Introduction

During drilling operations, the interaction between drilling fluid and formation can cause a reduction in the mechanical strength of the formation. Faults and large-scale natural fractures in the formation can serve as migration pathways for the drilling fluid, leading to a series of issues such as wellbore instability, sloughing, lost circulation, and so on (Bozorgi et al. 2022; Fang et al. 2023; Li 2022; Li et al. 2022; Sheng et al. 2021; Wang et al. 2016). These problems result in decreased production efficiency, increased extraction costs, delays in construction progress, and a decrease in the overall economic benefits of the well.

When encountering faults during drilling, the fault plane may become a pathway for the transport of drilling fluid, causing drilling fluid loss. When there are highly permeable formations near the fault, drilling fluid may even pollute the formation and aquifer (Alawattegama et al. 2015; Ethridge et al. 2015; Llewellyn et al. 2015; Reagan et al. 2015). Moreover, it increases the contact surface between the drilling fluid and the formation, leading to a decrease in the mechanical strength of the formation and changes in the in-situ stress field. Therefore, many scholars have conducted research on the mechanism and influencing factors of fault activation.

With continuous research, numerous scholars have found that clay minerals in rock formations undergo a process of self-absorption when exposed to water, leading to hydration expansion and a subsequent reduction in the strength of the rock mass (Al-Maamori et al. 2019; Yang et al. 2020; Zhang et al. 49,50,c). Generally speaking, different types of clay are formed by the arrangement of tetrahedral and octahedral sheets in different patterns. If a clay consists of one tetrahedral sheet and one octahedral sheet, it is called a 1:1 (T–O) clay. On the other hand, clays with a 2:1 (T–O–T) structure, such as montmorillonite or illite/smectite mixed layers, have a stronger attraction to water (Abbas et al. 2021; Choo and Bai 2015). The extent of self-absorption and hydration is greater with a higher clay mineral content. The hydration process can cause the formation and propagation of new cracks, with multiple microfractures intersecting to form macroscopic fractures (Ma et al. 2016; Sui et al. 2018; Xue et al. 2018). Furthermore, different types of clay minerals have varying effects on the hydration of shale, resulting in different changes in the micro-pore structure, porosity-permeability properties, and mechanical properties after hydration (Al-Maamori et al. 2016a, b; Al-Maamori et al. 2016a, b; Liu et al. 2017; Ma and Chen 2014). Moreover, the anisotropy of shale introduces a lot of uncertainties in the actual drilling process. Studying the anisotropy of shale can provide some reference for the safe mud density window during drilling operations (Zheng et al. 2019, 2023).

Currently, research methods on fault analysis primarily fall into two categories: quantitative analysis using computational models and qualitative analysis through numerical simulations to investigate the factors influencing fault activation. Studies have found that changes in pore pressure and elastic shear stress are the main factors that induce fault instability (Hu et al. 2018; Khan et al. 2020; Zhang et al. 2020). The mineral composition of the fault plane can affect the frictional strength and thus control the stability of the fault. With an increase in layered silicates, the frictional strength decreases (Zhang et al. 2019). Temperature also plays an important role in controlling the stability of fault gouge. Within the range of 30–300 °C, higher temperatures lead to more pronounced instability of the fault gouge (An et al. 2020), and Mohr–Coulomb Envelope can effectively reflect the impact of mining activities on fault stress (Ji et al. 2012; Zhao and Jha 2021). To investigate the mechanical characteristics and stability of faults under mining influence, theoretical formulas have been derived to calculate the normal and shear stresses on the fault plane. Mining operations induce additional normal and shear stresses on the fault plane, with an increase in shear stress playing a dominant role (Li and Zhou 2019; Zhu et al. 2016). Mining operations on the working face can lead to a decrease in normal stress on the fault plane. The additional tensile stress generated can reduce the shear strength of the fault plane, promoting fault activation. The displacement difference between the rock masses on both sides of the fault plane also increases with the increasing dip angle of the fault (Guo et al. 2023, 2022; Wang et al. 2020). Different types of faults have different abilities to resist sliding. Due to the higher normal stress, reverse faults have greater shear strength and are less prone to shear slip, but they continuously accumulate energy (Kong et al. 2022). The possibility of fault activation increases with larger elastic modulus, higher Poisson’s ratio, and smaller cohesion of the rock masses in the fault zone (Zhang et al. 49,50,c).

This paper selects shale from the M area of the Ordos Basin for study. The rock samples that need to be soaked are immersed in water-based drilling fluid with a drilling pressure difference of 2 MPa and a temperature of 50 °C. Through mechanical experiments on original rock samples and samples immersed in water-based drilling fluid, the influence of water-based drilling fluid on the mechanical properties of shale is analyzed. Based on the spring combination model and fault activation theory, the factors influencing fault activation instability are analyzed, providing a certain reference for assessing the risk of fault activation and slip.

Mineral composition and structural characteristics

The rock samples were ground into powder and the clay minerals were extracted using a water extraction method. The samples were then prepared into thin sections, and the mineral composition of the whole rock and the clay mineral content were determined using an X-ray diffractometer. The test results are shown in Tables 1 and 2.

Table 1 XRD test results
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Table 2 Clay content test results
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The whole rock mineral analysis results of the sampled rocks (Table 1) indicate that the mineral composition of the sampled rock primarily consists of quartz and clay, with quartz content ranging from 34.0 to 54.1% and clay minerals comprising 9 to 40.1%. Additionally, there are significant proportions of feldspar, calcite, and in some tests, the presence of pyrite, siderite, and Analcime was observed. The clay mineral analysis results (Table 2) indicate that the clay minerals do not include montmorillonite, and the predominant types of clay are illite/montmorillonite mixed layers, illite, and chlorite. Illite/montmorillonite mixed layers make up 36 to 97% of the clay content, while illite is mainly found in the range of 21–32%, and chlorite ranges from 13 to 38%. From the analysis of the rock mineral composition in the working area, it is evident that clay content is high. Although there is no highly expansive montmorillonite in the clay, there is a significant presence of illite/montmorillonite mixed layers. Therefore, the shale in the working area still exhibits some degree of water sensitivity.

The scanning results of field emission electron microscope are shown in Fig. 1. The quality of storage space determines the strength of the reservoir capacity. In the M area of the Ordos Basin, the minerals in shale are oriented along the bedding direction (Fig. 1a), and the surface morphology perpendicular to the bedding is relatively dense (Fig. 1b). There are numerous microscopic fractures (Fig. 1c) and pores (Fig. 1d). Microscopic fractures are mainly elongated, while micro-pores are mostly circular to elliptical. This not only improves the storage space but also enhances the connectivity of each storage space, making it an excellent site and channel for the storage and migration of shale oil and gas. Simultaneously, as micropores and microfractures develop, under the pressure difference created by drilling fluid injection, the drilling fluid can enter the formation through microfractures. On one hand, this can lead to hydraulic fracturing of the existing microfractures, expanding them and further fracturing the formation. On the other hand, microfractures act as channels, increasing the chances of interaction between drilling fluid and clay minerals, reducing formation strength, and increasing the risk of drilling fluid entering faults, thereby potentially triggering fault activation.

Fig. 1
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Microscopic features of M district shale rock sample

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Mechanical properties and results analysis

The clay minerals in the M area shale contain illite/montmorillonite mixed layers and exhibit a certain degree of water sensitivity. Additionally, microfractures and micropores are well-developed, providing pathways for the interaction between drilling fluids and the formation. When drilling encounters faults, drilling fluid may leak, and its interaction with the formation can affect the mechanical properties of the formation. It can also impact the original stress field in the formation, subsequently influencing the faults and potentially causing fault activation and slip. Therefore, it is necessary to conduct experimental research on the changes in the mechanical properties of M area shale before and after immersion in drilling fluids.

The prepared shale samples were divided into two batches. One batch of the samples was kept in its original condition, and mechanical tests were performed. The other batch of samples was treated by immersion in water-based drilling fluid, and the same mechanical tests were conducted. Various tests were conducted, including indentation hardness tests, tensile tests, shear tests, and triaxial tests. For the indentation hardness and tensile tests, the samples were immersed for 24 h, 48 h, and 96 h. For the shear tests and triaxial tests, the samples were immersed for 48 h. In the shear tests, normal loads of 2 KN, 4 KN, and 6 KN were applied. In the triaxial tests, confining pressures of 0 MPa, 10 MPa, and 20 MPa were used. All samples that required immersion were soaked in a water-based drilling fluid at a drilling pressure difference of 2 MPa and a temperature of 50 °C.

Hardness characteristics

The hardness experiment was conducted using a 50 KN mechanical testing machine, with a maximum load of 50 KN. The rock samples used in the experiment were the original rock and those soaked in drilling fluid for 24 h, 48 h, and 96 h. Figure 2 shows the results of the indentation hardness tests before and after immersion. From the graph, it can be observed that the indentation hardness values decrease as the exposure time to drilling fluid increases. Compared to the original rock, the indentation hardness values after immersion have decreased by 9.23%, 51.50%, and 71.90% respectively. Furthermore, there is a significant drop in indentation hardness values between the immersion periods of 24 h and 48 h. After 48 h of immersion, the indentation hardness values are all below half of the original rock’s values. The clay minerals are well developed in the rock samples, and after soaking in drilling fluid, the clay minerals undergo hydration expansion, leading to a decrease in their strength, thereby affecting the overall strength of the rock sample (Al-Maamori et al. 2019; Liu et al. 2017).

Fig. 2
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Comparison of indentation hardness of M area shale under different conditions

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Tensile characteristics

The tensile strength experiment was conducted using a 50 KN mechanical testing machine, with a maximum load of 50 KN. The rock samples used in the experiment were the original rock and those soaked in drilling fluid for 24 h, 48 h, and 96 h. Figure 3 represents the results of the tensile tests before and after immersion. From the graph, it can be observed that tensile strength decreases with the increase in exposure time to drilling fluid. Compared to the original rock, the reduction in tensile strength is 13.28%, 21.22%, and 49.82% respectively. The microfractures and micropores are well developed in the rock samples. Under the influence of drilling fluid, the micro-fractures and micropores may further expand and extend, resulting in a decrease in the tensile strength of the rock sample (Yang et al. 2020; Zhang et al. 49,50,c). During the drilling process, the interaction between the drilling fluid and the wellbore rock leads to a decrease in the rock’s tensile strength. When the internal fluid column pressure exceeds the tensile strength of the wellbore rock, the rock undergoes tensile failure, forming cracks in the wellbore formation and resulting in wellbore leakage.

Fig. 3
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Comparison of tensile strength of M area shale under different conditions

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Shear characteristics

The instrument used in the direct shear experiment is a rock direct shear apparatus, with a maximum normal (axial) load of 1200 KN and a displacement of 100 mm. The maximum shear load is 600 KN with a displacement of 100 mm. The experimental rock samples were divided into the original rock and those soaked in drilling fluid for 48 h. The normal loads used were 2 KN, 4 KN, and 6 KN. The shear test results for the original rock and the rock soaked in drilling fluid for 48 h are shown in Figs. 4 and 5. Under the same conditions, a greater normal load results in a higher shear strength. However, after immersion, the microfractures and micropores inside the rock samples become more developed. In the experiments, as the normal load increases, the microfractures inside the rock samples further expand, leading to a greater decrease in shear strength. There is not much variation in cohesion and internal friction angle. During the drilling process, the interaction between drilling fluid and wellbore rock causes a reduction in the shear strength of the rock. When the internal fluid column pressure is lower than the shear strength of the wellbore rock, the wellbore rock undergoes shear failure, leading to wellbore collapse, stuck pipe, and other issues that can impact construction progress.

Fig. 4
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Comparison of shear strength of M area shale under different conditions

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Fig. 5
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Comparison of cohesion and internal friction angle before and after immersion in shear experiments

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Triaxial characteristics

The instrument used in the triaxial experiment is the TRC-100 high-temperature and high-pressure triaxial rheometer, with a maximum axial load of 2000 KN and a confining pressure range of 0–150 MPa. The temperature range is from room temperature to 150 °C. The rock sample dimensions are a diameter of 25–100 mm and a height of 100 mm. The experimental rock samples were divided into the original rock and those soaked in drilling fluid for 48 h. The confining pressures used were 0 MPa, 10 MPa, and 20 MPa. The triaxial test results for the original rock and the rock soaked in drilling fluid for 48 h are shown in Figs. 6, 7, and 8. As the confining pressure increases, the compressive strength of the rock sample also increases. However, after immersion, the compressive strength decreases, and the greater the confining pressure, the greater the decrease in compressive strength. This could be attributed to the fact that after immersion in drilling fluid, the microfractures and micropores inside the rock sample become more developed. Under higher confining pressures, these microfractures and micropores extend and propagate more extensively, leading to a greater reduction in compressive strength. The elastic modulus and Poisson’s ratio of the rock samples after immersion have all decreased to varying degrees under different confining pressures, although the trends are not very significant. Cohesion shows a slight increase, while the internal friction angle decreases slightly. The reason for this phenomenon may be the structural differences between the original rock and the immersed rock samples, particularly in the degree of development of microfractures and micropores. A higher degree of development can lead to lower strength, whereas a lower degree of development can result in higher strength.

Fig. 6
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Comparison of compressive strength of M area shale under different conditions

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Fig. 7
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Comparison of elastic modulus and Poisson’s ratio before and after immersion in triaxial tests

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Fig. 8
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Comparison of cohesion and internal friction angle before and after immersion in triaxial tests

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Research methods for fault activation and instability study

Methods for assessing fault activation and instability

Many scholars have conducted research and analysis on the mechanism of fault activation and put forward several methods for risk assessment of fault activation, including basic fault activation theory based on the Mohr–Coulomb criteria, critical pore pressure method (CPP), fault analysis and sealing technology (FAST), and three-dimensional evaluation method based on the ratio of transverse and longitudinal effective stress, and so on.

The basic fault activation theory based on Mohr–Coulomb criteria suggests that when a fault is subjected to engineering disturbance, Coulomb stress will be generated on the fault surface. If the Coulomb stress exceeds the ultimate shear strength of the fault surface, the fault will undergo activation and slip (Ji et al. 2012; Zhao and Jha 2021). The CPP method considers factors such as the stress field, pore pressure, and fault inclination in the fault area, and takes into account the water-holding capacity, slip tendency, and expansion tendency of the fault. However, this method does not consider the cohesive force of the fault area, and the calculated critical pore pressure for fault activation is overly conservative (Wiprut and Zoback 2000; Wiprut and Zoback 2002). The FAST method proposes that the fault rock may undergo deformation and lithification due to cementation, thereby restoring the cohesive force and tensile strength. It is necessary to consider the failure envelope of the fault rock in predicting fault activation (Mildren et al. 2005). The three-dimensional evaluation method is based on the ratio of transverse and longitudinal effective stress under three-way stress, combined with the risk assessment method for the fault activation of internal friction angle and cohesive force. The Q value of the fault is obtained and compared with the limit Q0 value. Based on the risk assessment standard table, the level of fault activation risk is evaluated (Leclère and Fabbri 2013).

Calculation models for fault activation and instability

After being influenced by external forces, the fault plane may cause stress disturbance, break the original equilibrium state of the fault, and cause fault activation. Therefore, combining the theory of fault activation and the spring combination model, a calculation model is established. It is assumed that the upper and lower plates on the fault are elastic bodies, and the contact between the two plates is regarded as the contact surface. The section parallel to the direction of the stratum is taken as the profile, and the unit thickness of the fault plane is taken as the research object, as shown in Fig. 9.

Fig. 9
figure 9

Mechanical model of rock mass in fault zone

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Assuming that the x and y directions in the legend are positive and represent the directions of the maximum and minimum principal stresses, respectively. Before the fault is activated and slips under disturbance, the elemental body remains stationary. By conducting a force analysis, the expressions for the normal stress σ and shear stress τ on the fault plane can be obtained as follows:

$$\sigma = \frac{{\sigma_{H} + \sigma_{h} }}{2} - \frac{{\sigma_{H} - \sigma_{h} }}{2}\cos 2\theta$$
(1)
$$\tau = \frac{{\sigma_{H} - \sigma_{h} }}{2}\sin 2\theta$$
(2)

where σH, σh is the horizontal maximum and minimum principal stresses of the stratum, MPa; σ, τ is the normal stress and shear stress acting on the fault plane, MPa; θ is the angle between the strike of the fault and the direction of maximum principal stress,

The Mohr–Coulomb criterion states that the ultimate shear strength of the fault zone rock mass satisfies Eq. (3). During mining operations, the stress changes caused by mining activities will break the stress equilibrium state of the original stratum. When the working face approaches the geological structure near the fault, Coulomb stress (f) will be generated on the fault zone. When the Coulomb stress (f) generated on the fault zone is greater than the ultimate shear strength (τ0) of the fault zone rock mass, the fault zone will slip, triggering fault activation phenomena. The expressions for the ultimate shear strength (τ0) of the fault zone rock massand the Coulomb stress (f) generated on the fault zoneareas follows:

$$\tau_{0} = \sigma \tan \varphi + c$$
(3)
$$f\left( {\sigma ,\tau } \right) = \left| \tau \right| - \nu \sigma$$
(4)
$$f\left( {\sigma ,\tau } \right) > \tau_{0}$$
(5)

where τ0 is the ultimate shear strength of the fault zone rock mass, MPa;\(\varphi\) is the internal friction angle of the fault zone rock mass; c is the cohesion of the fault zone rock mass, MPa; v is the friction coefficient of the fault zone, dimensionless; f is the Coulomb stress on the fault plane, MPa.

The maximum and minimum principal stresses are obtained from a combined spring empirical relation model. The combined spring model takes into account the influence of the geological rock mechanics, pore pressure, and tectonic effects on the earth’s stress. The calculation of each principal stress component is as follows:

$$\left\{ {\begin{array}{*{20}c} {\sigma_{H} = \frac{\mu }{1 - \mu }\sigma_{V} + \frac{1 - 2\mu }{{1 - \mu }}\alpha P_{p} + \frac{E}{{1 - \mu^{2} }}\varepsilon_{H} + \frac{\mu E}{{1 - \mu^{2} }}\varepsilon_{h} } \\ {\sigma_{h} = \frac{\mu }{1 - \mu }\sigma_{V} + \frac{1 - 2\mu }{{1 - \mu }}\alpha P_{p} + \frac{E}{{1 - \mu^{2} }}\varepsilon_{h} + \frac{\mu E}{{1 - \mu^{2} }}\varepsilon_{H} } \\ \end{array} } \right.$$
(6)
$$\sigma_{V} = \int\limits_{{H_{0} }}^{0} {DEN_{0} (h)gd_{h} } + \int\limits_{H}^{{H_{0} }} {DEN(h)gd_{h} }$$
(7)

where E is the elastic modulus of rock, MPa;\(\mu\) is the Poisson’s ratio of rock, dimensionless;\(\alpha\) is the Biot’s coefficient, dimensionless;\(\varepsilon_{H}\),\(\varepsilon_{h}\) is the structural strain coefficients along the direction of maximum principal stress and the direction of minimum principal stress, dimensionless;\(P_{p}\) is the formation pore pressure, MPa;\(\sigma_{V}\) is the vertical principal stress of the stratum, MPa;\(H_{0}\) is the the depth of logging starting point, m;\(H\) is the current calculated depth, m;\(DEN_{0} (h)\) is the density of the unlogged interval at a depth of point "h", kg/m3;\(DEN(h)\) is the logging density at a depth of point "h", kg/m3; g is the gravitational acceleration, take 9.8 kg m/s2.

By combining Eqs. (1–4), (6), and (7), we can obtain the expressions for the ultimate shear strength \(\tau_{0}\) of the fault zone and the Coulomb stress \(f\) as follows:

$$\tau_{0} = \left[ {\frac{\mu }{1 - \mu }\left( {\int\limits_{{H_{0} }}^{0} {DEN_{0} (h)gd_{h} } + \int\limits_{H}^{{H_{0} }} {DEN(h)gd_{h} } } \right) + \frac{1 - 2\mu }{{1 - \mu }}\alpha P_{p} + \frac{{\varepsilon_{H} + \varepsilon_{h} }}{1 - \mu }E - \frac{{\varepsilon_{H} - \varepsilon_{h} }}{{2\left( {1 + \mu } \right)}}E\cos 2\theta } \right]\tan \varphi + c$$
(8)
$$\begin{gathered} f\left( {\sigma ,\tau } \right) = \frac{{\varepsilon_{H} - \varepsilon_{h} }}{{2\left( {1 + \mu } \right)}}E\sin 2\theta - \nu \left[ {\frac{\mu }{1 - \mu }\left( {\int\limits_{{H_{0} }}^{0} {DEN_{0} (h)gd_{h} } + \int\limits_{H}^{{H_{0} }} {DEN(h)gd_{h} } } \right)} \right. \hfill \\ \left. {\quad \quad \quad + \frac{1 - 2\mu }{{1 - \mu }}\alpha P_{p} + \frac{{\varepsilon_{H} + \varepsilon_{h} }}{1 - \mu }E - \frac{{\varepsilon_{H} - \varepsilon_{h} }}{{2\left( {1 + \mu } \right)}}E\cos 2\theta } \right] \hfill \\ \end{gathered}$$
(9)

Equations (8) and (9) demonstrate that the key factors affecting the risk of fault activation and slip include the elastic modulus and Poisson’s ratio of the rock mass, the internal friction angle, the cohesion, the orientation of the fault with respect to the maximum principal stress, and so on. Combining the fracture pressure and closure pressure obtained from the field fracturing construction curve, we can determine the maximum and minimum principal stresses of a certain depth stratum. Then, by using Eqs. (6), and (7), we can derive the tectonic strain coefficient in the direction of the maximum and minimum principal stresses, which are 1.43 × 10–3 and 3.2 × 10–4, respectively.

To ensure the correctness of the computational model, the results obtained in this study are compared with those of Yu’s model, as shown in Fig. 10 (Yu et al. 2019). From the figure, it can be observed that under the same geostress conditions, the results obtained in this study are generally consistent with those obtained by Yu. Furthermore, this study investigates the intrusion of drilling fluids into the formation, which leads to a decrease in the mechanical properties of the rock formation. According to the empirical relationship model of combined springs, the formation stress will change, resulting in alterations in the stress conditions of the fault. After immersion, there is a significant decrease in the ultimate shear strength of the fault, leading to a decrease in fault stability (Fig. 10a). When the fault dip angle is small or large, there is little change in Coulomb stress on the fault surface. However, when the fault dip angle is between 30° and 60°, there is a noticeable decrease in Coulomb stress, although the magnitude of decrease is not as significant as that of the ultimate shear strength of the fault (Fig. 10b). Overall, the possibility of fault activation increases.

Fig. 10
figure 10

Verification of the relationship between the ultimate shear strength (a) of the shear surface before immersion and the Coulomb stress (b) and the angle of the shear surface, along with comparison to the post-immersion condition

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Combining field data and experimental results, the initial values are as follows: elastic modulus is 20 GPa, Poisson’s ratio is 0.22, internal friction angle is 52.15°, cohesion is 10.54 MPa, friction coefficient is 0.1. We assume a constant research depth and isotropic properties of the research object. The vertical stress is 67.2 MPa, and the pore pressure is 29.36 MPa. The maximum and minimum principal strain coefficients are 1.43 × 10–3 and 3.2 × 10–4, respectively. The Biot’s coefficient is taken as 0.65. We are investigating the effects of elastic modulus, Poisson’s ratio, internal friction angle, and cohesion on the ultimate shear strength of faults and the variation of Coulomb stress on fault planes with respect to angle.

Results

Effect of elastic modulus

Based on the experimental results, after immersing in drilling fluid for 48 h, the maximum decrease in elastic modulus is 66.91%. Taking elastic modulus values of 20 GPa, 16 GPa, 12 GPa, 8 GPa, and 6.6 GPa, and setting the internal friction angle and cohesive force to 1/4 of their initial values, the ultimate shear strength of the fault and the Coulomb stress on the fault surface were obtained as shown in Fig. 11.

Fig. 11
figure 11

The relationship between the ultimate shear strength (a), Coulomb stress (b) of fault planes and the included angle under different elastic modulus

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In the figures, it can be observed that the ultimate shear strength on the fault plane increases slowly with the increasing angle, and the ultimate shear strength on the fault plane decreases as the elastic modulus decreases, with a reduced magnitude of increase. The Coulomb stress on the fault plane initially increases and then decreases with the increasing angle. Within the angle range of 5°–80°, the Coulomb stress on the fault plane is positively correlated with the elastic modulus, while it is negatively correlated for angles less than 5° or greater than 80°. As the elastic modulus decreases, both the ultimate shear strength and Coulomb stress on the fault plane decrease. The minimum difference between the two curves gradually increases. Therefore, the fault will not undergo activation and instability.

Effect of Poisson’s ratio

Based on the experimental results, after immersing in drilling fluid for 48 h, the maximum decrease in Poisson’s ratio is 84.21%. Taking Poisson’s ratio values of 0.22, 0.18, 0.14, 0.10, and 0.035, and setting the internal friction angle and cohesive force to 1/4 of their initial values, the ultimate shear strength of the fault and the Coulomb stress on the fault surface were obtained as shown in Fig. 12.

Fig. 12
figure 12

The relationship between the ultimate shear strength (a), Coulomb stress (b) of fault planes and the included angle under different Poisson’s ratio

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In the figures, it can be seen that the ultimate shear strength on the fault surface exhibits a flattened inverted "S" shape, with the minimum value at 0° and the maximum value at 90°. As the Poisson’s ratio decreases, the ultimate shear strength also decreases. The Coulomb stress on the fault surface first increases and then decreases with the angle, and is negatively correlated with the Poisson’s ratio, i.e., the smaller the Poisson’s ratio, the larger the Coulomb stress. With the decrease of the Poisson’s ratio, the ultimate shear strength on the fault surface decreases, while the Coulomb stress increases, and the minimum difference between the two curves decreases slowly. In other words, as the Poisson’s ratio decreases, the Coulomb stress on the fault surface approaches its ultimate shear strength, the risk of fault activation and instability increases.

Effect of internal friction angle and cohesion

From Eq. (3), it can be seen that the internal friction angle and cohesion only affect the ultimate shear strength of the fault surface. Combined with the experimental results, the influence of drilling fluid on cohesion and internal friction angle is not significant. Therefore, internal friction angle and cohesion were respectively taken as 1/2, 1/4, 1/8, and 1/16 to study the effect of different internal friction angles and cohesive forces on the variation of the ultimate shear strength of the fault surface with the angle of inclination.

Figure 13 reflects the influence of different internal friction angles and different cohesive forces on the variation of ultimate shear strength with inclination angle on the fault plane. The smaller the internal friction angle and cohesive force of the fault rock mass, the smaller the surface frictional forces and various physicochemical forces acting on the components of the rock mass. As a result, the rock mass is more prone to disturbances, causing the ultimate shear strength on the fault plane to decrease with the decrease in internal friction angle and cohesive force, although the effect of cohesive force is relatively small. In (a), the ultimate shear strength on the fault plane increases with an increase in the inclination angle. As the internal friction angle decreases, the rate of increase in ultimate shear strength decreases and gradually approaches a constant value that does not vary with the inclination angle. In (b), the ultimate shear strength on the fault plane exhibits a relatively gentle inverse "S"-shaped curve with an increase in the inclination angle. As the cohesive force decreases, the trend of the curve remains the same, resulting in a decrease in the ultimate shear strength on the fault plane, although the decrease is relatively small.

Fig. 13
figure 13

The relationship between the ultimate shear strength of fault planes and the included angle under different internal friction angle (a) and different cohesion (b)

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Effect of friction coefficient

From Eq. (4), it can be seen that the friction coefficient of the fault plane only affects the Coulomb stress on the fault plane. The friction coefficient was taken as 0.1, 0.2, 0.3, and 0.4 to study the effect of different friction coefficients on the variation of Coulomb stress on the fault plane with the angle of inclination.

Figure 14 reflects the effect of different friction coefficients on the Coulomb stress on the fault surface with respect to the angle, which shows an increasing trend followed by a decreasing trend. Under the same friction coefficient condition, the larger the inclination angle of the fault, the greater the amount of fault slip, and the greater the degree of fault activation and damage. As the friction coefficient on the fault surface decreases, the Coulomb stress increases and the angle at which the maximum Coulomb stress occurs increases from 30° to 40°, indicating that the smaller the friction coefficient on the fault surface and the larger the angle, the greater the probability of fault activation and slip occurrence.

Fig. 14
figure 14

The relationship between the Coulomb stress and the angle for different values of the friction coefficient on the fault plane

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Effect of comprehensive parameters

When the elastic modulus is 6.6 GPa and the Poisson’s ratio is 0.035, the ultimate shear strength and Coulomb stress curves on the fault surface are obtained under different internal friction angles, cohesive forces, and friction coefficients, respectively taking 1/2, 1/4, 1/8, and 1/16 of the experimental results for internal friction angle and internal cohesion force, and taking 0.1, 0.2, 0.3, and 0.4 for the friction coefficient on the fault surface, as shown in Fig. 15. As the internal cohesion force, internal friction angle, and friction coefficient decrease, the ultimate shear strength on the fault surface continuously decreases while the Coulomb stress continuously increases. With the passage of time, the ultimate shear strength on the fault surface will continue to decrease while the Coulomb stress will continue to increase. When the Coulomb stress curve intersects with the ultimate shear strength curve, the fault is in a critical sliding state, and when the Coulomb stress curve exceeds the ultimate shear strength curve, the fault will slip, leading to the activation and sliding of the fault. Drilling fluid entering the fault surface can lubricate it and reduce the friction coefficient on the fault surface. Moreover, the mechanical strength of the fault rock will be reduced after prolonged contact with the drilling fluid and new fractures may even occur under high pressure. This further increases the risk of fault activation and sliding.

Fig. 15
figure 15

The relationship between the Coulomb stress and the ultimate shear strength on the fault surface under different internal friction angles, cohesive forces, and friction coefficients

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Based on the comprehensive analysis of the micro-pore structure of shale in the Ordos Basin’s M area, the mechanical property changes after immersion, and the qualitative risk assessment of fault activation and destabilization in the region, it is concluded that during drilling operations in this area, measures should be taken to enhance the inhibitive properties of drilling fluids and strengthen their sealing performance and mud cake quality. Efforts should be made to minimize the interaction between drilling fluids and the formation during the drilling process. Furthermore, it is advisable to choose a wellbore trajectory carefully, avoiding fault zones. The entry of drilling fluids into fault zones can lead to a reduction in the mechanical strength of faulted rock masses, increasing the risk of fault activation and slip. For situations where it is impossible to avoid faults, it is recommended to drill in a direction with lower shear stress to reduce Coulomb stress on fault planes and mitigate the risk of fault activation and slip.

Discussion

This article is limited to the changes in formation stress and the stability of faults caused by the invasion of drilling fluid into the formation. Many scholars believe that the increase in pore pressure is the main controlling factor for most fault activations, which leads to a decrease in effective stress on the fault plane and a reduction in its mechanical properties due to hydration. For a porous medium under constant principal stresses and minor principal stress, when the pore pressure increases, the Mohr circle tends to shift to the left. When the Mohr circle reaches the point of tangency with the failure envelope, it causes shear failure. When the shear stress on the fault plane exceeds the frictional resistance on the fault plane, it will lead to shear failure of the fault and trigger fault instability activation (Mildren et al. 2002; Rutqvist et al. 2015; Sleep Blanpied 1992; Shen et al. 2019). The mineral composition plays a decisive role in the frictional performance of faults. Although the increase in layered silicates leads to a monotonic decrease in frictional strength(Zhang et al. 2019), shale rich in layered silicates has stronger frictional stability compared to shale rich in carbonates(Fang et al. 2017). For shale with clay and organic matter content above 30%, it exhibits stable velocity strengthening behavior, while samples below this value show increased frictional strength and velocity weakening (Kohli and Zoback 2013). In addition, underground geothermal rocks experience shrinkage of surface cracks when encountering cold fluids, leading to a decrease in frictional force. Moreover, temperature can also alter the composition of the fault gouge through chemical reactions and accelerate fluid-assisted chemical processes (Chen et al. 2015; Hartog et al. 2012; He et al. 2016). In the actual drilling process, the expansion of reactive clay minerals in shale can be suppressed by adding polymers with fewer electronegative groups (such as imines and hydroxyls), multi-walled carbon nanotubes, and deep eutectic solvents to the drilling fluid (Abbas et al. 2021, 2022; Rasool et al. 2022). This helps to minimize the impact of stress environment changes caused by the interaction between the drilling fluid and the formation, thereby reducing the influence on the faults around the wellbore.

Conclusions

Through indoor experiments, the changes in the mechanical properties of rock mass before and after immersion in water-based drilling fluid were studied. Based on the results of the indoor experiments, combined with the spring combination model and the basic fault activation theory, a quantitative evaluation of fault activation risk was conducted. The conclusions obtained are as follows:

  1. 1.

    The shale in the M block of the Ordos Basin has a high content of clay minerals and exhibits some degree of water sensitivity. Additionally, there is a development of micropores and microfractures, providing migration pathways for drilling fluids and increasing the probability of interaction between drilling fluids and formations.

  2. 2.

    After immersion in drilling fluid, the mechanical properties of the rock samples have experienced varying degrees of decline. When immersed for 24 h, 48 h, and 96 h, the rock’s indentation hardness decreased by 9.23%, 51.50%, and 71.90%, respectively, while the tensile strength decreased by 13.28%, 21.22%, and 49.82%. After a 48 h immersion, under normal loads of 2 KN, 4 KN, and 6 KN, the shear strength of the rock decreased by 4.7%, 6.96%, and 12.16% respectively. Additionally, under confining pressures of 0 MPa, 10 MPa, and 20 MPa, the compressive strength of the rock decreased by 21.71%, 28.33%, and 30.44% respectively.

  3. 3.

    Based on the experimental results and incorporating the spring-combination model and basic fault activation theory, a computational model was established. In this model, the main influencing factors for evaluating fault activation instability include elastic modulus, Poisson’s ratio, internal friction angle, cohesion, and friction coefficient.

  4. 4.

    As the elastic modulus decreases, both the ultimate shear strength and Coulomb stress of the fault plane decrease, with maximum reductions of 4.9 MPa and 4.65 MPa, respectively. With a decrease in Poisson’s ratio, the ultimate shear strength of the fault plane decreases while the Coulomb stress increases. The maximum reduction in ultimate shear strength is 3.35 MPa, and the maximum increase in Coulomb stress is 3.26 MPa, leading to an increased risk of fault activation.

  5. 5.

    As the internal friction angle and cohesion decrease, the ultimate shear strength of the fault plane decreases, with maximum reductions of 27.79 MPa and 4.61 MPa, respectively, increasing the risk of fault activation and instability. A higher friction coefficient leads to a smaller Coulomb stress on the fault plane, with a maximum reduction of 6.43 MPa, indicating greater fault stability.

  6. 6.

    When drilling fluids invade the fault, the ultimate shear strength on the fault plane decreases while the Coulomb stress on the fault plane increases, increasing the risk of fault activation and instability. Therefore, the hydration inhibition of the drilling fluid should be strengthened, its sealing performance should be improved, and the wellbore trajectory should be optimized to avoid faults as much as possible and reduce the risk of fault activation and instability.