Undrained Shear Properties of Shallow Clayey-Silty Sediments in the Shenhu Area of South China Sea

Abstract

Suction piles are used to ensure wellhead stability during natural gas hydrate production in the Shenhu area of the South China Sea (SCS). Undrained shear properties of clayey-silty sediments play a critical role in the stability analysis of suction piles. However, it has not been fully studied. This study conducts a series of undrained triaxial shear tests on shallow clayey-silty sediments in the Shenhu area of SCS, and stress–strain curves under different overconsolidation ratio (OCR) conditions are obtained. OCR effects on undrained shear properties of clayey-silty sediments are discussed, and a model to predict the pore pressure coefficient at failure is proposed. Results show that the isotropic compression index is 0.175, and the isotropic swelling index is 0.029. The undrained shear strength is proportional to the effective confining pressure, and the proportionality coefficient is 0.42 for normally consolidated specimens, while the undrained shear strength of OC specimens nonlinearly increases with OCRs increasing. The proposed model aptly predicts the pore pressure coefficient at the failure of clayey-silty sediments of SCS with different OCRs.

1. Introduction

Natural gas hydrate (NGH) has great potential to become a major energy source in the future due to its vast reserve in nature [1], and more than 90% of the reserve is distributed in clayey-silty marine sediments [2,3,4]. In the north continental margin of the South China Sea (SCS), two in situ production trials have been performed, and results show that the depressurization method is technically feasible to exploit methane gas from hydrate-bearing clayey-silty sediments [5,6]. During the second production trial, potential risks of sinking and overturning of the wellheads are counteracted by embedding two types of suction piles [5]. Suction piles, which can also be deployed as deep mooring anchors and foundations for subsea infrastructure, penetrate the overlying strata for installation [7]. The sediments within the installed piles or anchors are normally considered to be remolded and would reconsolidate with time after installation [8]. Since it is well known that changes in porosities due to consolidation obviously affects the shear strength of unconsolidated sediments [9], the resultant changes in undrained shear strength (hereafter $S_u$) are required to access the stability of suction piles for various submarine engineering projects [10,11].

To date, a series of triaxial shear tests have been carried out to understand how the mechanical behaviors of hydrate-bearing clayey-silty sediments from SCS evolve during hydrate production [12,13,14,15,16]. Porosities of the host sediments remolded in those tests mainly range from 0.4 to 0.45, which represents porosities of sediments within the gas hydrate stability zone (GHSZ), and the bottom boundary of GHSZ in nature is generally hundreds of meters below the seabed [17,18]. The overlying strata, which are just below the seabed, can barely have low porosities, largely due to the weak consolidation stress [19]. However, the undrained shear strength of clayey-silty sediments from SCS with relatively high porosities has not been fully studied.

In nature, marine sediments tend to be overconsolidated due to various events in the consolidation history [8,11,13]. The degree of overconsolidation is widely quantified by using an indicator named the overconsolidation ratio (OCR), which is defined as the ratio of the preconsolidation pressure $p_{\mathrm{oc}}^{\prime }$ over the present effective stress $p_0^{\prime }$ applied on the sediments (i.e., $\mathrm{OCR}=p_{\mathrm{oc}}^{\prime }/p_0^{\prime }$) [11]. Research shows that OCR has significant impacts on the mechanical properties of marine sediments [20,21,22,23]. For example, overconsolidated (OC) samples with values of OCR larger than the unit show strain-softening and shear-dilation behaviors, while normally consolidated (NC) samples with OCR equal to the unit exhibit strain-hardening and shear-shrinkage behaviors [22]. In addition, NC samples and OC samples with values of OCR smaller than ~4 normally generate positive excess pore water pressures during undrained shearing, while OC samples with values of OCR larger than ~4 generally produce negative excess pore water pressures [22]. This implies that OCR affects the undrained shear strength of marine clayey-silty sediments through the excess pore water pressure developed during undrained shearing.

Since field measurements of pore water pressure within the deep-sea sediments are technically difficult and require high costs, aptly predicting how pore water pressure evolves during undrained shearing (e.g., suction pile penetration into or uplift from marine clayey-silty sediments) is of great significance to ocean engineering design. The prediction of pore water pressures in the field widely adopts Skempton’s Pore Pressure Parameters $A$ and $B$, also known as pore pressure coefficients, which characterize the change in pore water pressure induced by a change in applied stress [24]. The parameter $A$ at failure (hereafter $A_f$) is inherently linked to $S_u$, and a formula describing the relation between $A_f$ and $S_u/p_0^{\prime }$ has been proposed for NC sediments [22,25,26]. However, the effects of OCR on the undrained shear strength of remolded clayey-silty sediments from SCS remain elusive, and the OCR effects have not been included in the $A_f$ and $S_u/p_0^{\prime }$ formula.

Overall, since the undrained shear properties of clayey-silty sediments in the Shenhu area of SCS have not been fully studied, this study conducts a series of consolidated undrained (CU) triaxial shear tests on remolded clayey-silty specimens sampling from the overlying strata in the Shenhu area of SCS. Undrained shear behaviors varying with effective confining pressures and OCRs are analyzed in detail. Based on the relation between $S_u/p_0^{\prime }$ and OCR, a model is developed to predict the $A_f$ of clayey-silty sediments from SCS. These results aim to provide a reasonable evaluation of undrained shear strength for the geotechnical design and engineering of NGH production.

2. Materials and Methods

2.1. Test Materials

The clayey-silty sample used in this study is drilled into the Shenhu area of SCS provided by the Qingdao Institute of Marine Geology, and the burial depth is smaller than 2 m. The specific gravity $G_s$ of the sample is 2.55. The particle size distribution of the sample measured by the laser diffractometry method is shown in Figure 1, and the median particle size $d_{50}$ is 13.9 μm. The nonuniformity coefficient $C_u$ is 5.82 with a curvature coefficient $C_c$ of 0.75, and thereby test samples are poorly graded. In contrast to coarse-grained sediments [27,28], the water content limits of fine-grained sediments are also important basic properties. According to the Chinese Standard for Soil Test Methods (GB/T50123-2019) [29], the liquid and plastic limits of the sample are measured to be 67% and 37.6%, respectively.

2.2. Test Procedure and Method

2.2.1. Test Specimen Preparation

The procedure used to prepare test specimens was in accordance with ASTM D4767 [30], and a brief introduction is as follows: Firstly, the clayey-silty sample was air-dried for one month, and the air-dried sample was well mixed with a certain weight of de-aired water to obtain an initial water content of 15% by weight. Then, the moist sample was sealed and cured in a bag for at least 16 h. After that, the moist sample was compacted into a split mold with a diameter of 38 mm and a height of 76 mm layer by layer (i.e., 5 layers in total), and the top of each layer was scarified prior to the addition of the next layer. The porosity of remolded specimens was controlled to be 0.60 ± 0.006 (the void ratio $e$ = 1.5 ± 0.04), which is well within the porosity range of sediments in the overlying strata of SCS [31,32]. Finally, the specimen was carefully removed from the mold, covered with a rubber membrane, and placed in a triaxial cell.

2.2.2. Consolidation and Undrained Shear

All the remolded specimens were saturated at a back pressure of 900 kPa with an effective confining pressure of 30 kPa until the value of B (i.e., the increase in pore water pressure divided by that of the total confining pressure) was larger than 0.95. Both back pressure and confining pressure were applied with a loading rate of 1 kPa/min. Then, the specimens were isotropically consolidated under different effective confining pressures to simulate conditions of $p_{\mathrm{oc}}^{\prime }$= 100 kPa, 200 kPa, 400 kPa, and 600 kPa. The effective confining pressure was increased stepwise with 100 kPa to the desired value. The consolidation procedure continued until the volumetric change was less than 1 mm³/h. After that, four consolidated specimens were directly sheared to explore the undrained shear responses of NC specimens, and three OC specimens with OCR values of 2, 4, and 6 were sheared after a decrease in effective confining pressure to 100 kPa. The undrained shearing rate was 0.04%/min. The test was terminated when the peak deviatoric stress occurred or the axial strain reached 20% for the case with no peak deviatoric stress observed. The water content $w$ of specimens after shearing was measured according to ASTM D2216 [33], and the measured values were further used to calculate void ratios in terms of $e=G_s\cdot w$.

In this study, effective confining pressures of 100 kPa and 200 kPa were selected to represent the in situ effective stress condition of the overlying strata with a depth of ~10 m below sea floor (mbsf), generally consistent with the final penetration depth of suction piles used in the second production trial in SCS [5,7]. The larger effective confining pressures represent the preconsolidation pressures corresponding to different OCRs. In addition, the effective confining pressure during undrained shearing is the present effective stress $p_0^{\prime }$ according to the definition.

2.2.3. Method to Predict the Pore Pressure Coefficient at Failure ${\mathrm{A}}_{\mathrm{f} }$

In undrained triaxial shear tests, the relationship between the excess pore water pressure $\mathsf{\Delta }u$ and the stress state can be formulated as [24]:

$$\mathsf{\Delta }u=B\left[\mathsf{\Delta }{\sigma }_3+A\left(\mathsf{\Delta }{\sigma }_1-\mathsf{\Delta }{\sigma }_3\right)\right]$$

(1)

where $\mathsf{\Delta }{\sigma }_1$ and $\mathsf{\Delta }{\sigma }_3$ are increments of the major and minor total principal stresses, respectively. The pore pressure coefficient $B$ is defined as:

$$B=\frac{\mathsf{\Delta }u}{\mathsf{\Delta }{\sigma }_3}$$

(2)

For saturated specimens, the value of $B$ theoretically equals the unit, and Equation (1) can be simplified as:

$$A=\frac{\mathsf{\Delta }u}{\mathsf{\Delta }\left({\sigma }_1-{\sigma }_3\right)}$$

(3)

According to Equation (3), the pore pressure coefficient at failure $A_f$ is defined as:

$$A_f=\frac{\mathsf{\Delta }{u}_f}{\mathsf{\Delta }{\left({\sigma }_1-{\sigma }_3\right)}_f}$$

(4)

where $\mathsf{\Delta }{\left({\sigma }_1-{\sigma }_3\right)}_f$ is the principal stress difference at failure and $\mathsf{\Delta }{u}_f$ is the excess pore water pressure at failure.

In addition, the Mohr–Coulomb failure criterion is written as [9]:

$$\frac{1}{2}\left({\sigma }_1^{\prime }-{\sigma }_3^{\prime }\right)-\frac{1}{2}\left({\sigma }_1^{\prime }+{\sigma }_3^{\prime }\right)\sin {\phi }^{\prime }-c^{\prime }\cos {\phi }^{\prime }=0$$

(5)

where ${\phi }^{\prime }$ is the effective friction angle, and $c^{\prime }$ is the effective cohesion. Combining Equation (5) with Equation (4), the normalized undrained strength $S_u/p_0^{\prime }$ can be expressed as [26]:

$$\frac{S_u}{p_0^{\prime }}=\frac{\sin {\phi }^{\prime }+\frac{c^{\prime }}{p_0^{\prime }}\cos {\phi }^{\prime }}{1+\left(2A_f-1\right)\sin {\phi }^{\prime }}$$

(6)

To visualize Equation (6), the stress state of sediments at failure is shown in Figure 2. The solid-line circle is the effective stress Mohr circle, and the dashed-line circle is the total stress Mohr circle. The failure of the sediments occurs once the effective stress Mohr circle touches the failure line (FL). According to the effective stress principle [34], the distance between the total and effective Mohr circles is equal to the value of $\mathsf{\Delta }{u}_f$. Undrained shear strength $S_u$ can be depicted by the radius of the Mohr circle (i.e., $\mathsf{\Delta }{\left({\sigma }_1-{\sigma }_3\right)}_f/2$). The effective confining pressure $p_0^{\prime }$ is equal to the initial minor principal stress ${\sigma }_{30}$ for sediments under isotropic consolidation with initial major principal stress ${\sigma }_{10}$ = 0.

Finally, the pore pressure coefficient at failure $A_f$ can be predicted as [22]:

$$A_f=\left(1-\frac{1}{\sin {\phi }^{\prime }}\right)+\frac{1}{2\left(S_u/p_0^{\prime }\right)}+\frac{\left(c^{\prime }/p_0^{\prime }\right)\cot {\phi }^{\prime }}{2\left(S_u/p_0^{\prime }\right)}$$

(7)

where the value of ${\phi }^{\prime }$ is generally unchanged, and $c^{\prime }/p_0^{\prime }$ values of remolded specimens are normally so small that they can be ignored [22,35]. Values of $S_u/p_0^{\prime }$ are dependent on values of OCR [23,36].

3. Results

3.1. Isotropic Loading and Unloading Characteristics

The volume-change characteristics of statured clayey-silty sediments corresponding to effective consolidation stresses are key indices for the geotechnical design (e.g., stability and deformation problems) and important inputs for the numerical simulation (e.g., the Cam-clay model [9]). Figure 3 shows evolutions of the void ratio e of the specimens during isotropic loading and unloading in a semi-logarithmic coordinate. Since the specimen has no volume change, the void ratio is constant during undrained shearing. The solid lines denote the normally consolidated line (NCL) and the critical state line (CSL). NCL is related to the volumetric response under isotropic compression loading, whereas CSL is corresponding to the volume of specimens at a critical state (CS). The slope of NCL is the isotropic compression index $\lambda$, and that of CSL is the isotropic compression index at a critical state ${\lambda }_{\mathrm{cs}}$. Although values of ${\lambda }_{\mathrm{cs}}$ and $\lambda$ in Figure 3 are slightly different, NCL is approximately parallel to CSL which is in accordance with the critical state soil mechanics [9]. The dashed line is the swelling curve, and its slope is the isotropic swelling index $\kappa$ with a value of 0.029 in this study.

3.2. Normalized Undrained Shear Strength and Mohr-Coulomb Strength Parameters for NC Specimens

Figure 4 shows the stress–strain curves of NC and OC specimens. The failure point is marked by a star point. The failure of specimens is defined as deviatoric stress q attained at maximum or q at 15 % axial strain, whichever is obtained first during a test. Both increasing $p_0^{\prime }$ and OCR can reduce the porosity of specimens leading to enhancing the shear strength. In Figure 4a, the value of deviatoric stress at failure $q_f$ increases with increasing $p_0^{\prime }$, and values of $q_f$ are 95.21 kPa, 189.54 kPa, 295.36 kPa, and 449.36 kPa for $p_0^{\prime }$= 100 kPa, 200 kPa, 400 kPa, and 600 kPa, respectively. As shown in Figure 4b, the $q_f$ of OC specimens obviously increases with increasing OCR. In addition, the $q_f$ of OC specimen with OCR = 4 is 272.62 kPa, which is approximately equal to that of the NC specimen at $p_0^{\prime }$ = 400 kPa. It also can be seen in Figure 3 that the $e$ of the OC specimen with OCR = 4 is approximately equal to that of the NC specimen at $p_0^{\prime }=400 \mathrm{kPa}$. This finding infers that there is a corresponding relationship between $q_f$ and e for saturated clayey-silty sediments [37], which is consistent with previous results [9].

Relationships between undrained shear strength $S_u$ and effective confining pressure $p_0^{\prime }$ for NC specimens are plotted in Figure 5. The values of $S_u$ are proportional to that of $p_0^{\prime }$ as shown in Figure 5a, and the red fitting line can be described as:

$$S_u/p_0^{\prime }=0.42\pm 0.05$$

(8)

As shown in Figure 5b, the Mohr–Coulomb strength parameters can be obtained from the FL, in which ${\phi }^{\prime }=31.44°$ and $c^{\prime }$ = 6.93 kPa. Although ${\phi }^{\prime }$ is consistent with previous undrained shear tests results of clayey-silty sediments (i.e., ${\phi }^{\prime }=30.96°$), $c^{\prime }$ is far less than the previous result with $c^{\prime }$ of 70 kPa [38]. This difference could be attributed to the initial porosity of specimens in which 0.6 is selected in this study while ~0.45 is used in the study of Wang et al. [38].

The published results of the $S_u/p_0^{\prime }$ of NC clayey-silty sediments in other hydrate reservoirs obtained via CU tests are summarized in

Table 1. $S_u/p_0^{\prime }$ of clayey-silty sediments in other hydrate reservoirs.

Location	Test Condition	${\mathit{S}}_{\mathit{u}}/{\mathit{p}}_0^{\prime }$	${\mathit{\phi }}^{\prime }$	$\mathit{\alpha }$	Reference
Krishna-Godavari Basin, India	CU tests	0.31–0.4	25°	0.67–0.95	Priest et al. (2019) [40]
Krishna-Godavari Basin, India	CU tests	0.25	24°	0.61	Yoneda et al. (2019) [41]
Krishna-Godavari Basin, India	CU tests	0.27–0.43	21°–31°	0.65–0.86	Winters et al. (2014) [43]
Nankai Trough, Japan	CU tests	0.42	Not available	/	Priest et al. (2015) [42]
Nankai Trough, Japan	CU tests	0.29	34°	0.52	Yoneda et al. (2017) [39]
Shenhu Area, China	CU tests	0.39–0.43	31°	0.76–0.84	Wang et al. (2021) [38]

[38,39,40,41,42,43]. It can be seen that an average value of $S_u/p_0^{\prime }$ of 0.42 in this study is slightly different to certain published results but well within the overall range of published results (i.e., 0.25–0.43), especially for the results of Wang et al. [38] using similar test samples collected from SCS.

The relationships between $S_u/p_0^{\prime }$ and $\sin {\phi }^{\prime }$ are plotted in Figure 6. It is obvious that there is a linear trend, which can be described as [23]:

$$S_u/p_0^{\prime }=\alpha \sin {\phi }^{\prime }$$

(9)

where $\alpha$ is the empirical parameter. Since ${\phi }^{\prime }$ reflects the internal friction within sediments, $\alpha$ characterizes the effects of the intrinsic property of sediments (e.g., mineral component and particle size distribution) on $S_u/p_0^{\prime }$.

In this study, $\alpha$ is equal to ~0.8. In addition, the test results are mostly located between the scope of an $\alpha$ range from 0.65 to 0.95, which also can be seen in Table 1. However, the measured values of Yoneda et al. [39] are outside this scope. This is because the non-uniform deformation (i.e., shear banding or bottom failure) occurs during undrained tests leading to a resultant low shear strength [39]. Consequently, these findings infer that although values of $S_u/p_0^{\prime }$ differ between areas, the linear relationship shown in Equation (9) could be reasonably assumed for NC clayey-silty sediments of existing hydrate reservoirs.

3.3. Effects of OCR on $S_u/p_0^{\prime }$

According to critical state soil mechanics [9], the relationship between the normalized shear strength of NC specimens $S_u/p_0^{\prime }$ and that of OC specimens ${\left(S_u/p_0^{\prime }\right)}_{\mathrm{OC}}$ can be expressed as:

$$\frac{{\left(S_u/p_0^{\prime }\right)}_{\mathrm{OC}}}{S_u/p_0^{\prime }}={\mathrm{OCR}}^{\mathsf{\Lambda }}$$

(10)

where parameter $\mathsf{\Lambda }$ relates to changes in the $e$ of specimens during overconsolidation, which is equal to $\left(\lambda -\kappa \right)/\lambda$. In this study, $\mathsf{\Lambda }$ is calculated to be 0.83 according to $\lambda$ = 0.175 and $\kappa$ = 0.029, as shown in Figure 3. Combining Equation (9) with Equation (10), ${\left(S_u/p_0^{\prime }\right)}_{\mathrm{OC}}$ can be represented as:

$${\left(S_u/p_0^{\prime }\right)}_{\mathrm{OC}}=\alpha \sin {\phi }^{\prime }{\mathrm{OCR}}^{\mathsf{\Lambda }}$$

(11)

The experimental results of $S_u/p_0^{\prime }$ under different values of OCR are presented in Figure 7. It can be seen that $S_u/p_0^{\prime }$ increases non-linearly with increasing OCR, and $S_u/p_0^{\prime }$ = 0.96 for OCR = 2, $S_u/p_0^{\prime }$ = 1.36 for OCR = 4, and $S_u/p_0^{\prime }$ = 1.60 for OCR = 6. The red dashed line is drawn using Equation (11) with ${\phi }^{\prime }$ = 31.44$°$, $\mathsf{\Lambda }$ = 0.83, and α = 0.8 ± 0.15. Almost all of the experimental data fall within the range between the upper and lower limits.

3.4. Pore Water Pressure Responses

Figure 8 shows the excess pore water pressure response curves of NC and OC specimens. The pore pressure magnitudes are dependent on $p_0^{\prime }$ and OCR. As shown in Figure 8a, only positive pore pressure responses are observed for NC cases, which indicates that all tests show a contractive deformation behavior during shearing. As shown in Figure 8b, the excess pore water pressure response exhibits post-peak behaviors with OCRs increasing when the pore pressure at failure changes from positive with OCR = 2 to negative with OCR = 4. However, previous CU test results indicate that the negative pore pressure response tends to be generated only with OCRs greater than approximately 4 [22]. This infers that dilative deformation occurs in all the OC specimens, which is expected as all the scatters of OC specimens are below the CSL as shown in Figure 3.

According to the pore pressure responses, effective stress paths of NC and OC specimens can be plotted in Figure 9. The CSL is also plotted in each figure, of which the slope is 1.28. As shown in Figure 9a, it can be seen that all the specimens follow a typical effective path of NC sediments where the increasing q leads to an increase in pore pressure and a reluctant reduction in the $p^{\prime }$ until the specimen failure reaches the CSL. However, in Figure 9b, the effective paths of OC specimens first move above the CSL, accompanied by a decrease in pore pressure, and then drop back down, showing a typical effective path of OC sediments.

In general, the pore pressure response rarely causes dramatically post-peak behavior in the slightly OC specimen (i.e., OCR = 2), and its effective path would essentially not move above the CSL; as a result of that, a specimen with OCR = 2 would not exhibit significant dilative behavior [9]. Furthermore, the negative pore pressure response only appears until the accumulated dilatancy is greater than the total contractive deformation in the sediment during undrained shearing [44]. Mayne and Stewart [22] suggested that there is a critical value of OCR greater than ~4 dictating whether a negative pore pressure is generated in the OC specimen. In contrast, the test results show that the critical value in this study is less than this. Therefore, it is inferred that the clayey-silty sediments of SCS under OC conditions exhibit more dilative deformation during shearing than expected. Since the deformation response of sediments is related to its initial state [9], the OC specimens seem to undergo hardening due to secondary consolidation or thixotropy [8,45]. For example, the volume of the specimen with OCR = 2 is unexpectedly below the CSL as shown in Figure 3. There is one possible reason to explain this phenomenon attributed to the relatively high liquid limit and plasticity index of marine clayey-silty sediments. However, this finding requires further studies to benefit offshore exploitation infrastructure design.

4. Discussion

The conventional stability analysis that follows the safety factor aimed to avoid the ultimate stress states of the deposit under the load of the offshore infrastructure [46]. Both the total stress method and the effective stress method can be used to calculate the safety factor [47,48]. For a total stress analysis, the results in this study could provide a reference for quantifying changes in $S_u$ varying with effective confining pressures and OCRs regardless of pore pressure responses. On the other hand, when using effective stress indices (e.g., ${\phi }^{\prime }$ and $c^{\prime }$ for Mohr–Coulomb failure criterion), it is important to accurately evaluate the pore pressure in the ultimate state to ensure an acceptable safety factor. For example, it can be seen in Figure 2 that the solid circle essentially obtains the FL, while the dashed circle does not, so there is an overestimation in the shear strength if the pore pressure is ignored. However, the problem is measuring the pore pressure response in the deep sea [49]. Since the pore pressure coefficient at failure $A_f$ could directly evaluate the magnitude of excess pore pressure at failure under a given total stress boundary [50], here we propose a prediction model considering OCR effects to estimate $A_f$ of clayey-silty sediments.

The relationship between $A_f$ and OCR for experimental data is plotted in Figure 10. Values of $A_f$ decrease with increasing OCR, and $A_f$ = 0.14 for OCR = 2, $A_f$ = −0.04 for OCR = 4, and $A_f$ = −0.10 for OCR = 6.

Combining Equations (7) and (11), a semi-empirical model can be represented by:

$$A_f=\frac{1}{2}\left(1-\frac{1}{\sin {\phi }^{\prime }}\right)+\frac{1}{2\alpha \sin {\phi }^{\prime }{\mathrm{OCR}}^{\mathsf{\Lambda }}}$$

(12)

Note that in Equation (12), the parameters ${\phi }^{\prime }$ and $\mathsf{\Lambda }$ are almost intrinsic for a specific sediment, which can be obtained directly in NC specimens regardless of OCR. Values of parameter $\alpha$ could refer to results in this study. The red dash line is drawn using Equation (12) with ${\phi }^{\prime }$ = 31.44$°$, $\mathsf{\Lambda }$ = 0.83, and $\alpha$ = 0.8 ± 0.15, and it is consistent with the experimental data. In addition, there is a critical value between OCR = 2 and 4 regarding whether the remolded clayey-silty specimen develops negative pore pressure as shown in Figure 8b. This critical value of OCR = 3 could be directly calculated through Equation (12) provided that $A_f=0$. Similarly, it is concluded from the prediction model that there is the lowest limitation of negative $A_f=\frac{1}{2}\left(1-\frac{1}{\sin {\phi }^{\prime }}\right)$ provided that the OCR can reach infinity; however, the authors acknowledge that this limitation is a very conservative prediction.

To verify applications of the proposed model in other works, Figure 11 shows the comparison between measured values and predicted values of $A_{f, pre}$ using published test results of NC specimens from Table 1. In this figure, the closer the scattered points are to the 45° line, the better the prediction is. This indicates that the developed model can be used to predict $A_f$ of clayey-silty sediments as a reliable estimation and is easily applied in engineering design and practice where it requires two parameters for NC sediments (i.e., $\alpha$ and ${\phi }^{\prime }$) and four for OC sediments (i.e.,$\alpha$, ${\phi }^{\prime }$, OCR, and $\mathsf{\Lambda }$).

The proposed model could predict a reasonable $A_f$ value to access the geotechnical capacity of clayey-silty sediments under undrained conditions in terms of its effective stress indices. Considering current studies have accumulated a series of test results of effective stress indices, the proposed model could have important implications for the stability analysis of offshore facilities supporting NGH exploitation. Admittedly, the proposed model is limited by the uncertainties in geotechnical practice (e.g., structure and anisotropy in natural sediments). Therefore, further studies are required to improve it.

5. Conclusions

A series of CU triaxial compression tests have been conducted on NC and OC remolded clayey-silty sediment from the overlying strata on hydrate reservoirs in SCS to study the effects of OCRs on the undrained shear properties of remolded sediments. The main conclusions drawn are as follows:

• The isotropic compression index $\lambda$ and isotropic swelling index $\kappa$ are 0.175 and 0.029, respectively. There is a linear relationship between $S_u$ and $p_0^{\prime }$ for NC specimens with an average $S_u/p_0^{\prime }$ of 0.42, while values of $S_u$ of OC specimens nonlinearly increase with increasing OCR.
• Only positive responses in the excess pore pressure are observed in CU tests for NC specimens, which increase with increasing $p_0^{\prime }$. However, the increasing OCR leads to a reduction in excess pore pressure responses where there is a critical value of OCR = 3 dictating whether the remolded clayey-silty specimens develop negative pore pressure.
• Although values of $S_u/p_0^{\prime }$ of NC clayey-silty sediments differ between areas ranging from 0.25 to 0.43, it could be reasonably assumed as $S_u/p_0^{\prime }=\alpha \sin {\phi }^{\prime }$ where the $\alpha$ values mostly vary from 0.65 to 0.95. Moreover, values of $S_u/p_0^{\prime }$ of OC specimens can be well described by an exponential function related to the OCR and parameter $\mathsf{\Lambda }$.
• A model is proposed based on the relation between OCR and $S_u/p_0^{\prime }$ to predict the $A_f$ of remolded clayey-silty sediments of SCS. The prediction is in agreement with the experimental data in this study, as well as previous test results.

These results are helpful to understanding undrained shear behaviors of remolded clayey-silty sediments from overlying strata on hydrate-bearing reservoirs in SCS and provide a reasonable prediction of pore pressure response at failure for the stability analysis of suction anchors or other offshore facilities supporting NGH production.