In-situ rock stress is an important solid geophysical parameter in the lithosphere, and understanding the stress state is crucial for the applications of rock mechanics involved in mineral resource safe and scientific exploitation, mineralization mechanism research, tectonic activity analysis, and earthquake prediction (Haimson et al. 2003; Chang et al. 2010; Han et al. 2016; Du et al. 2017; Li and Cai 2018, 2022a; Li et al. 2022a). The origins of crustal stress are considerably complex and still unclear, and in-situ stress measurement is the most direct and reliable means to determine the stress vector information. The stress measurement began in the 1930s, that is, the original rock stress was successfully measured for the first time in a tunnel under the Hoover Dam by using the rock mass surface stress relief method (Cai 1995), thus creating a precedent for stress measurement. After decades of development, the theory of stress measurement has made tremendous progress, and various direct and indirect stress measurement techniques have been invented and applied worldwide (Ljunggren et al. 2003). Among these methods, the most commonly used are hydraulic fracturing and overcoring, which are widely used in underground rock engineering construction and earth science research. The abundant and reliable stress measurement data obtained by different techniques provides valuable information for exactly clarifying the features of regional tectonic stress fields and can be used to objectively and quantitatively establish the relationship between stress and rock mechanics and geomechanics issues.

The Jiaodong Peninsula situated in eastern China and bounded to the west by the translithospheric Tan–Lu fault (Fig. 1a) has huge reserves of gold resources and is the largest gold-producing area in China, with a cumulative proven gold reserve of over 5000 tons, accounting for about one-third of the national proven gold resource reserves (Song et al. 2018). In particular, the Zhao–Ping metallogenic belt, situated in the northwest of the Jiaodong Peninsula (Fig. 1b), is the most famous and the largest gold resource-rich area in the Jiaodong Peninsula, the proven gold resource reserves exceed 3000 tons (Xiao et al. 2018). The most prominent feature of mineralization in the Zhao–Ping metallogenic belt is the control of faults on ore deposits, which is also related to alteration (Li et al. 2013; Deng et al. 2019). There are multiple gold deposits of different scales distributed along the Zhao–Ping fault zone, such as the Linglong, Taishang, Dongfeng, and Shuiwangzhuang gold deposits. The Zhao–Ping metallogenic belt is adjacent to the Bohai Sea and has extremely complex geological structures. Fault structures affect and govern the stratigraphic framework, tectonic movement, magmatic activity, and mineral distribution in this area, and some faults are still active and exhibit multi-stage activity over time. Thus, regional microseismic activities are frequent, and small earthquakes occur occasionally. On the other hand, many gold mines are located in this region, and some of them have entered deep mining with a mining depth of more than 1000 m underground. The complex geological and mechanical environment makes mining quite difficult. During the production process, some gold mines have experienced different types and degrees of engineering geological disasters, such as rockbursts, roof falling, and spalling, seriously affecting the safe and efficient operation of mines. Numerous studies (Sbar et al. 1979; Ikeda et al. 2001; Zhao et al. 2013; Miao et al. 2016; Sakaguchi and Yokoyama 2017; Li et al. 2019c, 2021, 2023a; Luo et al. 2023; Li and Cai 2022b) indicate that rock stress is the fundamental factor resulting in the deformation and fracture of engineering rock masses and subsequent occurrence of dynamic disasters, and even dominates the faulting and seismic activities because of the long-term accumulation, concentration, and strengthening of rock stress in specific structural parts. In the past, the research on this region primarily focused on the basic characteristics of gold deposits, metallogenic regularity, as well as the fault activity and faulting history according to structural analyses. Nevertheless, because of the limited stress data, the investigation of the features of the entire tectonic stress field in this region is not sufficient, which limits the in-depth understanding of the stress province and geodynamics to some extent. Additionally, little attention has been paid to the correlation between geological structure evolution and in-situ stress and the activity of faults in the area from the perspective of the tectonic stress field.

Map displaying the geographical situation of the Jiaodong Peninsula. a After Deng et al. 2020; b Simplified geological map in and around the Zhao–Ping metallogenic belt (after Liu et al. 2021)

To that end, overcoring and hydraulic fracturing stress measurement campaigns were conducted in the Linglong gold mine and Shuiwangzhuang gold mine, respectively, in the Zhao–Ping metallogenic belt, and a large quantity of valuable stress data was identified. Subsequently, the distribution features and spatial variability of the contemporary stress field including magnitude and orientation were determined and predicted using the stress data, and the two measurement methods were compared to ensure the reliability of the measurements. In addition, based on the geological structure investigation and structural evolution analysis, the correlation between the stress field and regional geological tectonics in this region was discussed and examined from the perspective of stress field orientation. Finally, the stability of the geomechanical state of the regional fault structure under the effect of the current stress field was analyzed, and the potential slip and seismic risks of active faults were quantitatively evaluated accordingly. The findings are of considerable value in improving the prevention and control level of mine dynamic disasters and the understanding of earthquake disaster prevention and mitigation in this region.

The Zhao–Ping metallogenic belt is located at the east of the Tan–Lu fault and the northwest end of the Jiaobei uplift (Fig. 1), and it is a zone with frequent tectonic, fluid, metamorphic, magmatic, and mineralization activities. Tectonically, it is the Jiaodong uplift area of the second uplift zone of the Neocathaysian giant structure, or the Jiaoliao shield belonging to the Sino-Korean paraplatform. Mesozoic magmatism was intense, manifested by a large amount of granitoid intrusive rocks, broadly distributed intermediate-basic-acid dikes, and volcanic rocks developed along rift basins (Guo et al. 2020). The geological structure background formed by long-term geological evolution provides suitable conditions for the formation of this metallogenic belt. The veins are mainly composed of gold-bearing iron ore quartz vein type and gold-bearing quartz sulfide complex veins, with some veins being gold-bearing quartz sulfide network veins. The ore veins primarily occur in the low-sequence fault structural zone of Linglong mixed granite (Song et al. 2018; Feng et al. 2023). Because of the multi-stage activities of the structures and the multi-stage mineralization, the morphology and occurrence conditions of ore bodies are complicated, which has brought adverse effects on mining. The sedimentary strata in the region where this metallogenic belt is located are simple, and mainly composed of the Quaternary system (Fig. 2a). Magmatic rocks exist broadly, mainly in the Neoarchean Tangezhuang sequence and the Early Mesozoic Yanshanian Linglong sequence; the derived vein rocks are also relatively developed, and the lithology is primarily trondhjemite and sericite granite (Li et al. 2022c; Liu et al. 2023). In addition, there are scattered small Mesozoic-Cenozoic fault basins in the region, largely composed of Cretaceous volcanic rocks and terrestrial clastic rock series, and Cenozoic fluvial and lacustrine clastic rock series are deposited in some basins (Song et al. 2018). Linglong granite and Guojialing granite are the main host rocks of gold deposits in this region.

The structural forms in this region are fold structures and fault structures, with fault structures being the main type. The EW trending ancient basement fold structures, such as the Qixia anticline fold, which developed and formed in the Archean and Proterozoic, constitute the geological structure framework of the region. The EW trending fault surface outcrops are sporadic and the continuity is poor. Among the nearly EW-oriented faults, the Huang-Ye arc-shaped fault is a relatively large fault structure located on the north side of the metallogenic belt, with an overall inclination of 30°–45°, exhibiting extensional features. There are numerous and dense NNE–NE trending fault structures widely developed in the region, and the main fault structures from west to east include the Yuhuangding, Linglong, Zhao–Ping, and Luanjiahe faults (Fig. 2a), which are considered secondary faults of the Tan–Lu fault (Goldfarb et al. 2001). These faults are the main ore-controlling structures of the metallogenic belt and dominate the distribution of major gold deposits in this region. Among them, the Zhao–Ping fault is the most important ore-controlling structure in the metallogenic belt, with a length of 120 km and a width of 150–200 m, striking NNE–NE, dipping towards SE and a dip angle of 30°–70° (Wang et al. 2022). This fault controls gold deposits such as Xiadian, Dayingezhuang, Lingnan, Taishang, Dongfeng, and Shuiwangzhuang, as well as the Linglong goldfield, with a proven gold resource reserve of over 1200 tons (Song et al. 2018). The northern segment of the fault is bifurcated into two faults in the east of the Linglong goldfield, known as the Potouqing fault and the Jiuqujiangjia fault, respectively. The overall strike of the Potouqing fault is 60°, with a dip angle of 28°–45°, a length of 5500 m, and a width of 30–330 m. The Jiuqujiangjia fault is situated in the footwall of the Potouqing fault. It has a strike of approximately 33°, a dip of SE, and a dip angle of 23°–60°, and the exposed strike is approximately 6 km long and 8–460 m wide, with an average of 80 m. The gold ore bodies in the region often occur in hydrothermal alteration zones where the footwall of these fault zones has undergone extensive cataclastic deformation (Fig. 2b).

Additionally, the Tan–Lu fault is one of the most active seismic zones in the Chinese mainland, which has an important influence on the emergence of earthquakes in the Jiaodong Peninsula, including the Zhao–Ping metallogenic belt. The seismic tectonic environment in the Jiaodong Peninsula and its offshore areas is considerably complex, with multiple moderate to strong earthquakes occurring in history, such as the Ms 6.0 Weihai offshore earthquake in 1948 and Ms 7.4 Bohai Sea earthquake in 1969 (Wang et al. 2013), which is one of the regions with high seismic activities in eastern China. The modern tectonic activity is strong, with occasional occurrence of small earthquakes, showing remarkable spatial-temporal clustering phenomenon. Monitoring data shows that since 1970, the Jiaodong Peninsula and its offshore areas have experienced at least 4000 earthquakes with magnitudes greater than or equal to 2.0, including about 10 earthquakes with magnitudes greater than 5.0 (Peng et al. 2024), which are primarily governed by deep active fault zones in this region and distributed in a belt along the active fault zone. In general, the focal depth is in the range of 3–48 km. Especially recently, the Yantai area and the Bohai Sea near the Zhao–Ping metallogenic belt experienced an earthquake with a magnitude of 3.1 in 2022 and an earthquake with a magnitude of 4.4 in 2022, respectively.

Simplified geological map of the Zhao–Ping metallogenic belt. a After Guo et al. 2020; b Its profile map (after Feng et al. 2023)

3.1 Overcoring

The overcoring (OC) technique developed in the 1960s is a mature and effective indirect measurement approach for rock stress in underground caverns, which is one of the suggested approaches for evaluating the stress state promulgated by the ISRM (Sjöberg et al. 2003). It is a three-dimensional stress measurement method that allows for measuring the complete stress state of a point by stress relief measurement in a borehole, which is a significant advancement in stress measurement techniques. Due to its outstanding advantages, this technique has become a widely used stress measurement method worldwide, especially in the construction stage of engineering. Except for some methods that attempt to directly determine the crustal stress state, most techniques involve measuring the strain or displacement generated by the disturbance of the original rock stress state. By assuming rock behavior, strain or displacement is associated with stress (Leite et al. 2010). The OC technique is to separate the core completely from the surrounding rock mass around the borehole wall by the drilling technique and to measure the deformation or strain response of concentric small boreholes in the drilled core at the same time. Subsequently, the stress can be computed based on the rock constitutive relation, namely, the correlation between the relieved rock deformation or strain and the far-field stress (Eq. (1)) (Cai et al. 2002; Li et al. 2022a). The quality of the measurement results of this technique highly depends on the following aspects: (1) establishing the rock constitutive relationship as reasonable as possible, that is, the relationship between stress and deformation or strain; (2) the mechanical properties of rock samples can be determined accurately; (3) there should be sensitive enough testing instruments to accurately measure the tiny deformation or strain of the core caused by local disturbance; and (4) obviating the effect of temperature in the measurement process.

where ε_θ, ε_z, and γ_θz are the circumferential, axial, and shear strains, respectively; ε_±45° is the strain at 45° to the axis; σ_x, σ_y, σ_z, τ_xy, τ_yz, and τ_zx denote the six stress components; E and υ represent the elastic modulus and Poisson’s ratio, respectively; θ denotes the separation angle between the strain gauge and the X-axis; K₁, K₂, K₃, and K₄ are the four correction coefficients; P_c represents the confining pressure; and r and R stand for the inner and outer radii of the core, respectively.

At present, in the OC technique, hollow inclusion strain gauges used to measure the deformation or strain of the small borehole are all performed by bonding resistance strain gauges on the borehole wall. The resistance strain gauge is very sensitive to the temperature change. As the temperature changes, its resistance will change accordingly, and the corresponding output voltage will be generated in the bridge, and then the false additional strain value will be calculated. Hence, the influence of temperature change on the strain must be eliminated through temperature compensation measures. The traditional temperature compensation approach does not apply to cemented strain gauges, and the complete temperature compensation technology developed by Cai et al. (2010, 2013) solves this problem well. After temperature calibration and correction, the actual strain value induced by stress relief is acquired. In addition, when calculating stress using the measured strain values of small boreholes, it is necessary to know the deformation parameters i.e., elastic modulus and Poisson’s ratio, of the rock. Traditional calculation theories suppose that the rock is linearly elastic, and its deformation parameters are constants. In fact, rocks are generally nonlinear, and their deformation parameters vary with the stress level. Thus, a stress calculation approach with deformation parameters corresponding to the stress level has been proposed (Li et al. 2023b). Based on the actual strain values obtained and the deformation parameters at each measurement position determined by the confining pressure calibration test, the stress values involving magnitude and azimuth at each measuring point can be yielded. In the calculation program, a double iterative algorithm is developed and employed to ensure the accuracy of the stress calculation results.

When using the OC technique for stress measurement in the Linglong gold mine, the new technologies and approaches introduced above were applied. Moreover, a high-precision automatic strain acquisition system was also adopted in the measurement process, ensuring the records’ accuracy. In addition, the selected measuring points are representative in geology, and they are independent of the influence of artificial excavation sections and geological structures (such as faults and joints), i.e., located in the original rock stress zone. Consequently, the measurement results can fully characterize the regional stress state. The measurement process and the instruments and equipment used comply with approaches recommended by the ISRM (Sjöberg et al. 2003). The schematic diagram of the measurement equipment and field operations in the OC method is illustrated in Fig. 3. Based on the on-site stress relief test results, the confining pressure calibration results, and the temperature calibration results, the three-dimensional stress tensors of eighteen measurement points were calculated using relevant formulas and combined with the double iterative algorithm, as shown in Table 1. In Table 1, the “dip” is based on the horizontal plane, with an upward angle being positive and a downward angle being negative. The “direction” is 0° towards due north, and 360° when rotated clockwise once. The burial depth of the OC stress measurements in the mine covers 250–970 m, and there are multiple measurement points at some depth levels. To ensure the quality and comparability of the measured stress data, a globally recognized World Stress Map (WSM) quality ranking system (Heidbach et al. 2010) is used to check the stress data, and the stress data can be ranked as Category B.

Schematic diagram of the OC method for the stress measurement. a Typical measurement instruments and equipment. b Field operations

3.2 Hydraulic fracturing

The classical hydraulic fracturing (HF) technique is a reliable and effective method developed in the 1970s for directly measuring rock stress in the deep crust, which is also one of the recommended approaches promulgated by the ISRM (Haimson and Cornet 2003; Li et al. 2024) and has been widely applied in various major underground engineering practices, as well as in continental scientific deep drilling and geodynamic research on active fault zones (Zoback et al. 1980; Shamir and Zoback 1992; Zhang et al. 2017; Heidbach et al. 2018; Li et al. 2019b, c; 2023b). This technique is the latest development in the field of rock stress measurement and can provide stress information at greater depths than other methods. The basic principle of the HF method is to fix a pair of expandable rubber packers at a predetermined drilling depth section, seal a small section of the borehole as the test interval, and then pump high-pressure fluid (usually water) into the test interval until the rock on the borehole wall ruptures, thus inducing the generation of artificial hydraulic fractures in the strata around the borehole wall. In the HF test, with the increasing hydraulic pressure in the isolated section, the tangential effective stress on the hole wall will gradually decrease and finally become tensile stress. When it outweighs the tensile strength of rocks, fractures will appear on the borehole wall. According to the water pressure and crack position when the borehole rock wall is initially fractured as well as the water pressure when the rock wall is re-closed and re-opened, the stress tensor can be calculated based on some necessary assumptions (e.g., the basic elastic relationship exists between the recorded pressure and stress, as well as between the direction of rupture and the direction of stress) and theoretical calculation formulas (Eq. (2)). Note that the vertical stress is estimated based on the overburden weight.

where σ_H, σ_h, and σ_v are the maximum horizontal, minimum horizontal, and vertical principal stresses, respectively; P_s is the instantaneous shut-in pressure; P_r is the fracture reopening pressure; P₀ is the pore pressure and is equivalent to the hydrostatic pressure; γ is the average rock density and is assumed as 2.65 g/cm³; and H is the depth.

As shown in Eq. (2), the key pressure values used to calculate in-situ stress are selected from pressure-time records. Hence, the reliability of stress calculation results in the HF technique is largely decided by the accuracy of identifying the critical pressure on the pressure-time curve (Haimson et al. 2003). During the HF test, three critical pressures i.e., the breakdown pressure P_b, the fracture reopening pressure P_r, and the instantaneous shut-in pressure P_s, can be recorded, which are utilized to estimate the field principal stress. P_b is the peak pressure reached at the beginning of the hydraulic fracturing, which usually occurs in the first pressure cycle. Under the pressure P_r, the induced hydraulic fracture can be reopened during the pressure cycle after fracturing. To determine the P_r, the approach of superimposing the rising part of the pressure-time record in the post-fracture cycle with the corresponding part of the fracture cycle record can be used (Lee and Haimson 1989). P_s is the pressure reached after the pump is shut-off following breakdown or fracture reopening as the induced hydraulic fracture is closed, which is roughly equivalent to the stress acting perpendicular to the fracture surface. Theoretically, there should be an obvious inflection point in the test-interval pressure drop following pump shut off to indicate fracture closure, which can be adopted to calculate a more accurate P_s value. In practical testing, the inflection point is usually ambiguous, so to determine the inflection point, calculation methods such as single tangent, d t/d P, d P/d t, Muskat, and pressure-flow are available. Due to the differences in applicability and accuracy of these methods, it is recommended to use at least two or more calculation methods to accurately determine P_s (Haimson and Cornet 2003).

In a vertical or sub-vertical borehole in which a principal stress is parallel to the borehole, the fracture surface produced during HF is generally parallel to the borehole axis, and two fractures appear simultaneously at exactly opposite positions around the borehole (Fig. 4). Subsequently, the fractures will propagate along the orientation perpendicular to the minimum horizontal principal stress that provides the minimum resistance. In other words, the direction of fracture propagation is in line with the maximum horizontal principal stress orientation. The azimuth of the fracture can be identified according to the fracture trace on the borehole wall by using an impression packer and a compass or by using geophysical approaches such as a borehole televiewer (Ljunggren et al. 2003).

Illustration of a single-loop HF test system with a cross-section of an HF test zone showing the direction of fracture initiation and extension parallel to that of the maximum horizontal stress

Unlike most other measurement methods such as the OC technique, the HF technique does not require the use of precision instruments in the borehole to monitor the strain at a specific point. On the contrary, it directly estimates the average stress on a large area by recording hydraulic pressures. It uses simple downhole testing tools so that the method can theoretically be tested at any depth underground (Haimson 1978), which is an important reason why it has been widely applied since its proposal. The traditional HF method is two-dimensional, and for vertical drilling, the determined stress components are the maximum and minimum horizontal stresses. Because the principal stress orientations in the tectonic passive zone and the terrain flat zone are generally near the horizontal and vertical (Ljunggren et al. 2003), it is usually postulated that the components determined in vertical boreholes are these two principal stresses. Due to the attributes and efficiency of the HF method, it is particularly suitable for testing in the early exploration stage of engineering projects without accessible underground passages.

In the Shuiwangzhuang gold mine, the HF test was carried out by using a single-loop water channel measurement system in a deep borehole, and the testing processes followed relevant technical specifications (Liu et al. 2023). The final depth of the borehole is 1881.08 m. Combined with the field geological data, core conditions, core histogram, and logging data, the relatively complete section of the borehole wall was selected as the interval for fracturing testing, and a total of 21 sections of stress tests and 2 sections of impression orientation tests were completed. The fracturing process needs to be repeated 3–4 times in each testing section, and the repeated cycles yield redundant readings of the key pressures. According to the pressure-time curve recorded in the tests (Fig. 5), it can be concluded that the test effect is relatively ideal overall, the regularity of repeated measurements in each cycle is good, and the characteristics are consistent. Accordingly, the characteristic pressure points when the rock fractures can be clearly distinguished, and thus the in-situ stress state of each testing section can be determined with more confidence. Note that the single tangent, d t/d P, d P/d t methods with good applicability were adopted to determine the average P_s values of the fracturing planes of each test section, and the P_b, P_r, and in-situ tensile strength (T) of rocks at the test section were identified from the pressure-time records. The detailed pressure parameters and derived in-situ stress calculation results for each testing depth are listed in Table 2. The depth of the test sections varies from 318.80 to 1824.10 m. Based on the WSM quality ranking system (Heidbach et al. 2010), the determined stress measurements can be ranked as category D.

Typical pressure-time curves at different test depths in the Shuiwangzhuang gold mine (Liu et al. 2023)

4.1 Stress magnitudes

For the OC stress measurements (Table 1), the σ₁ determined at each measuring point is almost horizontal, with an included angle less than 15.8° to the horizontal plane, which is called the σ_H. For the σ₂ and σ₃, one is nearly horizontal and has an included angle less than 15.1° with the horizontal plane, which is regarded as the σ_h; and the other is nearly perpendicular, with an included angle smaller than 20° to the vertical plane, which is referred to as the σ_v. This confirms the hypothesis that a principal stress direction is vertical in the HF stress measurement is reasonable.

For the OC and HF stress measurements, within the measurement depth range, σ_H value is concentrated in 11.22–60.26 MPa, averaging 30.53 MPa; σ_h value ranges from 6.61 to 36.17 MPa, averaging 18.60 MPa; and σ_v value is between 6.63 MPa and 48.27 MPa, averaging 23.36 MPa, which are all compressive stresses. According to the relevant judgment standards of stress level in underground engineering (Li et al. 2022b), when σ_H value is within the range of 0–10 MPa, 0–18 MPa, 18–30 MPa, and greater than 30 MPa, it represents low, medium, high, and ultra-high stress levels, respectively. Among the 39 groups of OC and HF stress data, there are 10 groups with σ_H between 10 MPa and 18 MPa, accounting for 25.64%, with a buried depth of 250–528.6 m; 11 groups confined to 18–30 MPa, accounting for 28.21%, with a buried depth of 290–1045.5 m; and 18 groups larger than 30 MPa, accounting for 46.15%, with a buried depth of 570–1824.1 m. Apparently, the stress level in the Zhao–Ping metallogenic belt is considerably high overall. In particular, the shallow part within 300 m of the Linglong gold mine is at a high-stress level, and it reaches an ultra-high stress level after exceeding the depth of 570 m. The Shuiwangzhuang gold mine is at high and ultra-high stress levels beyond a depth of 1000 m. Moreover, compared with the crustal stress database of continental China (Xie et al. 2003), the Zhao–Ping metallogenic belt is further proven to be at a high stress level. The ore rocks in metal mines are basically hard rock lithology, and in mining, a large amount of deformation energy is often accumulated in the hard rock mass under the high-stress environment. Under certain triggering conditions, if the deformation energy accumulated in rock masses is suddenly released in the form of kinetic energy, it is easy to trigger dynamic disasters such as roof falling, spalling, and rockburst, posing a serious threat to the safety of underground personnel and facilities.

The individual σ_H, σ_h, and σ_v magnitudes provided in Tables 1 and 2 as a function of depth (H) are plotted in Fig. 6 with their respective linear fitting formulas. The line of σ_v = 0.027 H that was fitted by Brown and Hoek (1978) based on collected global stress data is also juxtaposed against the three principal stresses for comparison. The σ_H value obtained by the OC method is significantly greater than that derived by the HF method, showing a distinct discrete pattern (Fig. 6a). These two types of σ_H data exhibit almost different distribution forms, although they are linearly fitted together, resulting in a relatively low linear correlation. This interesting phenomenon may be caused by the following two reasons: firstly, the granite core obtained by drilling in the Linglong gold mine is relatively complete, and its elastic modulus is much larger than that of the granite core exposed by the HF drilling in the Shuiwangzhuang gold mine, which is conducive to the formation of a larger σ_H in the Linglong gold mine; secondly, the core and logging data of the HF borehole in the Shuiwangzhuang gold mine show that there are many fractured zones in the deep part of the borehole, especially in the depth range of 1131.40–1722.82 m and 1765.69–1821.93 m, which will lead to a lower stress level at the measured location. These factors result in the crustal stress of the Shuiwangzhuang gold mine being at a relatively low level throughout the entire Zhao–Ping metallogenic belt. Note that the independent σ_H data yielded from the OC and HF techniques present a good linear correlation. In comparison, the σ_h and σ_v increase approximately linearly with depth, showing a fairly high linear correlation (Fig. 6b and c). This indicates that the σ_h and σ_v determined by the OC method follow the same distribution pattern as those obtained by the HF method, although the σ_h and σ_v obtained by the OC method are slightly larger than the corresponding σ_h and σ_v obtained by the HF method. Moreover, the consistency between the self-weight stress estimated by the overburden weight and the vertical stress measured by the OC method indicates that the estimated self-weight stress can represent the vertical stress well, and the error between them is very small within the upper crust. The best-fit linear relationships of the σ_H, σ_h, and σ_v with depth are identified as follows:

Principal stresses variation with depth

Equation (3) constitutes the stress distribution model in the Zhao–Ping metallogenic belt, which is roughly consistent with the stress distribution patterns in the adjacent Bohai Strait (Zheng et al. 2017), the entire Shandong region (Li et al. 2017), and the Chinese mainland (Yang et al. 2014), but there are certain differences in the stress gradients and constant terms in each regression equation. This may be caused by the different databases used in regression calculation, the different statistical depth ranges, and the geological tectonic factors affecting the in-situ stress included in the regression results, and it also implies that the stress field in each area has its own distinguishing features.

In addition, these two gold mines have the same or similar geodynamic environment. To further compare the differences in stress fields between them, the relationship between the three principal stresses and depth of these two gold mines are presented in Table 3. The stress gradient of the Linglong gold mine (0.0575, 0.0296, and 0.031 MPa/m) is much greater than the corresponding stress gradient of the Shuiwangzhuang gold mine (0.0229, 0.0192, and 0.0265 MPa/m), and the difference between them may be caused by the following reasons: (1) From a mathematical perspective, the difference is largely associated with the data volume and testing depth in diverse mines; and (2) The differences in fault structures and rock mass properties in different measurement points have a significant impact on the stress measurements. The σ_H values at depths of 300, 600, 900, and 1200 m are calculated using their respective regression equations. Evidently, the stress values of the two gold mines are quite different, reflecting the uneven distribution of stress intensity in the Zhao–Ping metallogenic belt. The difference between local fault structures and local force sources is the main reason for the uneven distribution of stress fields. Notably, under the same or similar regional tectonic setting and stress environment, areas with fairly high-stress levels are prone to strong earthquakes (Xie et al. 2011), and accordingly, more attention should be paid to the area where the Linglong gold mine is located with high-stress values.

4.2 Stress regime

At present, the investigation of the stress field distribution characteristics is primarily according to the spatial linkage of the three principal stresses, which are the main indicators to characterize the basic features of the stress field in a region. The existing stress data indicate that the three principal stress magnitudes are generally unequal, and the stress magnitude and direction are unstable in time and space because the in-situ stress state is often affected by non-structural factors such as topography and geomorphology and changes to varying degrees. The in-situ stress field was divided into three categories: geostatic field, geodynamic field, and quasi-hydrostatic pressure field (Li and Miao 2016). Among the three principal stresses in the geostatic field, the maximum principal stress is approximately vertical and is roughly equal to the self-weight stress, while the intermediate and minimum principal stresses are in the horizontal orientation. Among the three principal stresses of the geodynamic field, the maximum principal stress is in the near horizontal orientation. The three principal stresses in the quasi-hydrostatic pressure field are approximately isotropic. In this study, among the three principal stresses obtained from the two gold mines, the maximum principal stress is approximately in the horizontal orientation, which belongs to the geodynamic field type. The determination of macroscopic stress field types can serve the design and safety production of mines in this region.

According to the three principal stress magnitudes, three categories of stress regimes, i.e., reverse (σ_H > σ_h > σ_v), strike-slip (σ_H > σ_v > σ_h), and normal (σ_v > σ_H > σ_h) faulting, were differentiated by Anderson (1951). The stress regime reflects the relationship between the fault geometry and the stress. Under different stress regimes, rock mass and geological structures (such as faults) have different mechanical response behaviors and activity modes. According to statistics (Table 4), among the 39 sets of stress data, the magnitude relationship of the three principal stresses in four groups is σ_H > σ_h > σ_v, accounting for 10.26% of all sets, belonging to a reverse faulting stress regime, which is in favor of the gestation and activity of reverse faults; the magnitude relationship of the three principal stresses in 24 groups is σ_H > σ_v > σ_h, accounting for 61.54%, belonging to a strike-slip faulting stress regime, which favors the formation and activity of strike-slip faults; and the magnitude linkage of the three principal stresses in the remaining 11 groups is σ_v > σ_H > σ_h, accounting for 28.20%, belonging to a normal faulting stress regime, which is beneficial to the formation and activity of normal faults. The normal faulting stress regime is reflected by the stress data of the Shuiwangzhuang gold mine. In summary, the stress regime of the Zhao–Ping metallogenic belt within the tested depth range is primarily characterized by σ_H > σ_v > σ_h, as also observed from Fig. 6, which is reasonably in line with the dominant stress regime revealed in Jiaodong Peninsula (Li and Cai 2018) and North China (Xie et al. 2011) and conforms to the motion features of fault structures in the Zhao–Ping metallogenic belt.

On the other hand, the stress regime in the study area is somewhat random with depth, but it also reflects certain regularity. Overall, the stress regime changes from the shallow-dominated reverse faulting type to the middle-dominated strike-slip faulting type and then to the deep-dominated normal faulting type, as shown in Fig. 7a. Moreover, according to statistics, the zoning of stress regimes in this area is noticeable. Generally, the proportion of these three determined stress regimes is significantly different at different depths. Specifically, strike-slip and reverse faulting stress regimes coexist at depths of 250–290 m, accounting for 57.14% and 42.86%, respectively; the stress regime at depths of 318.8–702.5 m is strike-slip faulting; strike-slip, reverse, and normal faulting stress regimes coexist at depths of 818.4–1379.5 m, accounting for 66.67%, 8.33%, and 25.00%, respectively; and the stress regime at depths of 1459–1824.1 m is normal faulting (Fig. 7b).

In addition, the stress regimes of the two gold mines are also different to some extent (Table 4). The maximum horizontal principal stress in each set of stress data of the Linglong gold mine is greater than the vertical component, indicating that the horizontal stress of this gold mine is dominant within the measured depth range, belonging to a typical tectonic stress field type, with the strike-slip stress regime being absolutely dominant. The theoretical consistency of the stress regime is reflected in the fact that there is no significant variation in the mechanical state of the rock and geological structure within the entire research depth, which has a positive effect on the stability of underground roadways and stopes. Note that at the same depth (such as 290 and 970 m), there are also significant differences in stress regimes, indicating that the relationship between σ_v and σ_h in local locations in the Linglong gold mine is unstable. The stress regime of the Shuiwangzhuang gold mine is related to its depth. That is, when the depth < 702.5 m, the stress regime is primarily strike-slip faulting type, while the depth ranges from 702.5 m to 1824.1 m principally shows a normal faulting stress regime. Thus, with increasing depth, the vertical principal stress in this gold mine gradually changes from the middle principal stress to the maximum principal stress. In other words, the stress field in the shallow part of the gold mine is predominantly dominated by the horizontal tectonic stress, while the stress field in the deep part appears to be predominantly driven by gravity. This result indicates that the Zhao–Ping metallogenic belt is in a complex stress regime. The stress regime closely corresponds to the regional stress conditions, and it is considered that the regional stress conditions are caused by different mechanical mechanisms.

a The stress regimes variation with depth and b the proportion statistics of different stress regimes in diverse depth intervals

4.3 Stress ratios

The dimensionless stress ratio (i.e., the ratio of two principal stresses out of three) is an effective parameter for characterizing the state of stress and has a high indicative value for tectonic and engineering applications. Four representative stress ratios, namely, the ratios of σ_H to σ_v (K_H), σ_h to σ_v (K_h), (σ_H + σ_h)/2 to σ_v (K_av), and σ_H to σ_h (K_Hh), are computed, and the functional relationships between these stress ratios and depth are given, as shown in Fig. 8. Overall, within the measurement depth range, the closer to the surface, the more scattered the distribution features of these stress ratios, and the fluctuation amplitude decreases as the depth increases. Specifically, the power form expressions are employed to fit the relationship between K_H, K_h, K_av, and depth (Fig. 8a-c), and the fitting results demonstrate that all three stress ratios exhibit a significant nonlinear downward trend with depth, approaching 0.93, 0.73, and 0.83, respectively. This also means that the dominant role of σ_H weakens with depth. After the depth exceeds 1000 m, these three stress ratios begin to stabilize. K_H and K_h are two useful indicators reflecting the impact of geological structures on stress, which are of great help to mining engineering construction, optimization, and design. K_H is limited to 0.92–2.64, with an average of 1.49. The significant difference between σ_H and σ_v indicates that the tectonic process has a clear directionality in different depths. K_h ranges from 0.68 to 1.15, averaging 0.82. From an engineering perspective, the influence of K_H and K_h must be fully taken into account in engineering practice. For example, the ideal cross-sectional shape of a roadway and a stope is an ellipse. If the ratio of the horizontal axis to the vertical axis of the ellipse and the ratio of the horizontal stress to the vertical stress acting on the cross-section are equal, the tangential stress values at each point on the boundary of the roadway and the stope are equal, that is, they are in a state of uniform compressive stress. This is very beneficial for reducing stress concentration in the surrounding rock of the tunnel and stope and ensuring their stability.

On the other hand, K_av can indicate the degree of rock compression in the crust. The greater the K_av value, the higher the degree of rock mass compression, and vice versa. K_av is distributed between 0.81 and 1.86, averaging 1.16. It shows that the shallow stress state in the Zhao–Ping metallogenic belt is predominantly controlled by tectonic stress, while the deep stress state is principally governed by self-weight stress. Furthermore, it is speculated that there may be a quasi-hydrostatic pressure field in the deep rocks in the study area. Based on 116 sets of stress data determined in many countries around the world, the best fitting equations of the relationship between K_av and depth (i.e., inner and outer envelopes) in the world are obtained (Brown and Hoek 1978), as provided in Fig. 8c, and their changing trends are similar to the results of this study. The K_av values obtained in the study area are located between the Hoek-Brown inner and outer envelopes, but markedly greater/smaller than the K_av value indicated by the inner/outer envelope. This finding indicates that stress distribution has strong regional features, which are not only associated with the lithology of a specific area but also prominently affected by regional tectonic activities. Thus, the determined stress pattern reflects the lithology as well as the historical and modern tectonic movement nature of this area.

In addition, K_Hh can reflect the anisotropy of horizontal principal stress to some extent. The distribution of K_Hh in the tested depth is relatively scattered, primarily concentrated between 1.25 and 2.96, averaging 1.79. Overall, K_Hh is large, which indicates that the anisotropy of horizontal stress is high and the tectonic activity is strong in the σ_H azimuth. Moreover, there is no clear functional relationship between K_Hh and depth, although a linear regression is used to roughly express the changing trend of K_Hh with depth (Fig. 8d). This may be due to the limited amount of stress data in the study area and the large differences in data volume at different depths. According to the theory of elasticity, the difference between σ_H and σ_h is closely associated with the shear stress in the rock mass. The failure of crustal rocks is usually triggered by shear stress. If the shear stress outweighs the shear strength of the rock mass, it will fracture and easily form geological structures such as faults and joints. The widely developed fault structures in the study area are probably associated with the higher horizontal differential stress in this region. Furthermore, the field investigation results of the rock structural plane of the mine roadway in this area also suggest that small-scale joints and cracks are also widely distributed. More importantly, in some special parts of the mining engineering system, such as in roadways, goaf, and other free faces, high differential stress is easily formed, which may lead to the deformation and failure of poor structural planes and rock masses. For the mine itself, the high differential stress in the surrounding rock will cause changes in the stored energy of the rock mass and may lead to engineering disasters such as spalling, roof falling, and even rockburst, which has a very adverse impact on the stability of underground mining projects. Some previous studies believed that high stress, especially high differential stress, in the rock mass is also a necessary condition for rockburst occurrence (Li and Miao 2017). Only intact and high-strength rock masses can withstand high shear stress and sustain their stability. Hence, K_Hh also reflects the stress conditions of the engineering rock mass in this region, and the surrounding rock stability needs special attention in mine production.

Variations in a K_H, b K_h, c K_av, and d K_Hh with depth

4.4 Stress orientation

The knowledge of the stress orientation, especially the maximum horizontal stress orientation, is extremely important for understanding the regional tectonic background and the current movement characteristics of fault structures and tectonic plates (Shamir and Zoback 1992; Chang et al. 2010; Li and Cai 2018; Li et al. 2019b). The stress direction data obtained in the two gold mines in the Zhao–Ping metallogenic belt are plotted in the view of depth profile and rose diagram in Fig. 9. As shown in Fig. 9a, a small amount of σ_H direction in all data fluctuates with increasing depth (the fluctuating stress direction data comes from the Linglong gold mine), but most σ_H orientations are predominantly distributed in 91.3°–163.5°, averaging 110.2°. That is, the σ_H orientations of the majority of measurement points are well-oriented in the WNW–ESE orientation. This indicates that the stress orientation in this region is less influenced by tectonic and non-tectonic factors although the stress measurement points in the Linglong gold mine are adjacent to the Linglong fault and the measurement points in the Shuiwangzhuang gold mine may be within the influence range of the Potouqing fault, and the σ_H direction measured is comparatively stable and well constrained within the tested depth. Note that the change in local stress direction may be due to the impact or control of local geological factors and force sources, and the local heterogeneity generated in the rock stratum interferes with the stress direction to varying degrees, resulting in the local rotation or decoupling of the dominant WNW–ESE oriented regional tectonic stress pattern. This phenomenon can be expected normally due to the extremely complicated causes of rock stress. The degree of deflection in σ_H direction is dependent on the comparison between interface and geomechanical properties (Rajabi et al. 2016a, b).

In addition, the σ_H orientations of the 18 measurement sits (except three sits) identified in the Linglong gold mine by the overcoring method are similar, distributed in the range of N38.60°W to N88.70°W, averaging N57.56°W (Fig. 9b). The σ_H orientation of the two test sections measured by hydraulic fracturing method in the Shuiwangzhuang gold mine is N66.20°W and N71.50°W, respectively, with an average of N68.85°W, as shown in Fig. 9c. Apparently, the dominant stress directions revealed by diverse measurement techniques in the two gold mines are in good agreement. This not only suggests that the stress measurements in the two mines are reliable, showing the same type of stress pattern, but also implies that these mining districts belong to a similar or identical geological tectonic unit, and the force sources controlling the stress field of the entire study area may be consistent. The σ_H orientation plays a crucial role in the stability of subsurface excavations, especially in small-scale rock mechanics analysis. According to the theory of elasticity, the axis of the underground excavation, such as the roadway and stope, is best in line with the σ_H orientation, because under this condition, two smaller principal stresses act on the vertical section of the underground excavation, which is beneficial for its stability. Of course, this layout and design should also comply with the requirements of the mine engineering geological conditions and mining production operations.

a Variations in σ_H orientation with depth in the Zhao–Ping metallogenic belt and b The σ_H orientations on the rose diagrams of the Linglong gold mine and c The Shuiwangzhuang gold mine

On the other hand, according to the actual stress measurements interpreted by using different methods and focal mechanism solution information near the study area provided by other researchers in recent years (Ding et al. 1986; Wang et al. 2011; Zheng et al. 2013; Pei 2020; Zhang 2021), combined with the stress data identified in this study, the distribution and direction of σ_H in the study area and surrounding areas are drawn in a map view (Fig. 10a). This is a detailed tectonic stress field map of the Jiaodong Peninsula at present. Dramatically, although the near- and far-field stress indicators are located in diverse tectonic and geographical positions, the σ_H orientations determined in this study are in good agreement with those obtained by other researchers. Therefore, different stress measurements and focal mechanism information are consistent with the assumption of horizontal tectonic stress regulating the shallow stress pattern under normal circumstances. Moreover, the large-scale stress field map of North China (Fig. 10b), including more types of stress indicators and plate motion characteristics, shows the stress direction is roughly identical to that of this study, which is also in accord with the WNW direction of the Pacific plate subduction towards the Jiaodong Peninsula. This good regional consistency is not a coincidence, suggesting that the current regional stress field is quite stable in distinct geological backgrounds and further revealing that the study area and the vicinity may be dominated by similar or identical first-order tectonic stress patterns. Generally, the stress measurements in this area and surrounding areas indicate that the anisotropy in the σ_H orientation is not significant, and the stress field is represented by a WNW–ESE-oriented extrusion environment.

a σ_H orientations determined in and around the Zhao–Ping metallogenic belt and b present-day tectonic stress field directions in North China (after Xie et al. 2011)

5.1 Stress orientation reflected by geological structures

Structural planes, such as joints and fissures, as a kind of geological structure trace with no or minimal displacement in the rock mass, are associated with and derived from other geological structures under a certain tectonic stress field and can reflect the contour of main structures and the characteristics of tectonic movements in a region (Ding 2003; Hou et al. 2006). Most joints and fissures maintain a certain internal connection with tectonic stress. Understanding their regularity can infer the tectonic stress field and tectonic motion mode at the time of their formation, providing fundamental information for the mechanical analysis of the regional stress field and tectonic system. By drawing the geometric data of rock mass structural planes from field investigations and statistics into a rose diagram or isodensity diagram, the number, direction, and development characteristics of structural planes in an area can be intuitively and clearly displayed. Investigation of rock mass structural planes was conducted at several depth levels (580, 750, and 870 m) in a mine in the study area, and a large amount of geometric information of rock mass joints with a length of more than 20 cm was recorded. Isodensity maps of joint strikes at different depth levels were plotted through stereographic projection and cluster analyses, as presented in Fig. 11. It can be observed that there are two groups of dominant directions in the strike of joints at these depth levels. The dominant strikes of joints at the depth of 580 m are 64.52° and 127.08°, respectively (Fig. 11a), and the bisector direction of their acute angles is 95.80°; the dominant strikes of joints at the depth of 750 m are 161.88° and 139.21°, respectively (Fig. 11b), and the bisector direction of their acute angles is 150.55°; and the dominant strikes of joints at the depth of 870 m are 118.06° and 70.85°, respectively (Fig. 11c), and the bisector direction of their acute angles is 94.46°. According to Mohr’s shear fracture theory, the acute bisector of two groups of dominant joint strikes corresponds to the compressive stress orientation, while the obtuse bisector corresponds to the tensile stress orientation (Hou et al. 2006). Thus, the compressive stress orientation reflected by joint strikes is NW–WNW, which is roughly in line with the identified stress orientation, indicating that the joint investigation results agree well with the measured results. It should be noted that due to the complexity of the occurrence of structural planes in the strata, in some cases, it is not necessarily the case that the acute angle of joint strike corresponds to the compressive stress orientation and the obtuse angle corresponds to the tensile stress orientation, or even the opposite situation may occur. Consequently, it is not sufficient to judge the dominant direction of the stress field solely according to the statistical results of the structural plane strike, and other geological data, such as the source mechanism solution, must be supplemented.

Stereographic projection networks showing the relationship between the faults and the tectonic stress field

Additionally, as mentioned earlier, the Huang–Ye arc-shaped fault and Zhao–Ping fault are two representative faults in the study area, which form a conjugate structure on the transverse plane, with the rock mass sandwiched between them being the Linglong-type bedrock. These two faults have opposite inclinations, which are obviously the result of lateral compressive stress acting on the Linglong-type granite in their generation stage, resulting in the formation of a conjugate shear system on the profile (Miao et al. 2012). Based on the occurrence of these two faults, the relationship between these faults and the tectonic stress field can be obtained using a stereographic projection network (Cai 1995). As shown in Fig. 12, F1 is taken as the southwest end of the Huang–Ye arc-shaped fault, with a strike of 40°, an inclination of NW, and an average dip angle of 37.5°; and F2 is taken as the southwest end of the Zhao–Ping fault, with a strike of 20°, an inclination of SE, and an average dip angle of 37.5°. From the stereographic projection network, the σ₁ has an orientation of 120°, with a dip angle of 0°; the σ₂ has a direction of 210°, with a dip angle of 7.5°; and the σ₃ has a direction of 30°, with a dip angle of 82.5°. Hence, the maximum principal stress orientation inferred based on the fault characteristics is around 120° (i.e., N60°W), which coincides with the measured stress field orientation near WNW–ESE. It can be deduced that the stress measurement results appear to be in line with the conclusion of structural trace analysis by geomechanics methods.

A stereographic projection network showing the relationship between the faults and the tectonic stress field

5.2 Regional tectonic evolution

On the scale of the geological period, the stress field is constantly variable. During the long geological evolution process, the Jiaodong Peninsula where the Zhao–Ping metallogenic belt is located experienced multiple tectonic motions from the Indosinian period to the Yanshanian period and the Himalayan period. The characteristics of the current stress field are often the result of multi-period tectonic movements, and the impact of tectonic movements in different periods on the stress field varies.

During the Indosinian period, the collision between the southern margin of the North China plate and the Yangtze plate formed a nearly SN or NNE trending compressive tectonic stress field (Fig. 13a). In this period, in the structural layers of Jiaodong group and Jingshan group, fold structures were dominated by nearly EW and WNW direction, such as the Qishan syncline, Guandi syncline, and Qixia anticlinorium developed in the Jiaodong group, and the Magezhuang–Jigezhuang syncline, Nanhuangtong anticline, and Lugezhuang anticline developed in the Jingshan group (Liu 2017; Wang 2020), reflecting the effect of the SN trending compressive stress. During this long deformation period, the early stage was generally characterized by the formation of EW-, WNW-, and ENE-oriented structures, while the late stage was characterized by the formation of relatively open SN-oriented folds, with axial planes mostly tilting eastward (Lin et al. 2000). Under the effect of the SN or NNE trending compressive stress, two groups of torsional fracture planes in the NE–SW and NW–SE orientations were formed, and the NE–SW fracture plane was the most developed, which was reformed by the later Cathaysian and Neocathaysian structures.

During the Yanshanian period, the stress field formed by the Pacific plate pushing the Chinese mainland and the SN trending tectonic stress field in North China during this period were superimposed, resulting in the NW–SE trending compressive tectonic stress field in eastern China (Fig. 13b). The Jiaodong Peninsula is under its control and also exhibits NW–SE compression. At this time, this region is characterized by strong fault block movement, accompanied by further reconstruction and remelting of Linglong-type granite, forming an oblique ladder-like structural pattern with well-developed NE and NW trending fault structures, as well as accompanied by the formation of NE trending fold structures, such as the syncline structures in the Lower Cretaceous in the Jiaolai Basin (Lin et al. 2000; Shen 2006), which are the result of the sustained action of the NW–SE trending stress field in this period. The differential movement of the Jiaobei block contributed to the formation of the Jiaolai basin and the eruption of intermediate-basic volcanic rocks. Conversely, the formation of the Jiaolai basin and the further development of NW–SE-oriented stress promoted the development of NNE–NE trending structures in this area. Typically, the Zhao–Ping fault evolved from a reverse fault to a normal fault, and the contact part between the Linglong granitic rock mass and the Guojialing rock mass in its footwall evolved into the Jiuqujiangjia fault, which showed a downward trend of the upper wall and a small right-lateral strike (Yang et al. 2022), and its driving force may come from the upper uplift of the Guojialing rock mass under the effect of the NW–SE trending compressive stress.

During the Himalayan period, eastern China was subducted and pushed by the Pacific plate toward the Chinese mainland, the southwestern China was collided and squeezed by the Indian plate toward the NE direction, and the northern China was blocked or pushed southward by the Eurasian plate, leading to the stress field in the WNW direction in eastern China (Fig. 13c), which has continued to this day. In the process of stress transformation, the early structures were reformed to varying degrees. Under the action of WNW-oriented stress, faults in the ENE or near EW direction are generally in a tensile state, so they often become tensile fracture zones. The NE trending faults are all in a compressive state, exhibiting the activity characteristics of reverse faulting. For example, the Potouqing fault and its secondary faults have undergone inertial motion, and both the Potouqing fault and the Jiuqujiangjia fault have been transformed from early normal faults into reverse faults, while also exhibiting sinistral strike-slip movement with relatively small translational distances (Yang et al. 2022). At the same time, NW trending fault structures were formed in the area, which are the main ore-breaking structures and have sheared and reformed the previous structures, alteration, and mineralization.

In summary, the maximum compressive stress orientation of this region shifted from the nearly SN or NNE direction during the Indosinian period to the NW–SE direction during the Yanshanian period, and finally progressively became the WNW direction during the Himalayan period. The stress orientation identified in this study is the same as that in the Yanshanian period and Himalayan period, which also indicates that the current stress field in the study area basically inherits the stress field of the latter two periods, but is mainly dominated by the Himalayan period. This reflects that the maximum compressive stress direction that affects the current main tectonic movement in this region is the WNW direction, and also verifies the view that the stress field in an area is mainly controlled by the recent tectonic movement, particularly the active tectonic system. Note that the measured stress direction in the NE direction may be associated with the development of the historical stress field. Hence, the stress measurements further confirm the mechanical genesis and action mechanism of the geological structures in this region from practice, and the good coincidence between them precisely indicates the accuracy of the stress measurements.

Schematic diagram of tectonic stress field evolution in the Zhao–Ping metallogenic belt

5.3 Fault structure stability assessment

As mentioned above, the study area is a typical tectonic active area, which contains extensive active fault structures with diverse scales and orientations. Fault activity analysis is a key connotation for assessing crustal stability and seismic potential. The field investigation results of a large number of earthquake events indicate that when an earthquake occurs, some active faults may slip, and conversely, if a deep and large fault slips suddenly, it is likely to trigger an earthquake (Li and Cai 2022b). According to statistics, the vast majority of seismic activity is predominantly governed by fault zones and regional fault systems (Li et al. 2023a). Essentially, the gestation and emergence of faulting and earthquakes are a process of energy accumulation and mechanical instability (Reasenberg and Simpson 1992), which is highly dependent on the stress conditions. To exactly evaluate the potential slippage and seismic risks of active faults, besides considering the structural background and activity characteristics of active faults, analyzing the stability of the geomechanical state of faults under the action of the current stress environment is a crucial component. Thus, using the measured stress data to evaluate the fault activity, distinguish the frictional strength of faults, and discuss the possible seismic activity in this area has important seismic and geological significance.

Based on the Coulomb frictional failure criterion (Jaeger et al. 1979), when the mechanical state of the natural fault plane satisfies τ ≥ µσ_n (where τ is the shear stress, µ is the fault friction coefficient, and σ_n is the normal stress), the fault is in an unstable state and may experience slip and dislocation along the optimally oriented plane. Thus, the fault activity can be assessed by evaluating the limited friction coefficient. For cohesionless faults, the ratio of the maximum shear stress to the effective average stress, µ_m, can be expressed as a function of µ (Eq. (4), corresponding to the case where a critically oriented fault is at the friction limit; and when the friction limit is exceeded, the fault will slip along an angle β (Eq. (5) (Jaeger et al. 1979; Townend and Zoback 2000).

where µ_m is a dimensionless parameter and has a similar physical meaning to µ; β is the angle between the normal of a critically oriented fault plane and the σ₁ azimuth; and σ₁ and σ₃ are equal to the measured σ_v and σ_h, σ_H and σ_h, and σ_H and σ_v for normal, strike-slip, and thrust faulting regimes, respectively (Anderson 1951).

The parameter µ_m can be used to quantitatively weigh the stress accumulation level (SAL) in the upper crust. A larger value of µ_m indicates that the SAL is higher and the fault is more unstable, and vice versa. As the SAL reaches a critical range, the stress will be released and redistributed through regional fault activities or even earthquakes, to maintain the stability of the crust. When analyzing the fault stability in the study area, the appropriate µ value should be selected first. The determination of µ value is generally based on Byerlee’s law (Byerlee 1978), which indicates that when the stress value is less than 200 MPa, the µ value of most rocks is 0.85 in indoor experiments; when the stress value is more than 200 MPa and less than 2000 MPa, the µ value of rocks is 0.6, and the internal friction coefficient of crustal rocks is basically 0.6–1.0. Regarding the selection of µ values, many researchers worldwide have conducted extensive research on this issue, believing that there is a certain weakening of the fault friction coefficient under actual conditions and even the friction coefficient of some faults has been degraded to around 0.2 because of the special composition of fault gauges (Morrow et al. 1982; Tanaka et al. 1998; Chang et al. 2010; Wang et al. 2012; Li and Cai 2018; Li et al. 2019b, 2022a). That is, the friction coefficient of natural faulted rocks may be less than the scope delineated by Byerlee’s law. As a consequence, after comprehensive consideration, it is believed that the range of µ = 0.2–1.0 is more appropriate. In this case, the corresponding µ_m is in the range of 0.2–0.7. Generally, when µ_m is between 0.5 and 0.7, the SAL is relatively high, the fault is in the ultimate stress state, and the fault stability is in a critical state; and once µ_m exceeds 0.7, the fault is prone to sliding instability (Townend and Zoback 2000). As µ_m is between 0.3 and 0.5, the SAL is moderate and the fault is relatively stable; and as µ_m is smaller than 0.3, the SAL is low and the fault is in a stable state.

The relative relation between the maximum shear stress and the effective average stress yielded from the measured stress data and the variation in the calculated µ_m value with depth in this region are presented in Fig. 14. Apparently, as shown in Fig. 14a, the µ_m values in this area are basically greater than 0.2, but they are all lower than the upper critical stress limit value of µ_m = 0.7 for the emergence of frictional slippage on optimally oriented faults. As a result, under the current tectonic stress conditions, the possibility of shallow faults across this area being reactivated and experiencing shear failure is small overall. Specifically, the µ_m value is primarily concentrated in the range of 0.3–0.5, accounting for 43.59%, of which 23.08% comes from the Linglong gold mine and 20.51% comes from the Shuiwangzhuang gold mine. There is also a portion of the µ_m values distributed within the range of 0.2 to 0.3, accounting for 33.33%, all of which come from the Shuiwangzhuang gold mine. This implies that the stress accumulation in the shallow crust in this sub-area is generally at a moderate to low level and the likelihood of reactivation of the faults is relatively low at present. Only when the fault friction coefficient in this sub-area is as low as 0.2, the fault would lose stability and slip. The remaining µ_m values are limited between 0.5 and 0.7, accounting for 23.08%, all of which come from the Linglong gold mine. Part of the data in the Linglong gold mine reaches or exceeds the lower critical stress limit of µ_m = 0.5, indicating a relatively high level of stress accumulation in local sub-areas of the study area. In this case, some well-oriented faults may theoretically approach or reach frictional equilibrium and are likely to be reactivated to slide under the influence of endogenous or exogenous factors. In summary, the stress state derived from the stress measurements is completely in accord with the Coulomb friction failure criterion, with a friction coefficient of around 0.2–1.0; and some sub-areas in this region currently have high SALs, which can easily lead to local fault instability and new seismic activities. Additionally, the SAL in the Linglong gold mine is significantly higher than that in the Shuiwangzhuang gold mine, so the faults in the Linglong gold mine area are comparatively easier to reactivate. This finding implies that the region is in an imbalanced stress condition, and the SAL in different sub-areas is distinct, which is associated with geological factors such as local geological structure, differential uplift, heterogeneity of crustal structure, and interactions between local secondary blocks. These geological factors produce local heterogeneity in the crust, leading to local stress variation. Meanwhile, it may also reflect that the stress level in this region is still in a dynamic adjustment process due to seismic activity. Notably, although the assessment of the fault reactivation possibility in this area is confined to on-site testing and stress data analysis, investigations through other independent approaches (Li et al. 1991; Huang et al. 2007; Zheng et al. 2015; Li and Zheng 2022) also encourage the speculation that we proposed. Hence, Fig. 14a can afford a theoretical basis for fault slippage and earthquake prediction in this region.

In addition, as shown in Fig. 14b, the calculated µ_m value varies greatly with depth, and there is no remarkable functional relationship between them. However, overall, µ_m gradually decreases with depth. The µ_m value in the shallow part (less than 600 m) is relatively large, while the µ_m value in the deep part (greater than 600 m) is relatively small, which may be caused by the influence of non-structural factors in the shallow part. The µ_m values are clustered between 0.18 and 0.65, and the majority of them are principally in the range of 0.2 to 0.5, with an average of 0.37. This not only implies that this region is currently at a moderate to low level of stress accumulation overall, and locally at a high level of stress accumulation, but also indicates that regional faults are in a state of equilibrium or subcritical equilibrium. Furthermore, µ_m can also reflect the frictional strength of faults to some extent from the perspective of stress accumulation (Li et al. 2022a). If the SAL in the area where the fault is located is high, it often has a high frictional strength (Li et al. 2017; Zheng et al. 2017). Therefore, it can be deduced that the faults in the study area may have a medium to slightly high frictional strength at shallow depths. Nevertheless, there are still potential faulting reactivation and seismic risks in this area in the future. Moreover, according to the distribution range of µ_m values in this area, µ_m = 0.2 and µ_m = 0.5 are suggested as the lower and upper limits for predicting and analyzing future fault stability in this region, respectively.

a Evaluated SAL and b Changes in µ_m with depth

It should be emphasized that the activation mechanism of faults is extremely complicated due to many influencing factors. Fault slip can be caused not only by growing shear stress but also by descending normal stress or growing pore pressure. Some conditions under which fault reactivation may be induced are illustrated in Fig. 15. When a fault is subjected to a large horizontal stress and a minimum vertical stress, removing the overlying layer through some human activities (such as quarrying and mining) will weaken the vertical stress (Li et al. 2023a). As a result, the difference between horizontal and vertical stresses will correspondingly increase, which will expand the diameter of the Mohr circle presented in Fig. 15a, intersecting with the rock failure curve. If the vertical stress decreases sufficiently, it may induce shear sliding in the form of thrust faulting. Conversely, some conditions such as water storage in surface reservoirs and barrier lake reservoirs lead to a growth in vertical stress, thereby raising the difference between vertical principal stress and minimum horizontal principal stress. This will also enlarge the diameter of the Mohr circle (Fig. 15b), allowing the Mohr circle to intercept the rock failure curve, thereby increasing the chance of shear slippage in the form of normal faulting. This induced slip emerges preferentially when the maximum principal stress is perpendicular. Moreover, under any stress state, natural rainfall or injection of fluids into faulted areas will increase the reservoir pressure, and local strong fluid pressure disturbances reduce effective stress (Fig. 15c). When the reservoir pressure increases rapidly enough to cover the pore elastic effect, shear slippage is likely to arise in the intermediate principal stress plane. In stress environments adapted to this mechanism, many faulted areas have experienced fault sliding and seismic events (Manga et al. 2016; Grigoli et al. 2018; Lei et al. 2019). In particular, if the horizontal stress is dramatically changed by fluid removal, fault sliding will probably take place, as revealed by theoretical models (Segall 1989).

Mohr-Coulomb representation of different conditions under which fault reactivation may be induced: a The reduction of the vertical stress σ_v; b The increase of the vertical stress σ_v; and c The reduction of the effective stress (i.e., the increase of the reservoir pressure P_i due to fluid injection)

1. (1)

   The two types of stress data in the Zhao–Ping metallogenic belt exhibit almost different distribution forms, resulting in a relatively low linear correlation. The overall stress level is considerably high, and the distribution of stress intensity is uneven, which can be attributed to the difference between local fault structures and local force sources. The stress regime is primarily characterized by σ_H > σ_v > σ_h, which conforms to the movement features of fault structures in the Zhao–Ping metallogenic belt. Moreover, the stress ratios K_H, K_h, and K_av exhibit a significant nonlinear downward trend with increasing depth, approaching 0.93, 0.73, and 0.83, respectively, and the distribution of K_Hh in the tested depth is relatively scattered, primarily concentrated between 1.25 and 2.96, averaging of 1.79.

2. (2)

   The σ_H orientation measured in the Zhao–Ping metallogenic belt is comparatively stable and well-constrained within the tested depth and is well-oriented in the WNW–ESE direction, which is less affected by tectonic and non-tectonic factors. The determined σ_H direction is roughly identical to various stress indicators and plate motion characteristics.

3. (3)

   The orientation of the principal compressive stress in the Zhao–Ping metallogenic belt reflected by joint strikes is NW–WNW, which is roughly in line with the measured stress orientation. Furthermore, the stress orientation in this area inferred based on the fault characteristics also agrees fairly with the measured stress orientation near WNW–ESE. Additionally, the maximum compressive stress orientation shifted from the nearly SN or NNE direction during the Indosinian period to the NW–SE direction during the Yanshanian period, and finally progressively became the WNW direction during the Himalayan period. This indicates that the present-day stress field in this area basically inherited the stress field of the latter two periods, but is mainly dominated by the Himalayan period.

4. (4)

   The µ_m values in the Zhao–Ping metallogenic belt are basically greater than 0.2, but they are all lower than the upper critical stress limit value of µ_m = 0.7 for the emergence of frictional slippage on optimally oriented faults. Thus, under the current tectonic stress conditions, the possibility of shallow faults across this area being reactivated and experiencing shear failure is small overall. Nonetheless, a relatively high level of stress accumulation exists in local sub-areas of the study area, and thus some well-oriented faults may theoretically approach or reach frictional equilibrium and are likely to be reactivated to slide under the influence of endogenous or exogenous factors. Moreover, according to the distribution range of µ_m values in this area, µ_m = 0.2 and µ_m = 0.5 are suggested as the lower and upper limits for predicting and analyzing future fault stability in the area, respectively.