1 Introduction

The Bohai–Zhangjiakou Seismotectonic Zone (BZSZ) is situated in the northern part of the North China seismic region and is over 700 km long and 250 km wide in the NW–SE direction. The BZSZ, containing nearly 20 discontinuous NW–NWW-trending faults (Gao and Ma 1993; Xu et al. 1998; Fang and Zhang 2009; Suo et al. 2013; figure 1), is a left-lateral slip structure and has an important controlling effect on regional tectonics (Hou et al. 1999; Fu et al. 2004).

Figure 1
figure 1

Seismotectonic sketch map in North China (after Xu et al. 1998). BZSZ: Bohai–Zhangjiakou Seismotectonic Zone, TLSZ: Tancheng–Lujiang Seismotectonic Zone, HPSZ: Hebei Plain Seismotectonic Zone, and FWSZ: Fenwei Seismotectonic Zone.

Full size image

Several earthquakes have occurred in the BZSZ (Gao and Ma 1993; Fu et al. 2004; figure 1), including the 1679 Sanhe–Pinggu earthquake (Ms = 8.0; Xiang et al. 1988) and the 1976 Tangshan earthquake (Ms = 7.8; Chen et al. 1979; Liu et al. 2007) that have caused significant damage to life and property. During the past several decades, studies have been performed to analyse and explain the seismogenic mechanisms of these earthquakes. The Tangshan earthquake for example, occurred in the contiguous part between the Yanshan fold belt and the depression of North China Plain. The observational aftershock sequence of the Tangshan earthquake was distributed primarily in the Tangshan fault-block in the NE 45 ∘ direction (Xue 1986; Liu et al. 2007). Furthermore, previous studies on earthquake geology demonstrated that the Tangshan earthquake was formed under the action of constant forces along the boundaries of an inhomogeneous medium, which led to the accumulation of elastic energy in the local area (Song et al. 1982; Mei and Liang 1989). In addition, Feng et al. (1996) studied and analysed the seismogenic condition and long-term precursors of the Tangshan earthquake.

It is important to study how tectonic stress accumulates in the BZSZ in North China during long-term compressional processes and what the tectonic stress accumulation state is in the lithosphere. These issues require considerable attention and need to be addressed in terms of geomechanics and numerical modelling because the tectonic stress accumulation state is an important indicator for earthquakes. The present study aims to analyse the tectonic stress accumulation state in the BZSZ using three-dimensional (3D) visco-elastic modelling and discuss the effect of Moho surface on this stress accumulation.

2 Geological setting

The BZSZ in North China extends along Bohai Bay–Tianjin–Beijing–Zhangjiakou. Based on interpretations from satellite photographs, the BZSZ may include a NWW trending hidden active fault, which is approximately 180 km long from Beijing to North Tianjin (Xu et al. 1998; Li et al. 1999). Recently, an increasing number of studies have focused on the deep structures of the BZSZ, where both Cenozoic tectonic activity and seismicity have been extremely intensive and frequent (Zhang et al. 2002; Wang et al. 2004).

In general, the BZSZ is a left-lateral slip and has an important controlling effect on regional tectonics in North China (Hou et al. 1999; Fu et al. 2004; Wang et al. 2005; Fang and Zhang 2009). Seismic reflection profiles across the BZSZ have shown the presence of several deeply buried faults cutting the lithosphere (Gao 2001; Lai et al. 2006). During the past several decades, continuous Global Positioning System (GPS) observations have revealed relative sinistral movement between the Yanshan Mountains and the North China Basin (Yang et al. 2002; Wang et al. 2005). In addition, some anomalous geophysical backgrounds of the lithosphere exist in the BZSZ. According to an investigation of magnetotelluric data, the BZSZ is also a low resistivity zone in the lithosphere under North China (Zhao et al. 1997).

Records indicate that seven historical and recent earthquakes with Ms ≥ 7.0 have occurred in the BZSZ (Fu et al. 2004; table 1), and the majority of these strong seismic activities have occurred at intersections between the NW-trending BZSZ and the NE-trending seismotectonic zones, such as the Tanchen Lujiang Seismotectonic Zone (Wang et al. 2005; figure 1). Based on studies of the field geology, crustal deformation, geophysical field, topography, seismic parameters and the relationship between NE- and NW-trending faults, the NW-trending BZSZ can be divided into four segments with various seismic characteristics and episodes, namely, the Penglai–Yantai, Tangshan–Bohai, Beijing and Zhangjiakou segments (figure 2; Gao et al. 2001).

Table 1 Catalog of strong earthquakes (Ms ≥ 7.0) in the BZSZ in North China since 1000–2000 AD (after Fu et al. 2004).
Full size table
Figure 2
figure 2

Fault distribution and tectonic segmentation in the BZSZ in North China. The BZSZ is divided into four segments: the Penglai–Yantai segment, Tangshan–Bohai segment, Zhangjiakou segment and Beijing segment. The faults data are from Gao et al. (2001) and Han (2009).

Full size image

Both paleo and modern tectonic stresses are fundamental datasets in Earth sciences (Zoback 1992; Sperner et al. 2003; Delvaux and Barth 2010; Ju et al. 2013a), and investigations into crustal tectonic stress are extremely important in Earth geotectonic studies (Lunina and Gladkov 2007; Ju et al. 2013a, ??b). In general, several types of data, including earthquake focal mechanisms, can allow and facilitate a revisiting of tectonic interpretations of the modern crustal stress field (Zoback 1992; Angelier 2002; Delvaux and Sperner 2003; Delvaux and Barth 2010). The average direction of the modern maximum principal stress axis in the BZSZ in North China is interpreted to be consistently NEE–SWW (figure 3).

Figure 3
figure 3

Modern tectonic stress field in North China (stress indicator data are from China Earthquake Networks Center).

Full size image

3 3D visco-elastic modelling

In this study, a 3D visco-elastic model was run using the Finite Element (FE) technique to study the stress accumulation state in the BZSZ in North China. FE modelling allows complex geometries (e.g., mechanical layers and faults) to be combined with realistic material parameters to produce physically realistic and mechanically rigorous models (Yin 1991; Smart et al. 2009; Ju et al. 2013b, 2014). The general-purpose FE code ANSYS was used in this study because it is well suited to analyse these type of problems over a wide range of scales in one, two and three dimensions (Hou et al. 2010; Jarosinski et al. 2011; Ju et al. 2013a, 2013b).

3.1 Geometry

In the present study, complex model geometries were constructed based on the CRUST 1.0 data (Laske et al. 2013; figure 4). A larger rectangular area including the BZSZ was selected to construct the model and to avoid the boundary effects. The x-, y- and z-axes indicate the east, north and vertical (depth) directions, and the depth ranges from the surface to 80 km underground. In the vertical direction, the 80 km depth was divided into four layers: the upper crust, middle crust, lower crust and upper mantle (figure 4).

Figure 4
figure 4

Three-dimensional finite element model in the Bohai–Zhangjiakou area. x: the east direction; y: the north direction; z: the vertical (depth) direction. For clarity, this showing model utilized a ratio of x : y : z = 1 : 1 : 10. (a) Upper crust layer, (b) middle crust layer, (c) lower crust layer, and (d) upper mantle layer.

Full size image

Multiple faults have developed in the Zhangjiakou–Bohai area in North China, and several important ones were selected to be included in the model because they were active in the Late Pleistocene and Holocene periods, and earthquakes had occurred at least once on these faults (table 2 and figure 4). In general, faults can be considered in two ways during FE modelling. The first approach implements the existing faults as discrete planes of weakness cutting the FE model. These planes are described by so-called contact elements, which are defined at opposite sides of pre-assigned faults (Smart et al. 2009; Fischer and Henk 2013; Ju et al. 2014). In the second approach, which was used in the present study, the entire FE model meshes continuously and the faults are represented by weakness zones (Fischer and Henk 2013; Ju et al. 2013a, 2013b).

Table 2 The important faults developed in the Bohai–Zhangjiakou area and their parameters (the data are after Gao and Ma 1993; Chen et al. 1999; Li et al. 1999; Gao 2001; Xu et al. 2002; Wang and Li 2005; Li et al. 2009; Hu 2010; Zhan et al. 2011).
Full size table

All the four layers and faults in the model were discretized using primarily three-node triangular elements with some four-node quadrilateral elements, and after meshing, there were approximately 28543 nodes and 158839 elements (figure 5).

Figure 5
figure 5

Meshing graph of the finite element model in the Bohai–Zhangjiakou area. There are altogether 28,543 nodes and 158,839 elements in the model.

Full size image

3.2 Material properties

In the present study, material properties were assigned to the elements representing different layers and faults. Mechanical behaviour in the elastic domain was described by Hooke’s law, whereas the viscous deformations obeyed Newton’s law of viscosity (Jaeger et al. 2007).

Young’s modulus and Poisson’s ratio are the most important elastic parameters in building materials (Martinez-Martinez et al. 2012; Ju et al. 2014, 2015), and can be calculated from the wave velocity and density data (Liu et al. 1986; Rao et al. 2006).

$$ E= \frac{\rho {V_{S}^{2}}\left( 3{V_{P}^{2}}-4{V_{S}^{2}} \right)}{{V_{P}^{2}}-{V_{S}^{2}}} $$
(1)
$$ \upsilon = \frac{{V_{p}^{2}}-2{V_{S}^{2}}}{2({V_{p}^{2}}-{V_{S}^{2}})} $$
(2)

where E is the dynamic Young’s modulus, υ is the Poisson’s ratio, ρ is the density, V P is the P-wave velocity, and V S is the S-wave velocity.

Previous studies indicated that the ratio between the dynamic and static Young’s moduli ranged from 0.8 to 3.0 (Mockovciakova and Pandula 2003; Martinez-Martinez et al. 2012; Yao et al. 2012) and that the dynamic Young’s modulus was usually larger (Yao et al. 2012). Unfortunately, this ratio has not been quantitatively calculated in the study area; therefore, based on the geological settings of the BZSZ in North China, a ratio of 2.9 was used to calculate the static Young’s modulus. The viscosities of the different layers in the visco-elastic FE model were based on the previous study results of Zang et al. (2003) and Shi and Cao (2008) (table 3).

Table 3 Material properties used in the visco-elastic finite element model.
Full size table

Because the fault zones were defined as ‘weak zones’ in the FE model, the elastic modulus was typically smaller, and the Poisson’s ratio was larger than that of a corresponding normal layer (Zeng et al. 2013). Therefore, in this study, the Young’s modulus and Poisson’s ratio were 50% and 105% of the corresponding normal layer, respectively (table 3).

3.3 Boundary conditions

According to the modern tectonic stress field shown in figure 3, the direction of the maximum principal stress axis is NEE–SWW in the study area. In addition, Li et al. (2006) calculated the current strain field with GPS data, and the average strain rate is approximately 0.5 ×10 −9/yr in the North China area. Based on previous studies (Xie et al. 2004; Wang et al. 2005; Li et al. 2006; Liu et al. 2012), the boundary conditions in this FE model were set as follows: (a) an average compressional displacement of 3.0 mm/yr was applied in the maximum principal stress axis NEE–SWW direction (Liu et al. 2012) with the horizontal displacement fixed on the west and south sides of the model, (b) the top of the model was set as a free boundary and the vertical displacement of the bottom was fixed to avoid movement and rotation of the model, and (c) a gravity load was applied to the entire model domain.

3.4 Modelling results

In the present study, the entire modelling process was performed in two steps. First, a gravity load was applied to the entire model domain. Once equilibrium was achieved, displacement boundary conditions were imposed to obtain the tectonic stress field. In the second step, each time step was set to 3 years, and the entire modelling process underwent 5000 steps.

The maximum shear stress accumulation was calculated and is shown at different depths in figure 6. In general, the maximum shear stress gradually increases with increasing depth, and a wider stress range exists in the lower layer (9 MPa at a depth of 25,000 m and 3.6 MPa at a depth of 5000 m; figure 6). In the lower layer, the maximum shear stress is higher in the Penglai–Yantai area, whereas in the upper layer, relatively high values are seen in the Zhangjiakou area (figure 6).

Figure 6
figure 6

The maximum shear stress accumulation after 15,000 years in the BZSZ in North China. (a) –5000 m, (b) –10000 m, (c) –15000 m, (d) –20000 m, and (e) –25000 m.

Full size image

The maximum shear stress is low in the fault zones in all layers (figure 6) because these fault zones were set as ‘weak zones’ in the FE model. They have relatively low strengths and cannot accumulate stresses; therefore, these weak fault zones will be easily fractured, resulting in earthquakes. Based on the modelling results, the upper layer of the Zhangjiakou area and the lower layer of the Penglai–Yantai area in the BZSZ in North China are more likely to experience earthquakes.

4 Discussion and conclusions

During the Paleogene, multiple extensional structures consisting of numerous NNE-trending faults and graben systems were developed. There are several NWW-trending faults perpendicular to these systems that adjust the extension rate of different sections, with the Bohai–Zhangjiakou fault zone being the largest strike-slip transform zone in the area. In the Neogene and Quaternary periods, the tectonic movements in North China changed dramatically, and the Bohai–Zhangjiakou fault zone became a huge regional structure controlling the northern margin of the North China Basin (Xu et al. 1998; Wang et al. 2005).

In general, the movements of plates from the external boundary conditions are the primary causes of tectonic activities in the Chinese mainland (Chen et al. 2001). However, Yuan et al. (1999) proposed that the upward force produced by mantle convection might be the main driving force for earthquakes in North China, which experienced strong events during the Mesozoic period (Wu et al. 2005; Zhu et al. 2011, 2012). Therefore, earthquakes in the BZSZ are influenced by many factors, such as horizontal plate tectonics and fluctuations in the Moho surface.

The Moho surface is an extremely important factor for the tectonic stress accumulation state in the BZSZ (Xue 1986; Liu et al. 2012). The Moho surface is deeper in the Zhangjiakou area (figure 7), and the modelling results indicate that the maximum shear stress is high in the upper layer of this region, whereas, in the lower layer, the shear stress is relatively low (figure 6). This reveals that the depth of the Moho surface affects the tectonic stress accumulation state. In addition, Gao et al. (2001) proposed that both the NE- and NWW-trending faults were seismogenic tectonics in North China; however, the NE-trending faults were earthquake-generating tectonics, such as the Tangshan and Xiadian Faults (Xue 1986; Xiang et al. 1988; Liu et al. 2007; Suo et al. 2013). However, based on an analysis of the prospecting trenches, the NE-trending faults may not be seismogenic. The seismogenic process and modern seismic activity in North China are primarily controlled by NWW-trending faults (Suo et al. 2013). Seismogenic tectonics control stress accumulations and changes in the lithosphere, and usually are the major faults in the system, while earthquake-generating tectonics are channel to release tectonic stresses (Li and Wang 1981). In the BZSZ, seismogenic tectonics and earthquake-generating tectonics are not the same, similar to the Mabian–Yongshan Seismic Zone (Li and Wang 1981).

Figure 7
figure 7

Depth map of the Moho surface beneath the BZSZ in North China. The western part of BZSZ has a deeper Moho surface, the maximum depth can reach about 44 km. The depth data are from CRUST 1.0 Model (Laske et al. 2013).

Full size image

In the present study, the maximum shear stress accumulation in the BZSZ was calculated and shown at different depths based on 3D visco-elastic modelling. The maximum shear stress in the BZSZ increases gradually with increasing depth, and there is a wider stress range in the lower layer. In the upper layer, the calculated maximum shear stress is high in the Zhangjiakou area, whereas in the lower layer, the values are relatively high in the Penglai–Yantai area, which may be affected by the depth of the Mohr surface. Based on the modelling results and their relationship with the Moho surface depth, a deeper Moho surface generally favours stress accumulation in the upper layer and limits its accumulation in the lower layer. Therefore, in the BZSZ in North China, the upper layer of the Zhangjiakou area and the lower layer of the Penglai–Yantai area are more likely to experience earthquakes in the future.