Rock Stress Measurement Methods in Rock Mechanics—A Brief Overview ()
1. Introduction
Understanding of the rock stress is of great importance and central concern in rock mechanics. Rock stress has a strong connection to a variety of issues in civil, mining, petroleum engineering, and geology and geophysics. Table 1 listed of activities where rock stresses play a critical role [1] [2] . The stability of underground openings such as mines, shafts, tunnels, or caverns in civil and mining engineering projects is largely determined by the distribution and magnitude of rock stresses [2] [3] . Excessive magnitude of rock stress around underground openings (stress concentrations) can result in the failure of the rock mass locally or on a larger scale, causing roof collapse, sidewall movement and/or ground subsidence [4] [5] [6] . There are a number of publications published since long time regarding the rock stress problems in civil and mining projects and a large amount of literature exists on the subject of rock stresses and these factors [2] [6] - [17] .
Rock stress is enigmatic and fictitious quantities and can be classified into in situ stresses and induce stresses (Figure 1). The other terms used for in situ stress are natural, primitive or virgin, which exist in rock mass before any disturbances of human activities. Alternatively the induce stresses are generated due to human activities in or on the rock for build of engineering structures, i.e., tunnel, surface or underground mining, caverns, highway slopes etc [18] . Overall, in situ stresses are product of geological events which have several cycle of thermal, mechanical and physicochemical geological processes and majorly contributed for in situ stresses. Different classifications of in situ stresses have been proposed by several authors. According to Voight (1966), in situ stresses can be divided into two main categories: gravitational and tectonic [19] . This tectonic stress can be further broken down into two subgroups: current and residual, whereas Obert (1968) composed in situ stresses into internal and external stresses [20] .
![]()
Table 1. Activities requiring knowledge of rock stress [1] [21] .
![]()
Figure 1. Rock stress types and sources of in situ stress.
External stresses contained gravitational and tectonic stresses (regional stresses), whereas internal stresses contained of residual stresses. Various other author classified the in situ stresses almost in same categories [17] [22] [23] [24] . This paper included the general agreement of all authors and followed the Fairhurst, (2003) classifications.
The details of each types of in situ stress can be obtained through the reference book of Amadei and Stephansson (1997) [1] . One of the sources of in situ stress is tectonic forces. Tectonic stress can be felt like earthquake (i.e., active tectonic stress), however, it can occur silently in most cases (i.e., passive tectonic stress) either at plate-scale or broad regional scale as shown in Figure 2 [25] . Passive tectonic stress may create greater vertical and horizontal stress thus it is the safety key for underground constructions, i.e., mining drift, caverns and tunnels etc. [26] .
Residual stresses (lock-in stresses) are the stresses that persist in a material even when no external loads or temperature gradients are present. These stresses are not caused by any external stimuli, but rather are inherent in the material itself. Residual stresses and strains can build up strain energy internally, which can have a major impact on the stability of rock structures, such as underground openings and surface excavations [25] . The stress brought by gravity’s force on a rock mass is known as gravitational stress. This stress is mainly caused by the weight of the overlying rocks and the self-weight of the rock mass. Gravitational stress can cause a significant amount of stress to be present in the rock mass, which can lead to instability and potential failure of the rock mass [27] . Terrestrial stress is the sum of all the stresses acting on a rock mass, including gravitational, tectonic, residual, and atmospheric stresses. These stresses can cause deformation in the rock mass, resulting in instability and potential failure [21] [28] .
Heidbach et al. (2018) presented the present-day in situ stress field on world map [29] . This project initiated in 1986 and continuous working in different phases. The latest phase end in 2016 and provided the World Stress Map (WSM) [29] . Authors outlined the 2016 WSM database release in detail and analyze the patterns of global and regional stress (Figure 3). For example, the WSM contained data on the present-day stress field of Saudi Arabia, primarily from petroleum wells in the country. According to the map, the majority of Saudi Arabia is in a region of normal to high tectonic stress, with some areas of very high stress in the northeast and southwest. Additionally, the WSM indicates that the region has seen a lot of activity in recent years, with many earthquakes recorded in the region over the past decade. This paper classifies methods under two main categories direct in situ measurement methods and indirect methods as shown in Figure 4. This paper will discuss methods of both categories with an emphasis on review of direct methods.
![]()
Figure 2. Forces controlling the present-day tectonic stress field at the plate-scale (large arrows) and broad regional scales (small arrows).
![]()
Figure 3. The World Stress Map (WSM) 2016 [29] .
![]()
Figure 4. Classification of in situ stress measurement methods [33] .
2. In Situ Measuremnt Methoeds
There are two main categories for in situ stress measurement methods which are indirect and direct methods. The indirect methods based on the observation of rock behavior without any major disturbance of rock, i.e., core discing, statistics data, borehole breakout etc. Whereas disturb the rock by develop crack or crack opening, and induced strain. The examples are Hydraulic fracturing and relief methods (Figure 4).
In this paper, brief review description is presented for indirect methods and direct methods, but more emphasized on direct methods. Indirect methods of measuring in-situ stress include the use of statistics from collected data (database), back analysis of large rock volumes, core discing, the acoustic method (Kaiser effect), strain recovery methods and borehole breakouts. Each of these methods has its own advantages and limitations, and they can be used in combination to achieve a more comprehensive understanding of the subsurface conditions (Table 2). For example, statistic of measured data (database) can be employed in hydraulic fracturing field data to improve the accuracy of determining the shut-in pressure or estimating the in situ tensile strength of hydraulic fractures [30] [31] . While core discing can provide detailed information about the stress state of a specific rock formation [32] as shown in Figure 5. The conditions for core discing are high in situ stresses and the brittle rock. The thickness of the chips depends on stress intensity. As stresses increases, the size of disc decreases and in extreme cases, the discs can become so thin. Borehole breakout is a phenomenon that occurs when the rock is unable to sustain the compressive stress concentrations around a borehole (Figure 6). Borehole breakouts can be used to identify the direction of maximum horizontal stress. This results in breakage of the wall on two diametrically opposed zones, called ‘breakout’. In relief method the large rock volumes (back analysis) can be used to estimate the magnitude of the in-situ stress [33] [34] . The main issue with relief methods is that they only involve a small volume of rock, making the measured stresses vulnerable to shifts due to tiny changes in the mineral composition and rock grain size. To obtain more accurate results, it is possible to measure the local or average stresses over a larger volume of rock by overcoring multiple strain gages in a large-diameter bored raise at various heights [35] [36] . Over the years, the Acoustic method (Kaiser Effects) approach has been researched as a viable technique for identifying in situ stressors. The approach is based on an observation Kaiser made in 1950 and strain recovery methods are used to determine the anisotropy of the rock formation and the orientation of the principal stress axes.
![]()
Table 2. Advantages and limitations of indirect in situ stress measurement methods.
![]()
Figure 5. Core discing rock sample from core drilling.
![]()
Figure 6. Expansion of borehole breakouts.
3. Hydraulic Methods
Hydraulic methods are one of the most widely used techniques for measuring in-situ stress levels. This method involves injecting pressurized liquids into an existing fracture in a rock formation, causing it to widen and create new fractures. By measuring the pressure response of these fractures, the stress levels of the material can be determined. Conventional or classical hydraulic fracturing and hydraulic tests on pre-existing fractures (HTPF) are two of the most used methods for measuring stress levels using hydraulic methods.
3.1. Conventional (Classical) Hydraulic Fracturing (HF)
Hydraulic fracturing (HF) was used in the 1940s, originally to stimulate production from low permeable oil-bearing formations. In 1957, Hubbert and Willis developed the classical concept of hydraulic fracturing to be useful for in-situ stress measuring. HF is the best-known method to evaluate in-situ stress at deeper levels [33] . A straddle packer is used to seal off a section of a borehole, which is usually no longer than 1 meter in length. This sealed off section is then pressurized with a fluid, usually water, at a slow rate. This causes tensile stresses to build up at the borehole wall until it ruptures, initiating a hydro fracture.
HF is used to measure the in-situ stress of subsurface rock by propagating a fracture in the rock. Two fractures begin on opposing sides of the borehole’s perimeter, with the fracture plane typically parallel to the borehole axis. The direction of the fracture is identified by looking at the traces on the borehole wall, and it spreads in the direction of least resistance. The components recorded in a vertical borehole are two of the primary stresses, and this orientation is related to the direction of the highest horizontal stress in vertical or sub-vertical boreholes [33] . This technique is two-dimensional and only measures the greatest and least normal stresses in the plane perpendicular to the borehole axis as presented in Figure 7. The setup of HF is provided under the next method which is hydraulic tests of pre-existing fractures (HTPF) since both share same setup as presented in Figure 8.
HF is an effective and cost-efficient in-situ stress measurement method, allowing for direct and accurate measurements at depths not accessible by other methods. It can measure stress in multiple orientations, providing a more comprehensive analysis of the stress field and its impact. Additionally, it is fast and non-destructive, making it a great option for stress measurements [37] . HF method can provide high confidence measurement of in-situ stress at several kilo meters depths [33] . “Rummel has successfully determined in situ stresses by hydraulic fracturing at a depth of approximately 6 km, using aluminum packers”. So far, hydraulic fracturing has been successfully used to measure in-situ stress at a depth of up to 9 km. Figure 8 shows the technique of HF [38] .
On the other hand, the main drawback of using hydraulic fracturing as an in-situ stress measurement method is that it has the potential to cause damage to the surrounding rock. Additionally, the measurements obtained may be affected by factors such as temperature, pore pressure, and the presence of fractures in the rock [37] .
3.2. Hydraulic Tests on Pre-Existing Fractures (HTPF)
Hydraulic Tests on Pre-existing Fractures (HTPF) is a method of measuring the horizontal stress in the rock mass by using hydraulic pressure to reopen existing fractures in the rock [39] [40] . It is used to determine the depth and orientation of existing fractures, and to measure the in-situ stress in the surrounding rock. The HTPF method can be used to measure the stress in the horizontal, vertical, and diagonal directions, and can provide information about the magnitude of the stresses in the rock [39] . Valette and Cornet presented both the theoretical foundations and practical implementation of HTPF, eliminating the need to create new fractures in the rock mass by instead re-opening existing fractures [33] .
![]()
Figure 7. Stress distribution and HF around a borehole.
![]()
Figure 8. Vertical down hole in situ stress measurement by (a) HF (b) HTPF.
Combining the HF and HTPF methods is often beneficial when the borehole is parallel to one of the principal stresses (typically the vertical direction). The HF method can be used to accurately determine the direction and magnitude of the minimum principal stress, while the HTPF results can be used to estimate the magnitude of the maximum horizontal principal stress and the vertical stress components, without taking into account either pore pressure or tensile strength [40] . When cost and time are the most important considerations, the HTPF method should replace hydro-fracturing only when the borehole axis is not expected to be parallel to the principal stresses, or when there are significant weak points in the rock mass [41] .
4. Relief Methods
The core purpose of relief methods is to detach a piece of rock from the stress environment in the surrounding rock mass and observe its response [1] . Relief methods can be categorized into two main groups: surface relief methods and borehole relief methods.
4.1. Surface Relief Methods
The rock’s response to stress reduction is measured by surface relief techniques like the flat jack method and the curved jack methods, which measure the distance between gauges (pins) on the rock surface before and after the relief. This technique is most appropriate for measuring tunnel surfaces, and for more information, readers should refer to Amadei and Stephansson [33] . Surface relief methods have a few drawbacks. Humidity and dust can affect the accuracy of the gages or pins used. Additionally, the strain or displacement measurements are taken from a rock surface that could have been altered due to the effects of weathering or the excavation process. To connect localized stresses in the sides of the excavation to the more distant stress components, estimates of stress concentration factors must be utilized [1] .
4.2. Flat Jack Method
Flat jack is one of the earliest techniques used in rock mechanics to measure in-situ stress within the rock mass [17] . During the 1950s and 1960s, it was suggested to assess the deformability of rock masses and it soon became widely used for calculating stresses [1] . One of the earliest methods of stress measurement in rock mechanics was the flat jack method [1] . Flat jacking is a method used to determine the in situ stress and also used in finding engineering properties of existing structures for structural evaluation. It is also used to determine compressive strength of masonry structures.
A flat jack is a thin, hydraulic load cell that is inserted into a typical mortar joint, in which a slot has been formed (Figure 9). When pressurized, the flat jack exerts stress on the surrounding masonry and by measuring surface deformations, information on the existing state of stress as well as the stiffness and strength of the masonry can be obtained. This method directly measures the actual state of compressive stress present within the masonry and is useful for determining stress gradients present within a masonry wall or column [42] . Mechanically, the route taken by the rock during a flat jack test can be represented as illustrated in Figure 10. The rock is thought to be elastic and to be compressed perpendicular to the jack surface [1] . The original spacing between two reference pins is marked as do, and the unidentified normal stress is marked as σ (at point A), When the slot is cut, the normal stress across the slot is reduced from σ to zero (at the free surface), and the distance between the pins is reduced by a magnitude of 2d (at point B). The pins restore to their initial position once the jack is pressured to the cancellation pressure pc. (Figure 11). The main benefit of the flat jacking technique was that it could be used with a basic extensometer (i.e., located between points A and B) without having to create unique tools or sensors that could fit into a narrow hole [17] .
Other advantages of flat jacking method are relatively straight forward, cost-effective, and can be implemented without needing to calculate the elastic modulus. On the other hand, flat jacking can only be used at the surface of the excavation, where rock is likely to be overly stressed, leading to an unreliable estimate [43] . A refined version of flat jacking method was done by Jaeger and Cook to make it suitable for measuring in-situ stress at deeper levels. The maximum depth they measure stress at was 7 m [17] . The advantages, disadvantages and limitation of flat jack methods are tabulated in Table 3.
![]()
Table 3. The advantages and disadvantages of flat jacking method.
![]()
Figure 11. Path followed by a rock during a flat jack test. The rock is assumed to be elastic (linear or non-linear) and under compression in a direction perpendicular to the jack surface.
4.3. Borehole Relief Methods
Borehole relief methods (also known as overcoring methods) are used to measure in situ stress based on the stress relief around the borehole. This method involves drilling a borehole into the ground, then measuring the amount of relief in the external forces around the borehole. The relief of external forces can then be used to estimate the magnitude of the in-situ stress as well as the lateral pressure coefficient [44] . Borehole relief methods involve three types: overcoring of measuring cells in pilot holes, borehole slotting and overcoring of boreholes bottom cells.
Overcoring of Measuring Cells in Pilot Holes
Based on overcoring principle, overcoring of measuring cells in pilot holes can be broken down into three further categories: soft inclusion cells, deformation meters to measure wall displacements during overcoring, and stiff/solid cells [33] .
- Soft Inclusion Cells
Soft inclusion cells are a technique used to measure in-situ stresses in rocks and soils by inserting a soft, pliable material into a borehole and measuring the deformation of the material to calculate the stress in the surrounding rocks [45] as shown in Figure 12 and Figure 13.
The core concept of a soft cell is based on the linear elasticity theory for continuous, homogeneous, and isotropic rocks. By measuring at least six strain components on the borehole wall in different orientations, it is possible to determine the total stress tensor at the test location. Moreover, there are recognized theories for detecting stress in anisotropic rocks [33] .
Based on the aforementioned concept, the most often used instruments are the CSIR cell, CSIRO cell, and Borre Probe cell [33] . In good rock conditions, these devices have a range of between 10 and 50 meters from existing free surfaces. Unbroken cores at least 150 to 300 millimeters in length are required to provide accurate results. In vertical water-filled boreholes up to depths of 500 to 1000 meters, many adaptations of the CSIR triaxial strain cell have been proposed and tested as presented in Table 4 [1] [33] .
![]()
Figure 12. Soft Inclusion Stress Cell shown with mechanical installation tools.
![]()
Figure 13. Soft inclusion stress cell (a) Mechanically activated (b) hydraulically activated.
![]()
Table 4. Characteristics of the most common soft overcoring cells.
The Borre Probe is a soft stress cell, which is used to measure the stress field within a single borehole measurement. It works by measuring the strains induced by overcoring in the rock and then calculating the stress from the measured strains. The Borre Probe is different from other stress cells in that it does not measure displacement but rather strains. This means that the Borre Probe is more accurate than other stress cells in determining the stress field in a single borehole [39] [43] . All three of these instruments have the advantage of being able to measure the 3D state of stress from a single measurement point as shown in Figure 14 and Figure 15. This is a major benefit that they all share [33] .
- Deformation Meters
The theory behind deformation meters is the same as it is for soft inclusion cells for measuring displacements. After being over cored, the instrument is inserted into a pilot hole. Instead of measuring strain during overcoring, these sensors measure one or more variations in pilot hole diameter. The Sigra in situ stress tool and the USBM gage are two commercial deformation-type gages (IST) [33] .
![]()
Figure 14. Principle of soft, 3D pilot hole overcoring measurement.
![]()
![]()
Figure 15. The Bore probe used for overcoring in pilot hole
- STIFF/SOLID CELLS
The disparity in material qualities between the rock and inclusion material causes stiff/solid cells, which are less common than the other two categories, to generally have problems [33] . Overcoring techniques performed in a borehole are among the most popular ways to relieve stress. The US Bureau of Mines stress gauge is one stress-measurement tool that makes use of the idea of overcoring. The USBM gauge is simply a cylindrical instrument with three pairs of pistons that are diametrically opposed and evenly distributed around the circumference. These pistons are coupled to cantilevers within the tool, which deflection is gauged by strain gauges. A tiny borehole, about the same diameter as the gauge (38 mm), is driven into the rock to be used with the USBM gauge. The pistons are initially tensioned to create adequate contact with the borehole walls before the gauge is placed into the hole (Figure 16(a)). Then, a drill bit with a bigger diameter (usually 150 mm) is used to overcore this small hole to a depth that extends at least one overcore diameter past the gauge (Figure 16(b)). A nearly stress-free circular rock zone will be produced by the overcoring process. The three sets of cantilevers monitor the radial deformation of the (inner) borehole as the stresses acting on this annular region are released [46] .
Table 5 denoted all direct methods of in situ stress measurement techniques advantages and limitations.
5. Use the Artificial Intelligence In-Situ Stress Measurement
One way in which Artificial intelligence (AI) can be used in in-situ stress measurement is through the application of machine learning algorithms to data collected from boreholes [47] [48] . Boreholes are drilled into the subsurface and instruments are used to measure various parameters, such as rock strength, pore pressure, and temperature [47] . These data can be used to train machine learning models, which can then be used to make predictions about the stress state at other locations in the subsurface (Figure 17). Overall, AI can greatly enhance
![]()
Figure 16. Stress measurement by overcoring, using a device such as the USBM gauge: (a) gauge is inserted into the pilot hole, (b) which is then overcored, creating an annular region (shaded) that is relieved of stress.
![]()
Table 5. Advantages and limitations of direct in-situ stress measurement Methods.
![]()
Figure 17. Flowchart for building the different RF, FN, and ANFIS models you can find the Acronym and the Description in [47] .
the efficiency, accuracy and robustness of in-situ stress measurement, by providing a fast and efficient way to analyze data and make predictions about the subsurface stress state.
There is a case study in this field, a geometric equation for borehole deformation under stress was developed using the basic principles of elasticity. The relationship between in situ stress and borehole deformation was then established, and a prediction model for in situ stress was proposed. Numerical simulations were used to analyze the deformation effect in different types of rock. The study also used an artificial neural network to predict the shear wave time difference using logging parameters such as density and natural gamma radiation. The results showed that the borehole geometry under stress was quasi-elliptic and that the predicted geometry was consistent with the actual geometry. The overall error of the in situ stress predicted using this method was less than 9.2%, with the highest accuracy in coal seams. This suggests that the proposed method is feasible [49] . Also, there are another paper aims to compare and improve the minimum horizontal stress estimation through various machine learning regression techniques, including parametric and non-parametric models. The study was based on 79 laboratory data and validated against 23 field data. The results showed that the artificial neural network was able to predict the minimum horizontal stress with an average error rate of 10.16% and a root mean square error of 3.87 MPa, which is a meaningful improvement compared to conventional in-situ measurement techniques [50] . On the other hand, an AI-based methodology is proposed to identify geomechanical parameters from borehole injection pressure curves obtained during hydraulic fracturing tests. A genetic algorithm minimizes the difference between observed and predicted pressure curves while an artificial neural network substitutes hydraulic fracture simulations to reduce computational time. A recursive strategy predicts pressure curves and a hyperparameter tuning technique selects appropriate neural network parameters. The framework was applied to a KGD problem and confirmed its ability to identify geomechanical parameters from fracturing tests [51] .
Another study that used machine learning to predict in-situ stresses from logging data was conducted by Ibrahim et al. 2021 [52] . In this study, the researchers collected logging data from boreholes drilled in the subsurface. They then used machine learning algorithms, such as Random Forest or Support Vector Machine, to train models on this data.
These models were able to predict the in-situ stresses at different locations in the subsurface with high accuracy. The results of this study showed that machine learning can be a powerful tool for in-situ stress prediction and can improve the efficiency and accuracy of subsurface stress measurements. However, the practical use of these AI models is still a concern as many require some level of expertise to be used, as they are not in a form of simple mathematical equations. There is still a need to explore advanced AI methods and the limited availability of data for AI simulations is also a major challenge [53] .
6. Conclusion
Knowledge of in situ stress have major impact to any infrastructure project related mining, civil engineering, geothermal, large underground opening etc. Therefore, this paper given a brief review of the in situ stress measurement methods and more emphasized on most common methods. Each method has their limitation for applicability. In direct methods are commonly used by experts without disturbing the rock mass. Some area where no access of underground opening for direct measurement of in situ stress, hydraulic fracturing tends to be appropriate choice at greater depth up to several kilometers. Applicable of HTPF technique if large amount of intersection of fracturing existing, which remove the ambiguity associate with conventional hydraulic fracturing. Relief methods used for in situ stress measurement where underground accessibility possible. Some methods can be carried out directly on rock core sample in laboratories without visiting the project site. At last authors tried to link Artificial Intelligence (AI) for measure the in situ stress which will be remain a major and interesting topic in rock mechanics.
Acknowledgements
The authors acknowledge the blind reviewer who makes possible our manuscript up to acceptance level in esteem journal. Also, very thankful to editor of WJET and SCIRP publisher for their kind support from submission to accepting the MS.