbolic (GQ/H) models, were implemented to simulate the nonlinear soil response under seismic loading.

The reference dynamic soil properties were assigned based on established empirical models: Darendeli [41] for sands, Vucetic and Dobry [42] for clays, and Menq [43] for gravels. To simulate realistic hysteretic behavior during cyclic loading, non-Masing rules were applied, allowing for more accurate modeling of unloading and reloading paths within the stress–strain loop.

To ensure that the model parameters matched the target modulus reduction (G/G_max) and damping (D) curves for each soil layer, the Modulus Reduction and Damping Factor (MRDF) optimization technique developed by Phillips and Hashash [44] was employed. This iterative calibration method adjusts model parameters to minimize the discrepancies between measured and target curves. For small-strain damping behavior, Rayleigh damping coefficients were calculated based on the first and fifth mode frequencies, following the methodology proposed by Kwok et al. [45]. This approach helps distribute damping effects more realistically across the frequency range relevant to site response. Together, these modeling strategies ensured that both the nonlinearity and energy dissipation characteristics of the reclaimed soils were accurately captured in the 1D SRA model.

5. Background of Nonlinear Constitutive Models

The DEEPSOIL program provides several nonlinear constitutive models for simulating dynamic soil behavior through stress–strain relationships that incorporate hysteresis. This study focuses on two models: the Modified Kondner–Zelasko (MKZ) and the General Quadratic/Hyperbolic (GQ/H) models, each with distinct approaches to capturing soil nonlinearity and cyclic response.

5.1. MKZ Model

The MKZ model describes the shear stress–strain relationship using the following empirical Equation:

$$\tau ={\displaystyle \frac{G_o\gamma }{{1+\beta \left(\frac{\gamma }{{\gamma }_r}\right)}^s}}$$

(1)

where τ is the shear stress, γ is the shear strain, G₀ is the small-strain shear modulus, γ_r is the reference strain, and β and s are fitting parameters. The reference strain γ_r is stress-dependent and calculated as follows:

$${\gamma }_r={\left({\displaystyle \frac{{\sigma }^{\prime } }{{\sigma }_{ref}}}\right)}^b$$

(2)

where, σ^′ is the effective vertical stress, ${\sigma }_{ref}$ is the reference stress, and b is empirical exponent. While the MKZ model reliably represents small-strain stiffness degradation, it lacks strength correction mechanisms, which can result in the under-prediction of shear strength at large strains and limited accuracy in high-strain regimes.

5.2. GQ/H Model

The GQ/H model extends the MKZ framework by incorporating both modulus reduction and ultimate shear strength behavior. The backbone curve is defined as follows:

$$\tau ={\tau }_{max} \ast \left[{\displaystyle \frac{1}{{\theta }_r}}\left\{1+\left({\displaystyle \frac{\gamma }{{\gamma }_r}}\right)-\sqrt{{\left\{1+{\displaystyle \frac{\gamma }{{\gamma }_r}}\right\}}^2-4 {\ast \theta }_{\tau } \ast {\displaystyle \frac{\gamma }{{\gamma }_r}}}\right\}\right]$$

(3)

where ${\tau }_{max}$ is the maximum shear stress, and θ_τ is a curve-fitting parameter. The parameter θ_τ varies with strain level and is defined as follows:

$${\theta }_{\tau }={\theta }_1+{\theta }_1 \ast {\displaystyle \frac{{\theta }_4 \ast {\left(\frac{\gamma }{{\gamma }_r}\right)}^{{\theta }_5}}{{{{\theta }_4}^{{\theta }_5}+\theta }_4 \ast {\left(\frac{\gamma }{{\gamma }_r}\right)}^{{\theta }_5}}}$$

(4)

To improve the fit to both modulus reduction and damping behavior, DEEPSOIL applies the MRDF method [44]. The correction factor $F\left({\gamma }_{max}\right)$ is expressed as follows:

$$F\left({\gamma }_{max}\right)=P_1-P_2 \ast {\left(1-{\displaystyle \frac{G{\gamma }_{max}}{G}}\right)}^{P_3}$$

(5)

where G (${\gamma }_{max}$) is the secant shear modulus at strain amplitude ${\gamma }_{max}$, $G_o$ is the initial shear modulus, and P1, P2, and P3 are empirical fitting parameters.

5.3. Hysteresis and Reversal Behavior

The GQ/H model also defines a detailed hysteresis formulation to capture unloading and reloading paths, improving the simulation of cyclic strain accumulation. The hysteretic stress response is given by

$$\begin{gathered} \tau =F\left({\gamma }_{max}\right)\left[-{\displaystyle \frac{{\tau }_{max}}{{\theta }_{\tau }}}\left\{1+{\displaystyle \frac{\gamma -{\gamma }_{rev}}{2{\gamma }_r}}\right\}-\sqrt[ ]{{\left[1+\left({\displaystyle \frac{\gamma -{\gamma }_{rev}}{2{\gamma }_r}}\right) \right]}^2-4 \ast {\theta }_r\left({\displaystyle \frac{\gamma -{\gamma }_{rev}}{2{\gamma }_r}}\right)}- \\ {G}_{\gamma max}\left(\gamma -{\gamma }_{rev}\right)\right]+G_{\gamma max}\left(\gamma -{\gamma }_{rev}\right)+{\tau }_{rev} \end{gathered}$$

(6)

where ${\gamma }_{rev}$ and ${\tau }_{rev}$ are the strain and stress at the reversal point and G (γ_max) is the tangent modulus at γ_max. This advanced hysteretic formulation enables the more accurate modeling of energy dissipation and precise prediction of cyclic response, particularly under strong ground motion conditions.

6. Results and Discussion

To evaluate the influence of constitutive model selection on seismic site response, the P1 profile was selected for detailed analysis. This site has a natural period of 0.60 s and a bedrock depth of 35 m, with an average shear wave velocity (V_s) of 232.3 m/s and a V_s30 value of 215 m/s. Figure 3 illustrates the depth-wise variation in implied shear strength for both the MKZ and GQ/H models. The GQ/H model consistently predicts higher shear strength values across the entire soil column, with the differences becoming particularly pronounced below 15 m. At greater depths, GQ/H estimates shear strengths up to 200 kPa, while MKZ predictions remain below 100 kPa.

To further understand this disparity, Figure 4 presents a comparison of model responses at a depth of 10 m. The shear stress–strain curves (Figure 4c) highlight the GQ/H model’s ability to capture the target shear strength due to its built-in strength correction mechanism. In contrast, the MKZ model lacks this mechanism, resulting in a significant underestimation of soil strength and a softer response throughout the entire strain range. The normalized modulus reduction curves (Figure 4a) show that GQ/H retains a higher shear modulus across a wide strain range, reflecting its stiffer behavior. Damping ratio curves (Figure 4b) indicate that while both models are similar at low strains, the GQ/H model predicts slightly higher damping at medium to large strains, more consistent with Darendeli’s reference curves. Overall, the GQ/H model more reliably captures the in situ strength, stiffness degradation, and damping behavior, and this pattern holds across other profiles (P2 and P3) as well.

Figure 5 and Figure 6 examine how these differences affect seismic response, focusing on the Gyeongju earthquake scaled to three intensity levels (0.11 g, 0.16 g, and 0.21 g). The surface response spectra, with an amplification ratio (AF) in Figure 5, show that the GQ/H model consistently results in higher peak spectral accelerations (PSA) and broader amplification bandwidths. These differences grow with increasing input intensity, highlighting how GQ/H’s higher implied strength limits nonlinear softening and allows more energy to reach the surface. In contrast, the MKZ model overestimates stiffness degradation and damping, resulting in reduced spectral accelerations.

Figure 6 shows the distribution of maximum shear strain and peak ground acceleration (PGA) with depth for profile P1. The GQ/H model produces significantly lower shear strains throughout the profile, particularly within the top 20 m, indicating its higher resistance to deformation under seismic loading. The MKZ model, constrained by its lower strength, yields elevated strain concentrations near the surface. The PGA profiles reveal that GQ/H transmits more acceleration upward, while MKZ exhibits attenuation due to its weaker response. These findings reinforce the importance of incorporating strength-corrected models, such as GQ/H, in site response analysis, especially under strong ground shaking.

To generalize these observations, Figure 7 compares key ground response parameters across all site profiles and input motions. Each plot is color-coded by the T_g/T_m ratio (site period to ground-motion period), which serves as an index for nonlinear behavior. In Figure 7a, MKZ consistently predicts higher maximum shear strains, particularly at low T_g/T_m ratios (shallow soil conditions), where nonlinear effects are dominant. These results underscore MKZ’s tendency to over-predict deformation due to its limited ability to reflect site-specific strength. Figure 7b shows that the MKZ model predicts a lower effective PGA (EPGA) than GQ/H, particularly when T_g/T_m is below 2. This again reflects MKZ’s higher energy dissipation via nonlinear damping.

Seismic amplification factors (F_a and F_v) were calculated as the ratios of spectral accelerations over defined periods of time. Specifically, F_a represents short-term behavior (0.1–0.4 s), while F_v reflects mid-to-long-term response (0.4–1.5 s). Figure 7c,d reveal similar trends for the amplification factors F_a and F_v: MKZ consistently under-predicts amplification, especially at high shaking intensities and low T_g/T_m values. GQ/H maintains a more realistic response, resisting stiffness loss and preserving spectral content, particularly in the short-term range.

These trends are further quantified in Figure 8, which plots the ratio of GQ/H to MKZ predictions as a function of T_g/T_m. For EPGA (Figure 8a), the ratio exceeds 1.1 for most cases with T_g/T_m < 2 and reaches values above 1.3 under high-intensity motions (0.21 g). At higher T_g/T_m values (T_g/T_m ≥ 4), the models converge, indicating more linear behavior. Similar trends are observed for F_a and F_v (Figure 8b,c), where GQ/H shows significantly higher amplification under shallow, nonlinear conditions. These results highlight a strong inverse relationship between T_g/T_m and model discrepancy, emphasizing the critical need for strength-calibrated models, such as GQ/H, when analyzing soft, shallow soil profiles.

Figure 9 compares the GQ/H model’s predicted amplification factors to those specified in the MOLIT (2018) [35] seismic code. The GQ/H model consistently predicts lower values, especially in the short-term range. The reductions in F_a are substantial, ranging from 35.7% at 0.11 g to 39.8% at 0.16 g and up to 43.9% at 0.21 g. The differences in F_v are more moderate, ranging from 8.6% to 11.8%. This discrepancy can be attributed to the contrasting site conditions—MOLIT values are derived from stiff inland soil profiles, whereas the current study focuses on soft, reclaimed ground. These findings further support the use of site-specific models in design and suggest that existing code provisions may be overly conservative for soft soil conditions.

In summary, based on the cases analyzed, and in the absence of direct validation against measured data, the GQ/H model exhibited more consistent behavior than MKZ in simulating the nonlinear response of reclaimed soils, particularly in capturing realistic maximum shear strains. Its ability to match target shear strength, maintain higher stiffness, and produce more realistic amplification responses underlines its value in modern seismic design. These results advocate for the integration of advanced, strength-consistent models in site response analysis and seismic code development.

This study acknowledges limitations, particularly the lack of validation against measured surface motion recordings for shallow-bedrock reclaimed sites in regions of moderate to low seismicity. To address this, future research is warranted to conduct physical tests, such as 1 g shaking table and centrifuge tests, which can simulate shallow bedrock site profiles and enable a more rigorous validation of the MKZ and GQ/H constitutive models. This study utilized two regionally recorded ground motions and one PEER NGA-WEST2 record; however, future studies should incorporate a broader range of input ground motions to validate and generalize the findings. Expanding the dataset would enable a more comprehensive evaluation of model performance under varying seismic conditions. Furthermore, although a 1D site response analysis was adopted in this study, previous research [46,47,48,49,50] has shown that such models may not sufficiently capture lateral heterogeneity, basin edge effects, and complex wave propagation [49,51,52]. To overcome these limitations, future studies should incorporate advanced 2D and 3D modeling approaches that more accurately represent topographic variations, impedance contrasts, and other site-specific features, particularly in reclaimed ground conditions.

7. Conclusions

This study presented a comprehensive comparison between the MKZ and GQ/H constitutive models in one-dimensional (1D) seismic site response analysis (SRA) for soft, reclaimed soils. The results provide key insights into how model selection affects predicted ground motion amplification and nonlinear soil behavior.

• The GQ/H model, which incorporates site-specific shear strength correction, offers a more accurate representation of stiffness degradation and nonlinear behavior. In contrast, the MKZ model, lacking strength calibration, consistently over-predicts shear strain and underestimates stiffness under strong shaking.
• The T_g/T_m ratio (site period to ground motion period) plays a critical role in amplifying model differences. At low T_g/T_m, the MKZ model significantly underestimates spectral amplification and overestimates deformation, highlighting the need for strength-adjusted modeling in shallow, soft profiles.
• Across varying input intensities, the GQ/H model consistently predicts higher short-term amplification factors (F_a) and effective peak ground accelerations (EPGAs) than the MKZ model. This suggests that traditional models, such as MKZ, may non-conservatively underestimate seismic demand, particularly under strong motions.
• When compared with amplification factors from the MOLIT (2018) [35] seismic code, the GQ/H model predicts significantly lower F_a values, by approximately 35.7% at 0.11 g, 39.8% at 0.16 g, and up to 43.9% at 0.21 g. These reductions are most evident in the short-term range, reflecting the limitations of code values derived from stiff inland soil profiles when applied to soft, reclaimed ground.

These findings underscore the importance of using strength-consistent nonlinear constitutive models, such as GQ/H, for site-specific seismic analysis, particularly in shallow, soft soil conditions. Incorporating such models can improve the balance between safety and economy in seismic design. The study further advocates for the re-evaluation of code-based amplification factors to reflect intensity- and period-dependent nonlinear soil behavior.