Multi-factor sensitivity analysis on the stability of submarine hydrate-bearing slope

Ling Kong, Zhen-fei Zhng, Qing-meng Yun, Qin-yong Ling, Yo-hong Shi, Jin-qing Lin

a School of Science, Qingdao University of Technology, Qingdao 266033, China

b Guangzhou Marine Geological Survey, Guangzhou 510760, China

ABSTRACT

There are many factors affecting the instability of the submarine hydrate-bearing slope (SHBS), and the interaction with hydrate is very complicated. In this paper, the mechanical mechanism of the static liquefaction and instability of submarine slope caused by the dissociation of natural gas hydrate (NGH)resulting in the rapid increase of pore pressure of gas hydrate-bearing sediments (GHBS) and the decrease of effective stress are analyzed based on the time series and type of SHBS. Then, taking the typical submarine slope in the northern South China Sea as an example, four important factors affecting the stability of SHBS are selected, such as the degree of hydrate dissociation, the depth of hydrate burial, the thickness of hydrate, and the depth of seawater. According to the principle of orthogonal method, 25 orthogonal test schemes with 4 factors and 5 levels are designed and the safety factors of submarine slope stability of each scheme are calculated by using the strength reduction finite element method. By means of the orthogonal design range analysis and the variance analysis, sensitivity of influential factors on stability of SHBS are obtained. The results show that the degree of hydrate dissociation is the most sensitive,followed by hydrate burial depth, the thickness of hydrate and the depth of seawater. Finally, the concept of gas hydrate critical burial depth is put forward according to the influence law of gas hydrate burial depth, and the numerical simulation for specific submarine slope is carried out, which indicates the existence of critical burial depth.

Keywords:

Submarine slope

Gas hydrate

Strength reduction finite element method

Instability mechanism

Sensitivity analysis

Critical burial depth

1. Introduction

Natural gas hydrate (NGH) is an ice crystal of natural gas formed with water at high pressure and low temperature. In recent years, NGH has been found in the ocean and the permafrost regions with global reserves that are two times that of the total carbon content of fossil fuels (coal, oil, natural gas) available on Earth (Hyodo M et al., 2013; Milkov AV,2004). NGH is also a high density and clean energy resource,so it is recognized as the most ideal new strategic alternative energy for the 21st century and it has the prospect of commercial development. However, due to the extremely harsh conditions of occurrence, NGH is unstable and very easy to dissociate with either the rise of temperature or the decrease in pressure, such as the drop of sea level, petroleum drilling/production operations. Generally, about 164 m3methane gas at standard conditions and 0.8 m3water can be released from 1 m3NGH. Once NGH is dissociated, the excess pore pressure will increase rapidly and the sediment’s strength will decrease, resulting in the softening or even liquefaction of gas hydrate-bearing sediments (GHBS), and this triggers the submarine landslide, which can demolish the drilling platform, submarine cables, oil pipelines and other offshore engineering facilities (Mark M et al., 2010; Sultan N et al., 2004). In addition, the dissociation of NGH can cause an explosion of marine methane flux, resulting in the deterioration of the marine ecological environment and accelerate the warming of the climate.

The South China Sea is rich in NGH with a resource of(643.5–772.2)×108t oil equivalent, amounting to 1/2 of the total onshore and offshore oil and gas resources of China(Song ZJ et al., 2003). China Geological Survey has embarked on the technical preparation and experimental simulation of NGH production in the sea area since 2011, and successfully tested the marine NGH in the Shenhu area in May 2017. The stability analysis of submarine hydratebearing slope (SHBS) to prevent the occurrence of submarine landslide is one of the key links to ensure the safety of hydrate test mining and commercial exploitation in the future. There are many influential factors on the stability of SHBS, most of them are random, fuzzy and variable, and the coupling between them is complicated (Locat J et al., 2002). Sensitivity analysis of influential factors should extract the sensitive factors which have important influence on the submarine slope stability from many uncertain factors, and then analyze the reason for instability of SHBS, in order to adopt a corresponding measure to reduce the risk of the test mining project of NGH (Wang HQ et al., 2014). Therefore, sensitivity analysis of the influential factors on the stability of SHBS is of great significance to find out the mechanism of its instability and ensure the safe exploitation of NGH.

In this paper, the mechanical mechanism of the instability of SHBS is deeply analyzed combined with the time series and type of submarine landslide. Taking the gas hydrate test production in the Shenhu area of the northern South China Sea as a background, the orthogonal test design method and the strength reduction finite element method (SRFEM) are used to analyze the stability of SHBS by multi-factor sensitivity analysis. Finally, the critical burial depth of natural gas hydrate is discussed. The aim of this paper is to further reveal the instability mechanism and the reasonable stability evaluation of SHBS.

2. Mechanical mechanism of the instability of submarine hydrate-bearing slope

Usually, submarine landslides are caused by external inducements such as earthquakes, volcanic eruptions, rapid accumulation of sediments, or excessive slope of the slope itself (Sultan N et al., 2004). However, increasing investigations have found that there is a spatial consistency between the submarine landslide zone and the gas hydrate distribution area, indicating that the development of submarine landslide is closely related to the formation and occurrence of NGH(Grozic, JLH. 2010; Li X et al., 2012; Chen SS et al., 2012).Fig. 1 shows a submarine landslide and hydrate revealed by a seismic reflection profile in the Shenhu area of the northern South China Sea. The typical geomorphologic structure of the submarine landslide related to NGH are clearly shown in Fig. 1:landslide sidewall, landslide valley, sliding surface, landslide mass, pear type fault, bottom simulating reflector (BSR,geophysical reflection mark of NGH) and so on.

The coupling interaction between NGH and submarine landslide is very complicated. On one hand, the collapse may be a favorable geological body for the formation and distribution of NGH. On the other hand, the collapse itself may be a tectonic effect caused by the dissociation of natural gas hydrate. The time series of formation and decomposition of submarine landslide and NGH were discussed in the reference (Zhang BK et al., 2014). The landslide of submarine hydrate-bearing sediments was divided into three types: postgas hydrate landslide, pre-gas hydrate landslide and syn-gas hydrate landslide (Fig. 2). It is very important to correctly identify the type of submarine hydrate-bearing landslide based on seismic profile data to reveal its instability mechanism.

Post-gas hydrate landslide means that the submarine landslide is triggered by the dissociation of NGH after its formation. The NGH has a high sensitivity to the temperature and pressure conditions of its environment, and it is easy to dissociate and dissipate with the change of the conditions. The hydrates dissociate slowly when the temperature and pressure conditions change slightly. Plume flow forms in the water,and pockmarks appear on the seabed. The shear strength of the overlying strata is reduced, and the decomposition zone is hollowed out to form the stress fragile zone, which leads to the occurrence of submarine landslide shown in Fig. 2a. The hydrate dissociates immediately when the temperature and the pressure conditions change dramatically, and the overlying strata lose support rapidly, which leads to large-scale landslide, fall or tsunami.

Fig. 1.Submarine landslide and BSR.

Fig. 2.Time-sequence relations between the gas hydrate and the landslide.

Pro-gas hydrate landslide means that the NGH is formed after the submarine landslide. After the formation of submarine landslide, NGH is easily formed within the landslide body or the sliding surface of the submarine landslide. The seismic reflection profile is characterized by large scale and good continuity of BSR, which can pass through the landslide structure, shown in Fig. 2b.

Syn-gas hydrate landslide refers to the formation of NGH in the process of a submarine landslide, but it is difficult to distinguish this process in reality, shown in Fig. 2c.Theoretically, the submarine landslide is a gradual process.Under the condition of good channel and gas source conditions, the pressure shield due to rapid deposition can form hydrate reservoirs. Since the Pliocene to Holocene, the deposition rate of the northern slope of the South China Sea is relatively high, and the continuous deposition tends to cause internal stress imbalance and sliding in sediments, which may result in the formation of hydrate deposits.

The stability of SHBS can be classified as a strength problem in mechanical mechanism. The shear strength of the GHBS decreases to the failure shear strength with the degree of hydrate dissociation, leading to slope instability. The gas hydrate formed in the granular pores of the soil matrix acts as pore filling, which causes GHBS shows the property of overconsolidation or compaction soil. The hydrates formed at the contact point of matrix soil particles play the role of particle cementation, which makes the GHBS shows the properties of cemented soil. All these make the strength and stiffness of GHBS significantly improved and the shear dilatancy is more obvious. The dissociation of NGH produces lots of water and gas. On the one hand, the cementation of soil particles weakens, the porosity increases, and the GHBS becomes under-consolidated soil or loose sand. On the other hand, the dissociated gas leads to the rapid rise of pore pressure and the decrease of effective stress, which leads to instability or static liquefaction of GHBS, and then leads to submarine landslide.

3. Sensitivity analysis of influential factors on the stability of submarine hydrate-bearing slope

3.1. Determination of influential factors and orthogonal test scheme

Orthogonal test is a kind of scientific analysis method used in multi-factor tests. It uses mathematical statistics and orthogonality principles to select representative factors from a large number of test data. By arranging the test scientifically and reasonably by orthogonal table, the influential degree of each factor on the sample index is reflected comprehensively.(Wang HQ et al., 2014; Xu F et al., 2013; Zhang XH et al.,2014).

The main influential factors of SHBS instability include geological tectonics, earthquake, volcano, sea wave, depth of sea water, depth of hydrate burial, thickness of NGH, the dissociation degree of hydrate, etc (Sultan N et al., 2004).Taking the gas hydrate test production in the Shenhu area of the Northern South China Sea as a background, this paper focuses on the sensitivity analysis of four influential factors,namely the degree of hydrate dissociation, the depth of hydrate burial, the thickness of hydrate, and the depth of seawater.

Based on the seabed geological data of the northern part of the South China Sea obtained from the Guangzhou Marine Geological Survey, five values of four influential factors are determined, as shown in Table 1. According to the basic principle of orthogonal test design, 25 kinds of orthogonal test schemes with 4 factors and 5 value levels are designed, as shown in Table 2.

Table 1.Influential factors and their values.

Table 2.Orthogonal test scheme of 4 factors and 5 levels and calculation results.

3.2. SHBS model and stability analysis method

The Guangzhou Marine Geological Survey conducted a large number of marine geological surveys in the northern part of the South China Sea. Based on the position of BSR in the seismic reflection profiles of the Shenhu area in the South China Sea, the actual burial depth, thickness and length of the hydrate layers are calculated through the time-depth conversion relations of the section. A typical SHBS model in the Shenhu area was established by using ABAQUS software as computing platform, shown in Fig. 3. The model has a slope length of 1800 m, a slope height of 200 m, an extension of about 1800 m of hydrate layer and a total span of 3200 m.The distribution of hydrate is approximately the same as the submarine surface. The soil of the submarine slope in the model is divided into four layers: overlying soil, the hydrate layer, surrounding hydrate soil, and underlying soil. The soil is assumed to be an ideal elastic-plastic material, which is subject to Mohr-Coulomb yield criterion. The boundary constraints on both sides in the model are fixed horizontal displacements and completely fixed constraints at the bottom.The loads are soil weight and overlying seawater pressure. A six-node second-order triangular plane strain element is selected. The model has 30 m top element size, 40 m bottom element size, and 20–30 m evolution from the top to bottom slope. The element mesh of the hydrate layer is refined to 10 m.The meshed model is shown in Fig. 4.

Fig. 3.Submarine hydrate-bearing slope (SHBS) model.

Fig. 4.Finite element meshing diagram of submarine hydrate-bearing slope (SHBS) model.

A number of studies show that the cohesion, the internal friction angle and elastic modulus of hydrate sediments are much larger than that of the surrounding soil. With the increase of hydrate saturation, the cohesion and elastic modulus increase accordingly, but the increase of the internal friction angle is not significant. In this paper, the sediment saturation of hydrate is 25% and the parameters of the soil in the hydrate layer are referred to the research results in the relevant references. The case data of typical submarine landslides in the northern South China Sea, exploration data,and the newly published literature data (Zhang BK et al.,2014; Su Z et al., 2012; Zhang GX et al., 2014; Liang J et al.,2013; Shi YH et al., 2015) are used to determine the mechanical parameters required for model calculation, as shown in Table 3.

Table 3.Soil mechanical parameters.

The SRFEM is used on the stability analysis of SHBS in this paper. The basic principle of the SRFEM is to reduce the shear strength parameters, i.e. the cohesion and the internal friction angle, continuously of the slope until the ultimate failure state is reached (Zhao SY et al., 2002; Liang QG et al.,2008). The sliding failure surface can be obtained automatically according to the elastoplastic finite element calculation results. The reduction coefficient used in the SRFEM is numerically equal to the safety factor, so the safety factor of the slope can be obtained as well. SRFEM overcomes the shortcomings of traditional slope stability analysis methods such as the limit analysis method and the numerical analysis method. It can not only obtain the slope stability safety factor, but also obtain information relating to stress, strain, displacement and sliding surface, etc. Taking the scheme 1 in Table 2 as an example, the plastic strain distribution of slopes corresponding to the different reduction coefficientsFris shown in Fig. 5. It can be seen from Fig. 5 that the range of plastic zone expands gradually with the increase of the reduction coefficientFr. The plastic zone is obviously connected whenFris increased to 2.792. It is shown that the submarine slope has reached the critical failure state at this time. The reduction coefficientFris the safety factor of slope stabilityFs, i.e.Fs=2.792. The safety factors of other schemes are obtained in the same way, as shown in Table 2.

Fig. 5.Plastic strain distribution under different reduction coefficients Fr (Scheme 1).

3.3. Results of sensitivity analysis of influential factors

The orthogonal design range analysis method studies the degree of sensitivity of each factor by identifying the order in which each factor affects the result of the index. Sensitivity analysis and calculation of the safety factor of submarine slope stability under 25 different calculation schemes are carried out by using the range analysis method, and the statistical results of the range analysis of the influential factors are obtained, as shown in Table 4. According to the criteria of sensitivity ofRjto various factors in orthogonal design range analysis, the sensitivity of influential factors on stability of SHBS is as follows: the degree of hydrate dissociation, the depth of hydrate burial, the thickness of hydrate and the depth of seawater.

The variance analysis method of orthogonal design is an effective scientific statistical method to test whether the mean value of samples is equal or not equal under the condition of the same variance for many normal populations. The variancesensitivity analysis method is based on the variance of the observation variables of these fluctuating data, and studies the factor variables which have significant influence on the observation index among the many factor variables. The concrete process of orthogonal design variance analysis method is to divide the sum of the square of the total variation of the data into the sum of the square of the variation of factors and the sum of the square of the random error, and then to make theFtest under confidence levelε=aand obtain the significance of the influence factors. The higher the significance of the factors, the higher the sensitivity.According to the orthogonal design variance analysis method,the safety factor of the submarine slope obtained from 25 orthogonal test schemes is analyzed under the confidence levelε=0.05, and the statistical results of the variance data are calculated as shown in Table 5.

Table 4.Results of range analysis of four kinds of influential factors.

Table 5.Results of variance analysis of four kinds of influential factors.

It can be seen from Table 5 that theFvalue of hydrate dissociation degree and hydrate burial depth is greater than the critical value ofF, and the influence is significant; theFvalue of hydrate thickness and seawater depth is less than the critical value ofF, and there is no significant effect on it.According to the criteria of variance analysis of orthogonal design, the sensitivity of four factors influencing the stability of SHBS are as follows: the degree of hydrate dissociation,the depth of hydrate burial, the thickness of the hydrate layer and the depth of seawater.

4. Discussion on the critical burial depth of hydrate

From the sensitivity analysis of the influential factors of submarine slope stability above, it can be seen that the depth of hydrate burial is the second sensitive factor, second only to the degree of hydrate dissociation, and the stability safety factor of submarine slope increases with the increase of buried depth. Then, is there a certain limit to the buried depth? When it reaches or exceeds this depth, the influence of hydrate dissociation degree on the safety factor of submarine landslide stability will disappear. We define this limit depth as the critical burial depth of the hydrate layer. This concept is similar to the boundary between deep and shallow buried in land tunnel excavation. The influence of tunnel excavation on the deformation of the ground surface will gradually decrease with the increase in burial depth.

In order to discuss the existence of critical burial depth of hydrate, the submarine slope model in Fig. 3 is still taken as an example. The thickness of the hydrate layer and the depth of seawater remain constant, the thickness of the hydrate layer is 30 m, and the depth of overlying seawater is 1400 m. By changing the value of the hydrate dissociation degree and buried depth, the initial burial depth of the hydrate layer is 300 m, and the change step is 20 m; the dissociation degree of each buried depth of the hydrate layer is 0%, 25%, 50%, 75%,and 100% respectively. Model parameters are determined in the same way as in section 3.2. Using the same calculation method as before, the stability safety factor of submarine slope under different buried depth and different dissociation degrees of hydrate is obtained, as shown in Table 6. Fig. 6 shows the variation of safety factor with the buried depth of submarine slope under different degrees of hydrate dissociation.

It can be seen from Table 6 and Fig. 6 that: (1) When thedegree of hydrate dissociation is constant, the stability safety factor of SHBS increases with the increase of hydrate burial depth. The greater the degree of hydrate dissociation, the greater the gradient of the slope safety factor with the change of hydrate layer, and the steeper the curve is. (2) When the depth of the hydrate burial is shallow, the degree of hydrate dissociation has a greater influence on the stability safety factor. The greater the degree of hydrate dissociation, the smaller the safety factor. (3) With the increase of the hydrate burial depth, the influence of the hydrate dissociation degree on the stability safety factor decreases gradually. When the depth of the hydrate burial is 400 m, the influence of the hydrate dissociation degree on the stability safety factor disappears. (4) It is obvious from Fig. 6 that the critical burial depth of the hydrate layer exists. When the burial depth reaches or exceeds this depth, the stability safety factor of SHBS calculated with different degrees of hydrate dissociation remains basically unchanged.

Table 6.Safety factors Fs under different degrees of dissociation and depth of hydrate burial.

Fig. 6.Relationship between buried depth of hydrate and the safety factor under different degree of dissociation.

5. Conclusions

(i) The dissociation of NGH produces plenty of water and gas. On the one hand, the cementation of soil particles weakens, the porosity increases, and the GHBS becomes under-consolidated soil or loose sand. On the other hand, the dissociated gas leads to the rapid rise of pore pressure and decrease of effective stress, leading to instability or static liquefaction of GHBS, and then leads to submarine landslide.

(ii) Taking the typical SHBS model in the northern South China Sea as an example, four important factors affecting the stability of submarine slope are selected, such as the degree of hydrate dissociation, the depth of hydrate burial, the thickness of hydrate, and the depth of seawater. According to the principle of orthogonal test, 25 kinds of orthogonal design schemes with 4 factors and 5 levels have been presented. The stability safety factors of submarine slopes are calculated by using the strength reduction finite element method, and the sensitivity analysis results of the influential factors of SHBS stability are obtained by means of orthogonal design range analysis and variance analysis. The sensitivity of the four factors is as follows: the degree of hydrate dissociation, the depth of hydrate burial, the thickness of hydrate layer, and the depth of seawater.

(iii) According to the influence of hydrate burial depth on the stability of submarine slope, the concept of critical buried depth of gas hydrate is put forward. The calculation and analysis of typical submarine slope models show that the critical burial depth of the hydrate layer exists. When the buried depth reaches or exceeds this depth, the influence of the hydrate dissociation degree on the safety factor of submarine landslide stability tends to disappear.

Acknowledgment

This work is funded by the National Natural Science Foundation of China (11572165) and the China Geological Survey (DD20160217), the anonymous reviewers, Dr. Yan Yang and Ziguo Hao gave valuable suggestions and comments on the manuscript, which is greatly appreciated.