Evaluating the Core-Based Stress Measurement in Mining Engineering—A Critical Review of the Diametrical Core Deformation Technique

Abstract

Accurate determination of in situ stress is fundamental for the safe and efficient design of underground construction projects such as tunnels, caverns, and deep mining excavations. Conventional techniques—particularly overcoring and hydraulic fracturing—have been widely adopted for decades, but their practical use is often constrained by high operational cost, rigorous field requirements, and logistical limitations at depth. As engineering projects advance into deeper and more complex geological environments, these constraints have prompted growing interest in laboratory-based, core-derived stress measurement approaches. Such methods utilize the stress-relief deformation that occurs when drill cores are extracted, enabling stress estimation without extensive downhole instrumentation. This paper presents a critical review of core-based stress measurement techniques based on a structured survey of peer-reviewed literature retrieved from major scientific databases (Web of Science, Scopus, and Google Scholar), covering studies published from the 1960s to 2025. The review examines Anelastic Strain Recovery (ASR), Differential Strain Curve Analysis (DSCA), Deformation Rate Analysis (DRA), acoustic-emission-based Kaiser effect approaches, and the emerging Diametrical Core Deformation Technique (DCDT). Recent studies show that DCDT, which measures instantaneous elastic diametrical deformation of cores, provides a more direct and physically transparent link to differential in situ stress, with reduced sensitivity to time-dependent effects. The DCDT, based on precise measurement of instantaneous elastic deformation upon coring, offers high-resolution stress estimation with minimal disruption to field operations. Its compatibility with optical scanning, laser micrometers, and CT imaging highlights its potential as a practical alternative to conventional techniques. A comparative synthesis of assumptions, accuracy, and applicability is provided, and key limitations and future research needs of core-based stress measurement methods are identified. The findings of this review provide practical guidance for selecting stress measurement techniques and support the application of core-based methods, particularly DCDT, in deep underground engineering, where cost-effective and reliable stress characterization is required.

1. Introduction

Underground constructions, such as tunnels, caverns, and deep mining excavations, play a vital role in modern infrastructure and resource development. With the increasing global demand for energy, transportation, and mineral resources, these engineering projects are extending to greater depths and more complex geological environments. Accurate measurement of in situ stress is fundamental to the design, safety, and long-term performance of underground engineering works. The state of stress within the Earth’s crust arises from both gravitational loading due to overburden and tectonic forces associated with crustal deformation [1,2,3]. These stresses are inherently anisotropic and heterogeneous, varying spatially with geological conditions and temporally due to excavation migration. Recent studies in deep geotechnical engineering have demonstrated that the in situ stress field is not static but evolves continuously with excavation, mining progression, and dynamic disturbances. Stress redistribution and concentration around underground openings are strongly influenced by depth, structural discontinuities, and stress path changes, and play a critical role in the initiation of rockbursts, spalling, and large-scale instability phenomena in deep tunnels and mines [4,5,6,7,8]. In engineering practice, the three principal stresses—vertical, maximum horizontal, and minimum horizontal—govern the mechanical behavior of rock masses and influence the stability of excavations [9,10]. Failure to account for these stresses can lead to severe geotechnical hazards, including rockbursts, spalling, fault reactivation, and ground subsidence. To prevent such occurrences and ensure safety and operational efficiency, it is crucial to understand and monitor the stress conditions within the rock. For example, in mining engineering, it is applied throughout the entire life cycle of a mine, from the early stages of exploration through active extraction and eventually to closure and site rehabilitation. In addition to large-scale stress evolution, the process of drilling and coring itself introduces complex unloading paths that may induce tensile cracking, microcrack growth, and localized damage near the core surface. Experimental and numerical investigations have shown that coring-induced unloading damage is strongly stress-dependent and may significantly alter the mechanical response of recovered cores under deep, high-stress conditions, thereby influencing the interpretation of deformation-based stress measurements [11,12,13].

Recognizing its critical importance, researchers and engineers have devoted extensive efforts over the past several decades to developing accurate and practical methods for in situ stress measurement. Among the wide range of proposed techniques, overcoring and hydraulic fracturing are currently regarded as the most mature and widely accepted methods, having achieved extensive scientific validation and commercial application [14,15,16]. Despite their reliability, these conventional techniques face significant limitations when applied to great depths or highly heterogeneous formations. The high cost, time-consuming field procedures, and equipment constraints often restrict their use, particularly in deep mining and tunnelling environments. Moreover, conventional in situ methods are typically conducted at limited locations and times, making it difficult to capture stress heterogeneity and stress evolution induced by excavation activities. In addition to the pre-existing stresses, operation-induced stresses also arise as a direct consequence of human activities such as excavation, drilling, blasting, or fluid injection. These processes disturb the original stress field, resulting in stress redistribution and concentration around openings, which can trigger various failure mechanisms. The growing need to monitor both in situ and induced stresses, especially under dynamic construction and extraction conditions, has highlighted the limitations of traditional field-based stress measurement techniques.

Against this background, increasing attention has been directed toward core-based stress measurement methods. These approaches infer in situ stress information from the deformation, strain recovery, or acoustic response of drill cores following stress relief during coring, thereby avoiding the need for complex downhole instrumentation and labor costs. Core-based techniques offer several distinct advantages. One of the primary benefits lies in their cost-effectiveness. Using drill cores that are from geological exploration or resource development eliminates the need for additional boreholes or complex downhole instrumentation. This approach significantly reduces both logistical complexity and financial expenditure, while also providing a more sustainable alternative to conventional field-intensive methods. These attributes are consistent with sustainable development objectives and governmental directives related to deep resource exploitation and underground infrastructure safety. Moreover, core-based methods are versatile, applicable across a wide range of geological settings and excavation stages, including deep or inaccessible environments where traditional methods may be impractical or unsafe. Importantly, several of these techniques—such as Diametrical Core Deformation Analysis (DCDA), Anelastic Strain Recovery (ASR), and Deformation Rate Analysis (DRA)—are sensitive to stress redistribution induced by excavation, enabling the detection of evolving stress changes during active construction or mining operations [17,18]. As a result, core-based approaches provide a complementary and, in some cases, alternative pathway for both estimating the pre-existing in situ stress field and monitoring stress evolution over time.

In the following sections, this paper presents a comprehensive review of both conventional and core-based stress measurement techniques. The discussion focuses on the theoretical principles, practical implementations, and limitations of each method. Particular emphasis is placed on the Diametrical Core Deformation Technique (DCDT), which represents an emerging approach within the broader family of core-based methods. Related methods such as ASR, DRA, Acoustic Emission (AE), Differential Strain Curve Analysis (DSCA) and DCDA are briefly introduced to provide a comparative framework.

To ensure transparency and reproducibility, this review is based on a structured literature survey of peer-reviewed publications retrieved from major scientific databases, including Web of Science, Scopus, and Google Scholar, covering foundational and recent studies from the 1960s to 2025. The selected literature was screened and synthesized according to measurement principle, type of stress information obtained, level of laboratory and field validation, and practical applicability in deep underground engineering. This analytical framework forms the basis for the comparative evaluation, synthesis of results, and identification of research gaps presented in this paper.

2. Conventional In Situ Stress Measurement Techniques

In situ stress measurement methods are typically conducted at a location far from mining activities to ensure that the site is beyond the zone of stress influence and to capture the far-field or pre-mining state of stress. Two commonly used in situ stress measurement techniques are overcoring and hydraulic fracturing. The overcoring technique is based on measuring stress relief resulting from overcoring a pilot hole. It assumes that the rock material is linear elastic, homogeneous, and isotropic in the vicinity of the borehole. This method requires measuring either the diametrical deformations or the strain changes during the overcoring process. The necessary rock properties, including Young’s modulus of elasticity (E) and Poisson’s ratio (ν), are obtained from uniaxial testing of the extracted rock core. The general procedure for overcoring methods is as follows (Figure 1): a borehole is drilled into the rock at the desired location where the in situ stress regime needs to be determined. A pilot hole—having a smaller diameter than the borehole—is then drilled at the end of the borehole, and the instrumented cell is pushed into the pilot hole. Subsequently, the borehole is extended by overcoring the pilot hole, and the strain changes or the diametrical deformations are recorded by the instrumented cell. The strain changes are commonly determined by soft stress cells, such as Council of Scientific & Industrial Research (CSIR), and Commonwealth Scientific and Industrial Research Organization (CSIRO) Hollow Inclusion Cell (HI Cell), using a temperature-specific gluing pack to attach the strain gauges to the rock mass. In terms of the determination of displacement deformation, the two prevalent displacement measurement instruments are the US Bureau of Mines cell (USBM) and Sigra Pty Ltd’s (Brisbane, Australia). In situ Stress Tool (SIGRA IST). These measurements can be used to calculate the in situ stress.

This technique provides highly accurate stress measurements and is applicable across a wide range of geological conditions. However, the thickness of the glue and its thermal sensitivity may influence the precision of the results. As with the USBM and SIGRA IST methods, the technique requires intact, continuous core samples for reliable measurement. In practice, obtaining such cores is often hindered by pre-existing fractures, core discing, and natural jointing, especially under the high stress conditions at great depth [20]. By comparing with the overcoring method, the hydraulic method has better performance in in situ stress measurement at shallow depth [21,22]. There are three subgroups in the hydraulic method, which are the hydraulic fracturing method, the sleeve fracturing method, and the hydraulic tests on pre-existing fractures method [23]. Hydraulic fracturing is one of the best-known techniques in hydraulic methods. It is not only useful for mining but also an important tool for many large projects, such as hydro power plants. The basic philosophy behind this technique is to force a borehole to create fractures by injecting fluid. The direction of crack propagation indicates the maximum stress direction. A graph like the one shown in Figure 2 is recorded for the hydraulic fracturing test. The curve reflects the pressure change with time. At the initial stage, when fluid injection begins at a certain flow rate, fluid pressure increases linearly with time until it reaches the “leakoff” point, where the straight-line AB ends as shown in Figure 2. The peak point “C” on this curve is labelled as the breakdown pressure. The most accepted definition of this point is that it represents the fracture moves from a ‘stable’ condition to an ‘unstable’ condition [24]. Then, from point “D” to “E”, the borehole gets into pressure relief-in and fracture propagation period until the fluid injection pumps are turned off when desired fractures are observed. After the pumps are turned off, the pressure drops suddenly, and this point is called shut-in pressure, also known as instantaneous shut-in pressure (ISIP); see point F on Figure 2. At the end of the test, fractures start closing, and the point is marked as closure pressure [25]. Hydraulic methods have the advantage of in situ stress estimation at shallow depths [23]. However, most underground mines are not shallow. Additionally, the equation of in situ stress and inner pressure is derived based on the assumption that the near-borehole stress field is linear, which is not accurate due to the stress concentration. Also, the pressure generated by injecting fluid in hydraulic methods may not always be uniform [26].

3. Principles of Core-Based Stress Measurements

3.1. Fundamental Mechanisms of Stress Relief After Coring

The fundamental principle of core-based stress measurement techniques is the stress relief mechanism that occurs when a rock core is extracted from its original in situ environment [10,27]. Before drilling, the rock mass is subjected to the three-dimensional principal stresses, which define the local stress state. During the coring process, material surrounding the borehole is progressively removed, and the rock segment enclosed within the core barrel becomes mechanically isolated from the surrounding rock mass. As a result, the boundary constraints imposed by the in situ stress field are released, leading to a partial or complete elastic recovery of the rock core.

This stress release induces deformation within the core, which can be measured as strain recovery or diametrical deformation, depending on the measurement approach. In an idealized case, the total stress removal is instantaneous, and the rock behaves as a perfectly elastic, homogeneous, and isotropic material. Under such conditions, the deformation of the core directly reflects the pre-existing stress field, and the relationship between stress and strain can be described by Hooke’s law for three-dimensional elastic solids [28,29]. However, natural rockmasses rarely meet these ideal assumptions. Factors such as microcracking, anisotropy, mineral fabric, poroelastic effects, and time-dependent behavior introduce nonlinearities in both the magnitude and the rate of strain recovery [30,31].

When the core is extracted, the outer cylindrical surface of the core experiences the largest relief, while the inner parts remain partially stressed until the stress gradually redistributes within the sample. This nonuniform stress release generates radial, circumferential, and axial strain components, the relative magnitudes of which depend on the original stress tensor and the rock’s elastic constants (E and ν). The resultant deformation pattern—whether measured as changes in diameter, strain over time, or surface displacement—encodes information about the original in situ stress orientation and magnitude.

The partitioning of deformation into instantaneous elastic recovery and delayed, hysteretic recovery is further influenced by rock brittleness. In brittle rocks, stress relief tends to activate microcrack opening, closure, and frictional sliding, increasing nonlinear and time-dependent deformation components. As a result, rocks with higher brittleness indices often exhibit a greater proportion of hysteretic recovery relative to purely elastic rebound, whereas more elastically compliant rocks show deformation dominated by instantaneous recovery.

In addition to the immediate elastic response, anelastic and viscoelastic deformation often occur following coring. This delayed recovery, driven by microcrack closure, internal friction, and time-dependent mineral rearrangement, is the basis for techniques such as ASR and DRA. These time-dependent strains typically follow an exponential or logarithmic decay function, reflecting the gradual approach toward mechanical equilibrium after stress removal.

Another important consideration is the influence of coring-induced damage. The drilling process introduces localized tensile and shear stresses near the core surface, potentially creating microcracks and altering the true deformation response. Such damage must be accounted for in both laboratory calibration and field interpretation. Temperature changes and fluid invasion during drilling can further modify the mechanical behavior of the core, contributing to additional strain components unrelated to the in situ stress field.

Despite these complexities, the mechanics of stress relief remain the fundamental link between measurable deformation and the in situ stress state, through proper understanding and modeling of this process, which often involves both analytical and numerical approaches. A core-based technique, such as the Diametrical Core Deformation Technique (DCDT), can effectively invert measured deformation to back-calculate the pre-existing principal stresses. This makes the study of stress relief mechanics not only a theoretical prerequisite but also the cornerstone of all subsequent analysis and interpretation in core-based stress measurement.

3.2. Concepts of Core-Based Methods

Although all core-based stress measurement methods are founded on the same principle of stress relief, they differ fundamentally in how they interpret and quantify the resulting deformation. These differences arise from the physical mechanisms emphasized—whether instantaneous elastic rebound, time-dependent anelastic recovery, or cumulative strain response—and from the instrumentation and analytical frameworks employed. Conceptually, these methods can be grouped into two broad categories: (1) those that infer stress from elastic recovery observed immediately after coring (e.g., DCDA), and (2) those that utilize time-dependent strain evolution following stress relief (e.g., ASR, DRA, DSCA). Each technique captures a different aspect of the rock’s mechanical memory, reflecting distinct assumptions about the elastic, anelastic, and viscoelastic behavior of the core material.

3.2.1. Kaiser Effect on the Rock Sample

The Kaiser effect is based on acoustic emission (AE), a phenomenon that occurs when acoustic waves are generated by sudden stress changes in a material. The Kaiser effect reveals that the material only emits an acoustic emission signal when its reloaded stress is higher than the previous one. The Kaiser effect was investigated on the rock samples for stress estimation [32]. It is found that during the laboratory compressive test on the intact rock sample, acoustic emission will occur since the rock was subjected to the in situ stress before the test. The experimental procedure of monitoring the Kaiser effect to determine the pre-existing maximum natural stress (${\mathsf{\sigma }}_{\mathbf{m}}$) in the rock was presented by Yoshikawa and Mogi (1981) [33]. The experiment requires a compression load cell to apply uniaxial stress on the rock cores and the transducer to record the Kaiser effect (Figure 3). In the test, a certain level of compressive stress is applied to the rock cores with a constant loading rate for at least two cycles (loading/unloading). Figure 4a shows the plot of two cycles of an ideal successive loading/unloading test. The cumulative number of AE hits increases dramatically after the pre-existing maximum stress value is reached. However, there are some cases in which the Kaiser effect cannot be easily observed. Yoshikawa and Mogi (1981) proposed that the plot of AE count rate for cyclic loading as a function of stress can provide a more accurate value when determining ${\mathsf{\sigma }}_{\mathbf{m}}$ since the point can be clearly determined at which the two cyclic loading curves separate from each other (Figure 4b) [33].

The manifestation of the Kaiser effect is strongly influenced by the loading path and confining pressure, particularly under stress conditions representative of deep underground environments. Under triaxial loading or elevated confining pressure, acoustic emissions may occur at stress levels lower than the true historical maximum due to microcrack frictional sliding, crack closure–opening hysteresis, or progressive damage accumulation, leading to a so-called false Kaiser effect.

In contrast, a true Kaiser effect is typically characterized by a sharp and reproducible increase in AE activity that consistently occurs at the same stress level across repeated loading cycles and under comparable confinement conditions. Distinguishing between true and false Kaiser effects commonly relies on diagnostic indicators such as the evolution of AE event rate and cumulative AE energy, the Felicity ratio, repeatability of AE onset stress during cyclic loading, and comparative testing under different confining pressures. Incorporating these criteria is essential for improving the reliability of maximum geostress determination using AE-based methods.

Although some authors have confirmed the good correlation of stress determination between using this AE method based on the Kaiser effect with other mature stress measurement techniques, the discussion on whether it is a reliable method to determine stress is still ongoing, and it is not commercially available. It is also noticed that this method can only be used to determine the pre-existing maximum stress instead of in situ stresses.

3.2.2. Anelastic Strain Recovery (ASR)

The ASR was developed based on the stress-induced elastic strain that is released instantaneously after a core is extracted from the rock mass and used for determining the horizontal stresses with the assumptions of overburden as one of the principal stresses and that the ASR compliances of rock are independent of the applied stress. Different methods and instruments have been designed to measure ASR of rock cores, such as standard rosette-type strain gauges [34,35], customized clip-on gauges [36], the instrument with LVDT transducers designed by the British Geological Survey and the University of East Anglia. All these instruments were designed to measure the strain recovery of rock cores after they were taken out of the rock mass. Although they tried to minimize the time elapsed between the core being extracted and the measurement being made, the strain recovery was started as soon as the core was being drilled. In 1991, Matsuki extended the application of ASR from the estimation of stresses in the horizontal plane to the three-dimensional in situ stresses [37]. It is stated that for an isotropic viscoelastic material, when the in situ stresses and the pore pressure were released stepwise at t = 0, anelastic normal strain recovered during the elapsed time in an arbitrary direction. The equation in this method shows that anelastic strain is affected by many parameters. That means the main factors that limited the application of ASR include temperature variation yielding thermal strains, dehydration of core samples, pore fluid pressure diffusion, non-homogeneous recovery deformation, rock anisotropy, drilling mud–rock interaction, residual strains, core recovery time, and the accuracy of core orientation [38].

3.2.3. Differential Strain Curve Analysis (DSCA)

The DSCA is one of the strain recovery methods, which was developed based on the assumption that the oriented micro-cracks were induced in the rock core samples by the stress relief when it was taken from the rock mass at depth, and their density is proportional to the relieved stress magnitudes. Strickland and Ren [35] proposed that hydrostatic pressure can be used to compress the rock samples, and the magnitude of hydrostatic pressure applied causes the crack closure related to in situ stress estimation. They thought the difference in the slopes of the pressure-strain curves was an indication of stress relief. Sample preparation for the DSCA test includes cutting the rock cores retrieved from underground into cubic samples, installing strain gauges on all six surfaces, and sealing the test cubes to protect the strain gauges during the hydrostatic pressure test. The hydrostatic pressure should be applied to the cubic rock samples for plotting the strain-pressure curve. According to Strickland and Ren [35], the effects of the cracks appear as the shape of the pressure-strain curve. An example of the pressure-strain curve is presented in Figure 5. The XYZ refers to the coordinate system in Figure 5a, the solid curve shows the normal strain parallel to the indicated direction, and the blue curve shows the slope of the corresponding strain (Figure 5b). Using the technique of Strickland and Ren, once one principal stress is known, the other two principal stresses can be determined based on the assumptions that the principal directions and magnitude ratios of the in situ stress coincide with the principal directions of the strain due to the closure of the micro-cracks.

This method requires the assumption that the cracks are mainly caused by stress relief, and the cracks caused by other factors, like temperature reduction, can be neglected, which is not true for most cases. Also, the studies found that the stress orientations determined with the DSCA method are not reliable compared to the results from other mature techniques [39].

3.2.4. Deformation Rate Analysis (DRA)

The Kaiser effect is characterized by a dramatic increase in inelastic strain under compressive stress with a constant stress rate when the applied stress exceeds the previous peak stress. Brace et al. (1966), Stevens and Holcomb (1980), and Kuwahara et al. (1990) have proposed that, in reference to the Kaiser effect, one can expect the inelastic strain to increase linearly under applied stress as long as the applied stress is less than the pre-existing peak stress [40,41,42]. Yamamoto et al. (1990) confirmed this concept by recording the strain behavior under uniaxial compression tests [43]. The experiment reveals that the pre-existing stress can be observed from the change in the gradient of the stress-strain relation. Two cyclic uniaxial loading tests were performed, and the differences in strain during loading between the two cycles were measured as a function. The sample preparation for conducting the DRA test involves collecting three cube samples from single core pieces at each depth, and the cube samples must be sawn into small pieces as several specimens for the uniaxial compression tests (Figure 6a). Then, apply uniaxial compression stress to the rock specimens for five to six loading cycles. Figure 6b shows the specimen preparation and the compressional axis of the UCS test to determine the horizontal stresses. Several tests need to be done in different directions since the principal stress directions are unknown. Vertical stress is considered one of the in situ stresses. Similar to horizontal stress, uniaxial compressive stress is applied vertically to determine the vertical stress.

3.2.5. Diametrical Core Deformation Analysis (DCDA)

Diametrical Core Deformation Analysis (DCDA) interprets the relationship between the in situ stress field and the elastic deformation that occurs in a rock core due to stress relief. It provides analytical basis for practical implementation known as the Diametrical Core Deformation Technique (DCDT). The essential premise of DCDA is that the principal stresses in a plane perpendicular to the rock core can be calculated from the core expansion after drilling. This is when the core is relieved of its boundary stresses. It undergoes a diametrical change in cross-sectional geometry (Figure 7). The magnitude and orientation of this diametrical deformation are theoretically related to the magnitudes and directions of the principal stresses acting at the time of coring.

In the conceptual model, the stress release process is treated as an instantaneous, linear-elastic response of a finite cylindrical body subjected to plane stress conditions. Prior to extraction, the rock around the borehole is in equilibrium under three principal stresses: the vertical stress (${\sigma }_{\mathrm{v}}$) and two orthogonal horizontal stresses (${\sigma }_{\mathrm{H}}$ and ${\sigma }_{\mathrm{h}}$). Upon coring, the lateral confinement is removed, resulting in radial expansion that varies as a function of depth, as shown in Equation (1). The UCS test needs to be done for determining the geomechanical properties in terms of Young’s modulus (E) and Poisson’s ratio ($\nu$). The maximum and minimum diameters (dmax and dmin) can be measured with high-resolution equipment. However, ${\mathrm{d}}_{\mathrm{o}}$ is unknown due to the material loss during drilling. It is not equal to the inner diameter of the drill bit. To solve this challenge, Li and Mitri developed an analytical model based on the volumetric strain change to determine ${\mathrm{d}}_{\mathrm{o}}$, which extended the DCDA so that it can not only determine the stress orientation but also the magnitudes of two principal stresses (Equation (2)) [44].

$$\begin{gathered} {\displaystyle \frac{1}{E}}\{{\sigma }_H-\nu h\}={\displaystyle \frac{d_{max}-d_o}{d_o}} \\ {\displaystyle \frac{1}{E}}\{{\sigma }_h-\nu {\sigma }_H\}={\displaystyle \frac{d_{min}-d_o}{d_o}} \end{gathered}$$

(1)

$$d_o=\sqrt{{\displaystyle \frac{\frac{{{(3d}_{max}}^2{{+3d}_{min}}^2{+2d}_{max}{d}_{min})}{8}[1-\frac{\nu }{E}\left({\sigma }_H+{\sigma }_h\right)]}{(\frac{1-2\nu }{E}\left({\sigma }_H+{\sigma }_h)+1\right)}}}$$

(2)

4. Evolution and Classification of Diametrical Core Deformation Technique

4.1. Historical Development of DCDT

The development of the DCDT is rooted in the concept of diametrical core deformation analysis, which was proposed by Funato and Ito [29] as a means to infer in situ differential stresses from core samples after stress relief. The concept originated from the recognition that when a cylindrical rock core is extracted from the rockmass and relieved of its in situ boundary stresses, its cross-section may deform in response to the original stress field. They derived the theoretical relationship between the difference of horizontal principal stresses (${\sigma }_{\mathrm{H}}-{\sigma }_{\mathrm{h}}$) and the measured difference between maximum and minimum core diameters in the plane perpendicular to coring. Ziegler and Valley evaluated the implementation of DCDA using photogrammetric core scanning, comparing its outcomes with independent indicators such as borehole breakouts and stress-induced core discing fractures [45]. Their study also investigated the extent to which elastic anisotropy influences the inferred stress magnitudes. Building on these developments, Li et al. applied DCDA to estimate biaxial stress conditions and proposed an analytical solution for determining the principal stress components in a plane perpendicular to the borehole and parallel to the exposed mining face [46]. They also extended DCDA to a practical technique (DCDT) for assessing mining front stability [47]. Later on, Meng et al. (2025) [48] estimated the in situ stress using DCDT at a depth of 500 m in the monzonitic granite of the North Tianshan Mountains in Xinjiang, China. This indicates that the magnitude of in situ stress derived from core samples using DCDT aligns well with hydraulic fracturing results [48]. Dargahizarandi et al. (2025) [49] developed an integration of DCDT with ultrasonic mapping for obtaining complete three-dimensional stress tensors and successfully applied the technique at an underground metalliferous mine in Australia.

4.2. Classification by Measurement Principle and Instrumentation

The successful application of the diameterical core deformation theory hinges on the ability to measure minute variations in core diameter resulting from elastic stress relief. For typical hard rock conditions, the differential deformation (d_max − d_min) is in the range of 10–50 µm for in situ stress differences between 5 and 20 MPa, assuming elastic moduli of 20–60 GPa. Thus, the metrological challenge is to achieve micron- or submicron-level precision while maintaining geometric and angular accuracy. Four major instrument configurations have been reported in the literature for DCDA: optical micrometer systems, laser micrometer systems, X-ray computed tomography (CT), and coordinate or optical scanning methods. Each setup offers distinct advantages in resolution, measurement environment, and data processing workflow.

4.2.1. Optical Micrometer Apparatus

Funato and Ito (2017) introduced one of the earliest purpose-built optical micrometer instruments for DCDA measurement [29]. The system employs a collimated LED light source that projects a shadow of the rotating core onto a charge-coupled device (CCD). The instrument automatically detects the shadow edges and records the instantaneous core diameter at regular angular intervals during continuous rotation on a pair of motor-driven rollers. The system achieves a measurement resolution of 0.01 µm with repeatability of ±0.2 µm, measuring cores ranging from 30–65 mm in diameter and 60–500 mm in length.

The optical micrometer method provides non-contact, high-precision measurements and avoids mechanical interference that could induce secondary deformation. Its typical acquisition rate (one full rotation every 90 s, with readings every 2°) ensures dense angular sampling for accurate 2θ fitting of the diametrical variation curve. The primary limitation lies in the need for clean, uniform core surfaces and careful alignment to minimize rotational runout. Nonetheless, the system remains a benchmark for laboratory-based DCDA studies where stability and submicron resolution are critical.

4.2.2. Laser Micrometer System

Li and Mitri expanded the DCDA methodology to mining-induced stress analysis by employing a laser micrometer system capable of 0.1 µm resolution [47]. Based on sensitivity analysis, the author demonstrated that such precision is required to detect the ovalization expected from stress differences of 10 MPa or less. The apparatus, developed using a Mitutoyo laser micrometer (Mitutoyo, Kawasaki, Japan), accommodates core diameters ranging from 30.5 mm (AQTK) to 85 mm (PQ), consistent with common exploration standards.

Laser micrometers offer several advantages: they provide traceable calibration, reduced operator dependency, and high repeatability, making them suitable for both laboratory and semi-automated industrial settings. The laser system records the core diameter while the sample rotates, producing a continuous circumferential profile. When combined with mechanical property testing (uniaxial compression for Young’s modulus (E) and Poisson’s ratio ($\nu$)), the results can be inverted to obtain both the magnitude and orientation of in situ stresses. The primary challenges include ensuring rotational stability and compensating for minor eccentricities or optical reflections from irregular rock textures.

4.2.3. X-Ray Computed Tomography (CT) Measurement

A non-contact alternative to surface micrometry involves using X-ray computed tomography (CT) to reconstruct the internal geometry of the core. Kim et al. applied CT-based DCDA to a 100 mm granodiorite core retrieved from a depth of 4.2 km in a geothermal project [50]. Each CT slice was processed using ImageJ software: the image was binarized, the contour selected, and an ellipse fitted to determine the major and minor diameters and the azimuth of the major axis. The resulting average horizontal stress difference was 13.3 MPa, in agreement with overcoring data from a nearby well.

This approach offers key advantages: the ability to analyze large or fractured cores, eliminate contact-induced errors, and simultaneously investigate internal features such as joints or anisotropy. It also facilitates coupling DCDA deformation with textural indicators like joint roughness coefficient (JRC) orientation. The limitations are primarily logistical—CT scanning requires specialized equipment and generates vast data volumes that demand careful slice alignment and calibration. Nevertheless, it has proven particularly useful for deep borehole or geothermal applications where sample integrity is critical.

4.2.4. Coordinate and Optical Scanning Techniques

For long or discontinuous cores, coordinate-measuring machines (CMMs) and structured-light or photogrammetric scanners provide a robust alternative to traditional micrometers. Ziegler and Valley (2021) evaluated DCDA and discing analyses using a CoreScan3 imaging system on the Basel-1 deep geothermal borehole (4.9 km depth) [45]. The setup captured overview and unrolled surface scans at 10 px/mm and 40 px/mm resolutions, respectively. Despite challenges with partial core orientation and segmentation, the study demonstrated that optical scanning can achieve the necessary angular precision for stress inversion while allowing integration with other visual features such as drilling-induced fractures and discing.

The main strength of CMM and optical scanning approaches is their ability to digitize and archive full 3D core geometries, supporting post-analysis and data sharing. Their flexibility makes them particularly suited for legacy core repositories and deep scientific drilling projects. However, measurement accuracy depends heavily on the fidelity of the 3D mesh reconstruction and on precise orientation referencing along the core axis.

All four methods meet the fundamental requirement of resolving micron-scale ovalization with high angular accuracy. Optical and laser micrometers remain the most widely adopted for controlled laboratory settings, offering superior repeatability and real-time measurement. CT and scanning-based techniques, while less common, provide valuable extensions for complex or deep-core conditions and allow the integration of mechanical, textural, and structural analyses.

5. Laboratory Verification and Field Application

The reliability of the diametrical core deformation analysis technique depends on laboratory verification and field validation under diverse geological and stress conditions. Since its conceptual development by Funato and Ito, DCDA and its practical implementation as the DCDT have undergone continuous refinement through analytical modeling, numerical modeling, and application in various underground environments.

Controlled stress-relief experiments have been fundamental to demonstrating the physical validity of the rock core deformation and stress relationship. Funato and Ito (2017) first established a linear elastic relationship linking in situ horizontal stress differences to the diametrical deformation of a recovered rock core [29]. Using optical micrometry with sub-micron precision, their laboratory experiments verified that core ovalization follows a 2θ periodicity consistent with the principal stress orientations and magnitudes predicted by elasticity theory. These results confirmed that diametrical strain recovery can serve as a reliable proxy for the differential horizontal stress in isotropic, homogeneous materials.

Following laboratory verification, DCDT has been deployed in a growing number of underground mining operations, providing both validation against established methods and novel insights into stress heterogeneity. The first major field validation was performed by Funato and Ito (2017) using oriented cores at the depths of 445 m, 486 m, and 588 m from a vertical borehole at Okayama, Japan, where the differential stresses determined from DCDA are closely matched by hydraulic fracturing results in both magnitude and orientation [29]. This demonstrated that stress information could be accurately retrieved from standard exploration cores without the need for expensive in situ instrumentation.

Further evidence of field robustness came from deep geothermal and scientific drilling applications. Kim et al. applied CT-based DCDA to 4.2 km cores in a granodiorite reservoir, finding a horizontal stress difference of 13.3 MPa consistent with nearby overcoring data [50]. Ziegler and Valley (2021) implemented high-resolution optical scanning on the Basel-1 geothermal borehole (4.9 km) in Switzerland, which validates DCDA-determined orientation against borehole breakouts and drilling-induced fractures [45]. Their results confirmed that the orientation of the maximum principal stress determined from DCDA coincided with borehole breakout data within 10°, supporting the method’s reliability even in deep and complex stress regimes.

Later on, Li and Mitri (2024) extended the method to mining-induced stress estimation in hard rock mines [51]. Using a laser micrometer system, the DCDT was applied to oriented cores extracted from production drifts in the Young-Davidson mine in Canada. The estimated stress magnitudes and orientations were cross-validated with stress measured by overcoring and numerical modeling, showing strong correlation, particularly in regions of high horizontal stress anisotropy. The method’s practicality—relying only on standard core drilling—proved particularly valuable in operational mines where intrusive in situ testing is logistically difficult or hazardous.

Most recently, Dargahizarandi et al. [49] combined DCDT with ultrasonic velocity mapping. This hybrid approach enables the determination of both azimuth and dip of the principal stress directions, thereby extending the technique to geological settings where the vertical stress is not aligned with the core axis. Field validation was complete in the Dugald River mine, Australia, which demonstrated excellent agreement with overcoring and numerical back-analysis.

6. Comparative Assessment of Core-Based Stress Measurement Methods

6.1. Overview and Rationale

Core-based stress measurement methods have emerged as effective, non-destructive alternatives to conventional in situ stress testing techniques such as overcoring and hydraulic fracturing. They utilize intact, oriented rock cores retrieved from boreholes or excavations to infer pre-existing stress conditions in the rock mass under controlled laboratory settings. These techniques exploit the stress-relief deformation that occurs upon coring and, through appropriate modeling, allow reconstruction of the original in situ stress state.

Compared to field-based direct methods, core-based approaches minimize operational disruption and logistical complexity. Laboratory environments provide the advantage of controlled temperature, humidity, and precision instrumentation, enabling measurements with micron-level accuracy. Since only representative cores are required, these methods exert minimal influence on ongoing mining or tunnelling operations, allowing concurrent stress monitoring during active production.

The importance of these techniques extends beyond mining to diverse engineering fields, including deep geological repositories, geothermal energy extraction, and large-scale civil tunnels. Their efficiency and adaptability have made them increasingly attractive for rapid, economical, and repeatable stress assessment in deep and complex environments where direct measurements may be impractical or unsafe.

6.2. Evidence from Previous Research and Theoretical Foundations

The reliability of core-based stress measurement methods has been substantiated through an extensive and evolving body of experimental and field research. Traditional core-based techniques (such as Anelastic Strain Recovery (ASR), Deformation Rate Analysis (DRA), and Differential Strain Curve Analysis (DSCA)) have laid the foundation for the more recently developed DCDA. A series of studies—including Seto et al. (1998), Villaescusa et al. (2002), Windsor et al. (2009), Lehtonen et al. (2012), Karakus et al. (2015), Bai et al. (2018), and Dinmohammadpour et al. (2022)—demonstrate that core-based approaches can achieve reliable estimates of in situ stress [52,53,54,55,56,57,58]. These results support the concept of rock “stress memory”—the capacity of rock to retain measurable deformation signatures of prior stress states.

The stress memory concept, however, is not without caveats. Many factors that influence the fidelity of core-based methods have been identified: loading duration and rate [59,60,61,62,63], time-dependent effects such as micro-crack closure or viscoelastic relaxation [64,65], changes in water saturation or thermal state [60,66], rotation of principal stress axes [56,60], and coring-induced tensile stresses or micro-damage [58,61]. Lavrov’s (2003) comprehensive review emphasizes that the retention and recoverability of stress-memory signals in cores are sensitive to these influences [12].

Against this backdrop, the Diametrical Core Deformation Analysis (DCDA) method represents a significant refinement in core-based stress measurement, offering a direct and physically transparent link between measurable core deformation and in situ differential stress. Unlike time-dependent recovery approaches such as ASR or DRA, DCDA relies on the instantaneous elastic response of a rock core following stress relief during drilling, thereby reducing uncertainty related to viscoelastic effects and post-recovery handling.

6.3. Comparative Evaluation of Conventional Methods vs. Core-Based Methods

In situ stress measurement techniques are classified into conventional methods and core-based laboratory methods. These techniques differ primarily in measurement scale, instrumentation, and operational complexity.

Conventional techniques, such as overcoring and hydraulic fracturing (HF), are widely regarded as reference methods for in situ stress determination. Overcoring determines the complete stress tensor by measuring strain relief using embedded strain gauges (e.g., CSIRO HI-cell, USBM cell) [22]. While highly reliable and well-calibrated, overcoring is time-consuming, costly, and operationally demanding, particularly in deep or fractured rock masses where borehole stability and access are limited [67,68,69,70]. Hydraulic fracturing infers in situ stress from induced fracture initiation and closure pressures and is especially suitable for deep applications [14,24]. However, HF relies on assumptions of stress uniformity and fracture behavior, and results may be affected by pre-existing fractures, fluid leak-off, and over- or under-pressurization [70,71,72].

In contrast, core-based stress measurement techniques utilize deformation recorded in recovered rock cores and offer advantages in terms of cost efficiency, logistical simplicity, and applicability where borehole testing is impractical. These techniques differ mainly in the type of deformation captured measurement:

• Kaiser-effect–based methods have been used to estimate in situ stress magnitudes under uniaxial and confining pressure conditions, with accuracy influenced by lithology, loading rate, and stress path [73,74,75,76,77]. Recent studies integrating acoustic emission with deformation rate analysis and non-oriented core re-orientation have improved practical applicability, although these methods generally estimate only the previous maximum stress rather than the full in situ stress tensor [78].
• ASR quantifies time-dependent strain recovery immediately after coring and is widely used for regional stress orientation in sedimentary basins and crystalline rocks [22]. However, ASR is sensitive to temperature, time delay, and viscoelastic effects, which limit its applicability for accurate stress magnitude estimation [79,80,81,82,83,84].
• DSCA relies on controlled hydrostatic loading to interpret microcrack closure, providing estimates of in situ stress magnitude but requiring complex sample preparation and careful crack characterization [85,86].
• DRA monitors cyclic strain rate changes under reloading to determine prior peak stresses, analogous to the Kaiser effect in acoustic emission studies, and reflects cumulative stress memory rather than instantaneous elastic deformation [87,88,89].
• DCDA measures instantaneous diametral expansion following coring, allowing direct inversion of differential horizontal stress using the elastic modulus (E) and Poisson’s ratio (ν).

Among these, DCDA and its practical derivative DCDT have gained attention for their simplicity, precision, and direct elastic basis. Recent developments—including optical and laser micrometer systems [29,44] and computed tomography (CT) and ultrasonic hybridization [49,50]—have expanded its applicability to deep mining and complex stress fields [48,90,91,92]. The comparative evaluation of the above-mentioned measurement methods has been summarized in

Table 1. Comparative summary of conventional and core-based in situ stress measurement methods.

Method	Measurement Principle	Key Instrumentation	Operational Complexity	Advantages	Limitations/Challenges
Overcoring	Stress relief measured via strain gauges in overcored rock	CSIRO HI-cell, USBM cell, SIGRA IST	High (multi-step field setup)	Direct, well-calibrated, long-established	Time-consuming, costly, and limited by borehole access
Hydraulic Fracturing (HF)	Induced fracture pressure vs. closure pressure defines stress	Downhole pressure transducer, fluid pump	High	Deep applicability, measures stress orientation	Assumes uniform stress field; possible over/under-pressurization
Kaiser Effect	Acoustic emission occurs only when reloaded stress exceeds the previous maximum (Kaiser effect)	AE sensors, pre-amplifiers, data acquisition system, UCS frame	Medium	Non-destructive, sensitive to prior maximum stress, useful for estimating σmax in intact cores	Only estimates the previous maximum stress, not the full in situ tensor
Anelastic Strain Recovery (ASR)	Time-dependent strain recovery after coring	Strain gauges, LVDTs	Medium	Non-destructive; captures 3D stresses	Sensitive to temperature, saturation, and delay after coring
Differential Strain Curve Analysis (DSCA)	Crack-closure under hydrostatic loading	Strain-gauge cubes, pressure cell	Medium	Simple setup; uses recovered cores	Assumes cracks solely due to stress relief; limited orientation data
Deformation Rate Analysis (DRA)	Inelastic strain rate change during cyclic loading	UCS frame, strain gauges	Medium	Low cost; captures stress history	Requires multiple specimens; empirical interpretation
Diametrical Core Deformation Analysis (DCDA)	Elastic diametral expansion after stress relief	Optical/Laser micrometer, CT, or CMM	Low	High precision, fast, non-destructive, uses standard cores	Sensitive to surface roughness, anisotropy, and coring damage

.

6.4. Challenges and Future Perspectives

Despite the growing maturity and demonstrated potential of core-based stress measurement techniques, several technical and methodological challenges remain, particularly for elastic-based approaches such as DCDA. Addressing these challenges is essential for improving accuracy and broader adoption in deep mining and underground engineering applications.

One of the primary challenges lies in the influence of rockmass anisotropy on deformation measurements and stress inversion. Many current DCDT implementations assume elastic isotropy; however, natural rocks commonly exhibit anisotropic behavior due to bedding, foliation, mineral alignment, or preferential microcrack orientation. Such anisotropy can distort the diametrical deformation pattern measured by optical, laser, or scanning-based systems, leading to biased estimates of stress magnitude and orientation if not properly accounted for. Future research should therefore focus on developing anisotropy-aware compensation algorithms that incorporate direction-dependent elastic properties, derived from laboratory testing, ultrasonic velocity measurements, or CT-based fabric analysis.

Another important challenge is the sensitivity of DCDT to coring-induced damage and surface roughness. Tensile stresses generated during drilling may introduce microcracks near the core surface, while irregularities in core geometry can interfere with high-resolution scanning measurements. Advanced surface correction techniques, damage-aware calibration models, and improved core preparation protocols are needed to separate stress-induced deformation from drilling-related artifacts.

Uncertainty in elastic parameters, particularly Young’s modulus (E) and Poisson’s ratio (ν), also remains a limiting factor, especially under deep, high-stress conditions where stress-dependent elastic behavior may occur. Future investigations should emphasize stress-dependent elastic characterization, coupled with numerical simulations, to better constrain parameter sensitivity and propagate uncertainty through the stress inversion process.

From a methodological perspective, most current DCDT applications focus on estimating the stresses in the plane perpendicular to the borehole axis. Extending the technique toward reliable three-dimensional stress reconstruction requires integration with complementary methods, such as ultrasonic mapping, acoustic emission analysis, or numerical back-analysis. Hybrid frameworks combining DCDT with multi-physics sensing technologies offer a promising pathway for overcoming current dimensional limitations.

Finally, broader field validation and standardization are required before DCDT can achieve widespread engineering adoption. Large-scale application across diverse lithologies, depths, and tectonic settings, combined with standardized data processing workflows and uncertainty reporting protocols, will be critical for establishing confidence among practitioners and regulators.

Overall, while core-based stress measurement techniques—particularly DCDT—offer significant advantages in terms of cost, practicality, and non-intrusiveness, continued methodological refinement is required. Advances in anisotropy compensation, high-resolution sensing, numerical modeling, and standardized validation will play a central role in realizing the full potential of these techniques for future deep mining and underground engineering applications.

7. Conclusions

This paper critically reviewed the development and application of core-based stress measurement methods, with particular focus on the Diametrical Core Deformation Technique (DCDT). Each method examined offers distinct advantages that address the limitations of conventional in situ stress measurement while also presenting its own challenges.

The ASR is an established laboratory technique that captures time-dependent strain recovery and has been successfully applied to determine regional stress orientations. However, it is highly sensitive to temperature variations, core damage, and time delays between coring and measurement. The DSCA method provides a simple experimental framework for stress magnitude estimation through hydrostatic crack closure, but its assumptions regarding crack origin and isotropy limit its broader reliability. The DRA offers a low-cost option to infer pre-existing stress through cyclic loading but requires multiple specimens and relies on empirical calibration.

The DCDA and its applied form, the DCDT, represent a recent evolution toward more precise, elastic-based core methods. By measuring instantaneous diametral deformation upon stress relief, DCDT directly links observable core geometry changes to the differential horizontal stress field. Optical and laser micrometers, computed tomography, and coordinate scanning systems enable sub-micron accuracy, making DCDT particularly effective for deep mining, geothermal, and underground infrastructure projects. Field applications have shown strong agreement between DCDT-derived stresses and results from overcoring and hydraulic fracturing, validating its use as a reliable and non-destructive alternative.

From a practical standpoint, DCDT demonstrates the highest potential for widespread implementation in modern underground construction and mining environments. The technique’s key advantages can be summarized as follows:

• Non-destructive and cost-effective: uses standard oriented cores without requiring additional drilling or complex in situ instruments.
• High precision: achieves sub-micron deformation resolution capable of resolving stress differences below 1 MPa.
• Operational simplicity: can be conducted under controlled laboratory conditions with minimal logistical demand.
• Compatibility with other methods: easily integrated with ultrasonic mapping, CT imaging, and numerical modeling for full 3D stress interpretation.
• Strong field validation: demonstrated agreement with conventional overcoring and hydraulic fracturing across diverse geological and depth conditions.

While DCDT continues to evolve, its combination of analytical rigor, practical applicability, and technological adaptability positions it as a promising and sustainable candidate for reliable, non-intrusive stress measurement in future deep mining and underground engineering applications.