Numerical Simulation for Shallow Strata Stability of Coral Reef in the Southwest of Yongshu Reef (South China Sea)

TANG Qinqin, ZHANG Jinchang, FENG Yingci, LI Jian, YAO Yantao, SUN Jie, and ZHAN Wenhuan, *



Numerical Simulation for Shallow Strata Stability of Coral Reef in the Southwest of Yongshu Reef (South China Sea)

TANG Qinqin1), 2), ZHANG Jinchang1), FENG Yingci1), 2), LI Jian1), 2), YAO Yantao1), SUN Jie1), and ZHAN Wenhuan1), 2), *

1) Key Laboratory of Ocean and Marginal Sea Geology, CAS, Guangzhou510301, China 2) University of Chinese Academy of Sciences, Beijing 100049, China

In recent years, infrastructure construction on coral reefs has been increasingly developed. Therefore, the shallow strata stability of coral reefs in the South China Sea should be evaluated. This study aims to investigate the profiles for the shallow strata of coral reefs in the southwest of the Yongshu Reef, particularly in the hydrodynamic marine environment, and to establish a geological model for numerical simulation using Geo-Studio. The shallow strata of the coral reefs include mass gravel, sand gravel, mid-coarse sand, silty sand, fine sand, and reef limestone. The shallow reef slope near the lagoon is similar to a ‘layer cake’, in which the side close to the sea is analogous to a ‘block cake’. The simulation results showed that coral reef stability depends on wave loads and earthquake strength and on the physical properties of coral reefs. The factor of safety for the outer reef is greater than 10.0 under static, wave, and seismic conditions; this indicated that the outer reefs were less affected by waves and earthquakes. However, the factor of safety next to the lagoon varied from 0.1 to 5.3. The variation was primarily caused by the thick strata of coral reefs close to the sea (reef limestone, typically with the thickness >10m and equivalent to a block). The soil and rock layers in the coral reef strata with thicknesses <10m showed weak engineering geological characteristics. Our findings can provide useful information to future construction projects on coral reefs.

coral reefs; rock mass structure; stability evaluation; numerical simulation

1 Introduction

A coral reef mainly comprises aragonite, magnesium calcite, and CaCO3up to 96% (Yangand Zhao, 1996). In engineering geology, a coral reef is regarded as a special type of rock and soil. Coral reefs can be used as the foundation of modern deep sea fisheries, marine energy development, submarine oil and gas resource development, tourism, transportation, and national defense; therefore, the reef is a valuable land resource in the tropical ocean and is economically, strategically, and scientifically significant to marine development and the protection of marine rights and interests (Zhao and Song, 1993). In addition, coral reefs have many engineering applications. For example, in the 1940s, the United States and Australia built several highways and airport runways in the Pacific Islands using coral reefs. Although these installations are still in use today, some engineering challenges have been reported with regard to coral reefs (Zhao, 1996a). Geotechnical engineering problems pertaining to the stability of offshore oil platforms were first discovered in the 1960s in the Persian Gulf of Iran (Guo, 2013); however, these problems did not attract much attention then. Challenges in coral reef construction have been widely reported since the 1970s (Rougerie and Wauthy, 1993; Sun and Huang, 1999; Wang, 2011; Barnes and Hu, 2016). Since then, the mechanical properties of coral reefs have been thoroughly investigated (Taylor, 1987; Zhao., 1996b; Zhan, 2006; Wang, 2008; Yuan, 2016). Although numerous studies have been conducted to analyze the stability of terrestrial slopes (Mao, 2011; Wu, 2011; Zou, 2012; Meier, 2013; Raj and Sengupta, 2014; Song, 2016), the behavior and mechanisms of the coral reef strata are still poorly understood.

We conducted a systematic investigation on the factors that exert an influence on the strata of the coral reef located southwest of the Yongshu Reef (Fig.1). The Yongshu Reef is located in the middle of the South China Sea Islands (9˚32΄–9˚42΄N, 112˚52΄–113˚04΄E). This reef is a semi-open atoll developed at the 2000-m deep seafloor (Zhu., 2014). Note that the coral reef growth did not begin at the depth of 2000m but was rather forced by the relative sea level rise. Coral reefs were already well developed after the late Oligocene; therefore, the reef limestone was developed from the Oligocene to the Quaternary Period (Zhu., 2014) (Fig.2). The shallow coral reef strata comprises six layers; namely, mass gravel, sand gravel, mid-coarse sand, silty sand, fine sand, and reef limestone (Zhao., 1992; Zhu., 1997). The shallow coral reef near the lagoon is similar to a ‘layer cake’, and the reef slope side close to the sea is analogous to a ‘block cake’. Numerical simulation was performed based on the changes related to the factors of safety and coral reef movements under static, wave, and seismic conditions. The results indicated that the physical properties of coral reefs (internal factors) are the predominant factors when evaluating their potential performance. Our investigation also showed that wave action and earthquake strength (external factors) played an important role in the failure mechanism of coral reefs that carried building structures.

Fig.1 (a) Map of study area located southwest of the Yongshu Reef. (b) Map of sediment distribution within the reef area and surface of reef area mainly covered by sand and gravel. (c) Typical engineering geological profile of shallow coral reef located southwest of the Yongshu Reef (modified from Yu et al., 2003, and Zhu et al., 2014).

Fig.2 Shallow strata information obtained during Nanyong-1 and Nanyong-2 drilling (modified from Zhu et al., 2014).

The engineering geological profile is not an actual geological section of the Yongshu Reef but a typical ‘lopolith’ structure of the coral reef stratum in the southwest of the Yongshu Reef. It shows that the bioclastic sandy gravel is the main layer in the shallow strata of coral reef. The deposition thickness increases with the decrease in the particle size of sand or gravel from the outer reef rim to the reef slope to the lagoon. The outer reef slope strata are formed by strongly cemented native reefs. The middle reef exhibits a gravel packing design with consolidated gravel and coralline algae and without loose sand debris. The gravel block is formed on the surface of the middle reefs; however, gravel and sand debris are found below their surface. Coarse, medium, and fine sand, including more broken coral branches and cemented fragments of reef limestone, are found in the inner reefs. Medium-fine sands with small size are formed in the lagoon and are similar to under-consolidated clay.

2 Numerical Modeling

2.1 Methods and Data

The stability in the coral reef shallow strata in the southwest of the Yongshu Reef was investigated using Geo-Studio. Geo-studio is one of the world’s most famous geotechnical engineering analysis software and was developed by the GEO-SLOPE company in Canada in the 1970s. The software can be used in geological engineering, geotechnical engineering, mining engineering, transportation, water conservation, and environmental engineering. Geo-Studio2007 comprises eight modules; namely, SPLOPE/W, SEEP/W, SIGMA/W, QUAKE/W, TEMP/W, CTRAN/W, AIR/W, and VADOSE/W. While facing a variety of problems, each module can independently analyze the data, and the data between the different modules can be transferred between them (Dawson, 1999; Zheng and Zhao, 2002; Zhao, 2003). In this study, SPLOPE/W, SEEP/W, SIGMA/W, and QUAKE/W (GEO-SLOPE International Ltd., 2008a, b, c and d) were coupled to one another to obtain the factors of safety for the coral reef shallow strata located southwest of the Yongshu Reef and to analyze its stability. The analysis program was formulated based on the rigid limiting equilibrium method (GEO-SLOPE International Ltd., 2008).

The length of the base was used to calculate the available resisting force of each slice which was calculated by multiplying the shear strength of the soil at the base center of the slice. Therefore, from the modified form of the Mohr-Coulomb equation for unsaturated soils, the available resisting force is

Similarly, the mobilized shear force of each slice is calculated by multiplying the mobilized shear stress at the base center of the slice with the base length as

The local stability factor of the slice can also be obtained when the available resisting shear force of a slice is compared to the mobilized shear force of that slice:

The slope stability factor (F) determinedthe finite element stress method is defined as the ratio of the summation of the available resisting shear force (S) along a slip surface to the summation of the mobilized shear force (S) along a slip surface. In the equation form, the stability factor (F) is expressed as

whereSis the available resisting shear force,Sis the mobilized shear force,LocalFis the local stability factor of a slice,Fis the stability factor of a slope,is the effective shear strength of the soil at the base center of a slice,is the base length of a slice,is the effective cohesion,σis the normal stress at the base center of a slice,τis the mobilized shear stress,is the effective angle of internal friction,μis pore water pressure, andis the angle defining the shear strength increase for an increase in suction.

Based on the collected geological and seismic data for the coral reef southwest of the Yongshu Reef (Zhao, 1992; Shan, 2000; Feng, 2005; Meng, 2013, 2014; Zhu, 2014), the coral reef profile was established and the simulation using Geo-Studio was completed; the rock and soil parameters of the software were obtained based on the Handbook of Rock Mechanical Parameters (The editorial board of Manual of engineering geology, 2007) (Table 1). Various boundary conditions were set according to hydrodynamic conditions and seismic effects of coral reefs. In addition, the model units and the actual structure of coral reefs were connected to an extent such that the model could reflect the actual situation of coral reefs and meet the analytical requirements of Geo-Studio.

Table 1 Data for all materials in the shallow coral reef strata

2.2 Modeling Approach and Setup

A generalization for the shallow profile of coral reef was completed using Computer Aided Design, saved in DXF format, and imported to Geo-Studio. The shallow profile of the coral reef is similar to a small heaved hill and is approximately 300-m wide and 5-m higher than the sea level, whereas the root is 20-m below the sea level. Mass gravel, sand gravel, mid-coarse sand, silty sand, fine sand, and reef limestone are found from the surface to the bottom of coral reefs. The approximate global element sizeis 3m, and the entire profile can be divided into 867 nodes and 781 elements (Fig.3). In the modeling process, long-term steady-state seepage conditions and pore pressures are first established using SEEP/W. Second, the initial total and effective static stress distribution is established throughout the coral reef. This can be performed using either a QUAKE/W static-type of analysis or SIGMA/Wanalysis; QUAKE/W static-type of analysis was used in this study. Therefore, a SLOPE/W sub-module for the coral reef factor of safety can be used to solve the static conditions. Wave loading analysis was conducted using SIGMA/W; the main purpose of this analysis was to apply wave action to the coral reef. Subsequently, the solved analysis was imported into the SLOPE/W sub-module to identify whether the coral reef was stable. Under seismic conditions, the earthquake-wave loading analysis can be solved using SIGMA/W, whereas the equivalent QUAKE/ W linear dynamic analysis can be computed by an earthquake loading type of analysis. All situations after the earthquake can be observed in the SLOPE/W sub-module.

Fig.3 Numerical analysis model of shallow coral reef under static, wave, and seismic conditions. (a) The static condition model was completed using the SEEP/W, SIGMA/W, and slope analysis modules. The blue arrows represent water pressure, and the weight loading was set by the density of different rocks and soils. (b) The wave condition model was completed using the SEEP/W, SIGMA/W, and slope analysis modules. However, a dynamic deformation with a wave load applied for 18s was selected for the SIGMA/W module. (c) The seismic condition model was completed using the SEEP/W, SIGMA/W, QUAKE/W, and slope analysis modules. The indication of a red point in the white box with red border was considered as a history point, and the change of seismic conditions could be recorded in detail over the time period of 18s.

‘The second Persian Gulf’ means that a large energy source exists in the South China Sea, such as wave power, which exerts great influence on reef islands (Zheng., 2011, 2012; Zong, 2014). The wave time cycle of periodical loading was assumed to be 4.5 and 3s under wave and earthquake conditions, respectively, acting for 18s (Yu, 1984; Li, 2005; Zhou, 2007; Li and Zhao, 2010; Wang, 2012) (Fig.4). However, in this analysis, the influence of the distance and depth of wave was not considered. Therefore, wave action was simplified as a tangential boundary stress associated with time (Hu., 2015; Wang., 2016; Jiang., 2017).

The great earthquakes of the South China Sea are mainly distributed in the Manila subduction region, and less seismic movement is observed in the Nansha Islands. However, earthquake action plays a crucial role in the stability of the reef slope compared to wave action, for an earthquake can also trigger the movement of ocean water. Wang. (1979) studied the earthquake that occurred on October 7, 1964 (=5.6) in the center of the South China Sea and found that its mechanism may represent horizontal compression within or across the plate. Chen (1993) conducted a study on the tectonophysical features and the seismic intensity regionalization of the South China Sea. Based on recent investigation on the seismic zoning of the areas surrounding Chinese sea, Guo. (1999) corrected the seismic zoning map of these areas and those located in its vicinity. This map was compiled in 1987. Wei (2001) discussed the epicenter and magnitude of an earthquake that occurred north of the Xisha Islands in the South China Sea in 1931. The magnitude7.1 of this earthquake was determined by the Xu- jiahui Observatory in Shanghai. Xu. (2006) determined the characteristics of the crustal structure and the hypocentral tectonics in the epicentral area of the Nan’ao earthquake (=7.5). From previous studies, we can infer that the Yongshu Reef can be classified as a seismic risk region with a potential seismic intensity between VI and VII. The seismic peak acceleration was 0.25(means the acceleration of gravity) (Fig.5), which is mainly based on the relation between seismic intensity and seismic peak acceleration in the South China Sea (Liu, 1982; Gao, 2000; Long, 2011; Liu, 2015). The procedure of the QUAKE/W module can be used to complete the analysis of the initial seismic state (0=0s) and earthquake shaking state (=18s) (Ma, 2005; Wu., 2011), whose=18s is consistent with wave action time under wave conditions.

Fig.4 Wave loading and earthquake-wave loading. The figure comprises four harmonic wave loads, and the wave load represents wave loading under wave conditions. However, the earthquake-wave load is a wave load influenced by an earthquake under seismic conditions. The inner and outer loads denote the tangential boundary stress imposed on the reef slope near the lagoon and the reef slope close to the sea, respectively.

Fig.5 Earthquake record under seismic conditions. The peak acceleration of the horizontal earthquake record was 0.25g, and the load acting time was 18s.

3 Results

3.1 Static Condition: Weight and Pore Water Pressure

The numerical result of pore water pressure (Fig.6) was very close to the actual water situation; this indicates that our simulation was performed under valid water conditions. The numerical simulation under the static condition shows that on the inner slope side, the factor of safety for the coral reef shallow strata was 1.1, whereas that on the outer slope side was 26.4 (Fig.7). Although both sides of the coral reef were stable, the difference between the factors of safety on the two sides was too large, and the outer reef was much safer than the reef next to the lagoon. The main reason was that outer reefs exhibited native reef structures, which were similar to that of ‘block cake’. The reefs next to the lagoon exhibited a non-cemented structure of fine and silty sands, and the stability of structure was relatively poor.

Fig.6 Pore water pressure counters under the static condition. Pore water pressure varied between 0 and 200kPa. Its values decreased from −20m to sea surface, and its contour was parallel to the sea surface. Other legends can be seen in Fig.3.

Fig.7 Coral reef factor of safety under static condition. (a) Inner slope factor of safety contours near the lagoon show that the minimum value for the factor of safety was 1.1. (b) is the amplification of (a) in the inner slope section. It is clear that small factors of safety are concentrated at the middle of the inner reef slope. (c) Outer slope factor of safety contours close to the sea show that the minimum value for the factor of safety is 26.4. (d) Amplification of (c) in outer slope section. It is clear that the small factors of safety are concentrated on the bottom of the outer reef slope. Other legends can be found in Fig.3.

3.2 Wave Condition: Weight, Pore Water Pressure, and Periodical Wave Loading

During wave action for 18 s, the factor of safety on the inner slope side was between approximately 0.6 and 1.1 and that on the outer slope side ranged from approximately 26.4 to 33.3 (Fig.8). The shape of the outer slope factors of safety versus time was analogous to the wave loading form (Fig.4); this implied that wave action showed greater impact in the reef slope near the sea rather than near the lagoon. The relative changes in coral reef movement can be seen in Fig.9. The reef slope toward the lagoon exhibited larger relative displacement (section of red rectangle) compared to the reef slope next to the sea. The inner slope side of the reef was unstable, whereas the outer slope side was safe for 18s. This indicates that the strata structure and physical parameters of rock and soil are closely correlated.

Fig.8 Critical factors of safety vs. time under wave conditions. (a) Diagram of inner slope factor of safety variation with time near the lagoon resembling a cosine function. Maximum and minimum are close to 1.1 and 0.6. (b) Diagram of outer slope factor of safety variation with time near the sea, which resembles a cosine function. However, its shape is apparently reversed in comparison with (a) and the maximum and minimum are 33.3 and approximately 26.4, respectively.

Fig.9 Relative movements of coral reef under wave conditions. The main areas of relative movements in the reef slope are highlighted by a red rectangle. The maximum of the deformed region is located on the inner reef slope near the lagoon.

3.3 Seismic Condition: Weight, Pore Water Pressure, Periodical Earthquake-Wave Loading and Seismic Loading

During seismic action for 18s, the inner reef slope side (close to the lagoon) factor of safety was between approximately 0.1 and 5.3, whereas that on the outer reef slope side (next to sea) ranged from approximately 14.0 to 68.2 (Fig.10). The shape of the factor of safety (outer reef slope) versus time was analogous to the recorded earthquake form (Fig.5). However, its maximum was asynchronous to the maximum value of the earthquake recorded; this indicates that the earthquake strength has greater impact on the reef slope near sea compared to that near the lagoon. In addition, the change of reef slope stability was controlled by seismic loading. The movement direction varied with time during earthquake shaking, whereas the liquefied zone increased with shaking time (Fig.11). The development of shaking and excess pore pressures caused other elements to reach the collapse surface or liquefy. Thus, the liquefied zone was expanded. The implication was that the risk of bank collapse existed at the inner slope side next to the lagoon in the shallow strata of the coral reef.

Fig.10 Critical factors of safety vs. time under seismic condition. (a) The diagram of inner slope factor of safety variations with time near the lagoon shows that the maximum and minimum values were 5.3 and approximately 0.1. (b) Diagram of outer slope factor of safety variation close to the sea, indicating that the maximum and minimum were 68.2 and approximately 14.0. Both (a) and (b) were similar to Fig.5 and their variation was synchronized.

Fig.11 Change of movement direction and liquefied zone during earthquake shaking. The red arrow represents the movement direction, and its directions change over time. The yellow section denotes the liquefied zone, and the liquefied zone increases with time for the period of 18s.

The coral reef factors of safety under static conditions are 1.1 and 26.4 on the inner and outer reef sides, respectively. The inner side factor of safety was between approximately 0.6 and 1.1, whereas the outer side factor of safety ranged from approximately 26.4 to 33.3 under wave conditions. The coral reef factors of safety under the seismic condition varied between 0.1 and 5.2 (near the lagoon) and between 14.0 and 68.2 (near the sea) (Table 2).

Table 2 Factors of safety for coral reef shallow strata under three conditions

4 Discussion

Our numerical simulation provided a typical, simplified coral reef structure model in the southwest of the Yongshu Reef. Based on the analysis, the potential behavior of shallow coral reef strata was clearly understood, and our engineering assessment was formulated. Trends and mechanisms are important in evaluating the potential performance of the coral reef slope as actual movement magnitudes.

The reef slope is safe under the static condition, particularly in the reef slope near the sea. Static conditions were accomplished only by exerting weight and pore water pressure, which is just an instantaneous situation. However, the simulation of static conditions solved the specific factors of safety, and the results can be considered as excellent background information. The inner side factor of safety (1.1) and the outer factor of safety (26.4) can serve as test data for wave and seismic conditions. In addition, the numerical results of the two conditions are in good agreement with the background data (Table 2). The artificial island in the southwest of the Yongshu Reef has been stable, and the thick reef limestone lopolith plays an important role inside the shallow reef strata (Nansha integrated the scientific expedition of the Chinese Academy of Sciences, 1997). The subjunctive static conditions experiment also demonstrated that the coral reef slope was stable without other interferences.

Wen and Wang (2014) believed that excess pore pressure induced by waves is one of the most important parameters for evaluating the stability of the sea bed. Under the wave condition, the wave action, whose periodical loading time cycle was assumed to be 4.5s, was simplified as the tangential boundary stress associated with time (Fig.5). The excess pore pressures derived from cyclic wave loading caused the reef slope close to the lagoon to be at a greater risk of bearing capacity failure during the 18-s period. The critical factors of safety under wave conditions (0.6–1.1 and 26.4–33.3) fluctuated around the static condition (1.1 and 26.4), which is consistent with the conclusions of Liu. (2015). The reef slope near the lagoon may be unstable owing to its soil and rock structure even though wave action is very small within the lagoon compared to the wave action on the outer reef slope and the action influenced by earthquake.

Aydan (2016) concluded that the major deep-seated slope failures are greatly influenced by the geological structure of rock mass and by the shaking characteristics of earthquakes. When an earthquake (peak acceleration of 0.25) occurs near the coral reef, the outer reef slope remains stable, whereas a sliding risk may exist inside the reef slope. Parameters such as weight, pore water pressure, periodical wave loading, and seismic loading were applied under seismic conditions to analyze the slope stability of the coral reef. Periodical wave loading under the seismic condition was different to that observed under the wave condition, which was the simplified ocean water movement during the earthquake. In this simulation process, seismic loading was uniform, unlike the case of the actual earthquake in the southwest of the Yongshu Reef (ocean earthquakes always trigger tsunamis and give rise to storms or typhoons in the meantime). The stability of the reef slope next to the lagoon and sea does not accord with the actual seismic condition. Nevertheless, such differences help us realize the considerable influence exerted by the physical properties of coral reef.

This simulation method was effective in exploring coral reef stability and can be improved by incorporating more factors, such as wave action and seismic intensity between the outer reef and the lagoon, in future study. Nonetheless, the simulation provided a semi-quantitative evaluation for coral reef stability, which can be viewed as a guideline to any coral reef stability assessment. Finally, the simulation results suggested that the influence of wave and earthquake on coral reef stability should be the main focus during the construction engineering. Moreover, the construction of buildings should be avoided in the reef next to the lagoon because of the low stability of that reef.

5 Conclusions

The exhaustive behavior and mechanisms of the coral reef strata in the southwest of the Yongshu Reef were obtained by utilizing the Geo-Studio software; this software implements a two-dimensional solution based on the finite element method to simulate the reef slope process under static, wave, and seismic conditions. We found that the physical properties of the coral reef dominate its potential performance (failure mechanism of coral reef) under three conditions. Specifically, the following conclusions were derived.

1) Excess pore pressures develop during the shaking; by promoting other elements to reach the collapse surface or liquefy, the liquefied zone expands with time. Moreover, the effective shear strength of a slope reduces, thereby decreasing the factor of safety. Furthermore, the magnitude of the factor of safety for the coral reef slope under seismic conditions is larger than that under wave conditions (both are solved using a software with dynamic capabilities). This indicates that earthquake shaking has a greater impact than wave action on the stability of the reef slope in the southwest of the Yongshu Reef.

2) The reef slope toward the sea (outer reef slope) is stable under static, wave, and seismic conditions. However, the reef slope close to the lagoon (inner reef slope) may potentially become unstable under wave and seismic conditions. These can be attributed to the shallow strata for the ‘layer cake’ structure of the reef slope next to the lagoon and the ‘block cake’ structure reef slope near the sea. The great difference in the factors of safety between the outer and inner reef slope suggests that coral reef stability is mainly dictated by the reefs physical properties, even though wave action and earthquake are considered as the main external influencing factors in actual engineering works.

Acknowledgements

This work was funded by the Science and Technology Basic Resources Investigation Program of China (No. 2017 FY201406), the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDA13010104), the National Natural Science Foundation of China (Nos. 41376063, 41606069 and 41776058), the National Basic Research Program of China (No. 2013CB956104), and the Natural Science Foundation of Guangdong Province in China (Nos. 2015A030310374 and 2017A030313243). We thank the anonymous reviewers for careful and constructive comments that helped to improve the manuscript significantly.

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(Edited by Xie Jun)

(Received March 29, 2017; revised July 5, 2017; accepted October 25, 2017)

© Ocean University of China, Science Press and Springer-Verlag GmbH Germany 2018

. E-mail: whzhan@scsio.ac.cn