Overcoring Stress Measurement: 2D and 3D Methods, Reliability Ranking and a New Analysis Tool

1  Principle of overcoring

Overcoring estimates in-situ stress by measuring the strain or deformation recovered when a volume of rock is isolated from the surrounding stress field. A pilot hole is drilled from the end of a larger borehole, an instrumented cell is installed in it, and the rock around the cell is then cut free with a larger concentric core barrel (Figure 1). As the annulus advances past the cell, the rock core unloads and the instrument records the elastic response (Amadei and Stephansson, 1997).

Figure 1. Overcoring sequence: access hole, pilot hole, cell installation, overcoring and core recovery .

The stresses are not measured directly. They are back-calculated from the recovered strains or displacements with linear elasticity, so the result depends on two things at once: the quality of the strain record and the elastic properties assigned to the core. The elastic modulus and Poisson's ratio are normally obtained from a biaxial (pressure-chamber) test on the recovered overcore. Overcoring is one of the most widely used methods, with two families of instruments: 3D cells that recover the full stress tensor from one test, and 2D cells that recover the stresses in the plane perpendicular to the borehole.

2  3D overcoring

3D cells bond strain gauges to the pilot-hole wall, or embed them in a soft inclusion, at several orientations. Common instruments are the CSIRO Hollow Inclusion (HI) cell, designed for shallow holes; the ANZI cell, used in shallow and deep holes and installed with glue; and the 3D Sigra IST (Figure 2). The ANZI cell carries 18 gauges in three sets of six: circumferential (ψ = 90°), axial (ψ = 0°) and inclined (ψ = 135°), spaced at 60° around the hole. HI cells typically carry 12 gauges.

Figure 2. Overcoring cells: CSIRO HI cell, ANZI cell, Sigra IST (2D and 3D) and CCBO cell (Zoorabadi, 2022).

Each strain measured in a specific direction is a linear function of the six stress components in borehole coordinates. The relations come from the elastic solution for a hole in an infinite medium (Leeman and Hayes, 1966), with correction factors k1 to k4 for the stiffness of the HI cell inclusion (Worotnicki and Walton, 1976). Rotating the borehole stresses into North, East and Vertical coordinates gives one equation per gauge, εᵢ = aᵢ · σ, and the tensor is the least-squares solution:

Six independent gauge directions are the theoretical minimum; the rest provide redundancy (n − 6 degrees of freedom). That redundancy allows a standard deviation of the residual strains, 95% confidence limits on each component (Student t at n − 6 degrees of freedom) and a correlation coefficient. Judgement can be used to exclude unreliable gauges, based on the recorded strain-time curves (Figure 3), the biaxial test response and signs of debonding. However, the need to exclude gauges, or a large scatter between them, is itself a sign of cell installation or functionality problems, measurement issues, or departure from the CHILE assumptions (Continuous, Homogeneous, Isotropic, Linear Elastic). Each of these reduces the reliability of the back-calculated stress tensor. The eigenvalues and eigenvectors of the tensor give σ1, σ2 and σ3 with their trend and plunge.

Figure 3. Typical gauge strains recorded against overcore distance for a 3D cell (left) and an overcore prepared for the biaxial test (right) (Zoorabadi, 2022).

The main strength of a 3D test is that it needs no assumption about the vertical stress. Its main weaknesses are its dependence on glue bond quality, its sensitivity to temperature and its exposure to stress-induced microcracking during overcoring (Section 4).

3  2D overcoring

2D cells measure the change in pilot-hole size rather than surface strain. The 2D Sigra IST contacts the wall through spring-loaded pins and records radial displacement in three to six directions; the US Bureau of Mines three-component gauge measures three diameters at 60° (Merrill, 1967; Hooker et al., 1974). No glue is needed, so 2D tests are quicker and tolerate wet or cold holes. The measured quantity is the radial strain εr = Δr/a, equivalent to the diametral strain Δd/d, positive for dilation.

For plane strain, the Kirsch solution gives, for a direction θ measured clockwise from the top of the hole:

Here x′ is the top-of-hole direction, y′ is horizontal, and z′ is the hole axis. Three unknowns need at least three readings on different diameters; θ and θ + 180° measure the same diameter. Four to six readings give n − 3 degrees of freedom for error estimates. As with 3D cells, scatter between the recorded strains, or the need to exclude readings, indicates lower reliability of the back-calculated stresses.

A single 2D test resolves only the stresses in the plane normal to the hole. The axial stress cannot be separated from the mean in-plane stress, because it adds the same constant to every direction. Two approaches are used:

•      In-plane solution: solve for σx′, σy′ and τx′y′ with an assumed σz′, then report the in-plane principal stresses P and Q and their orientation.

•      Horizontal solution: assume the vertical stress is principal and equal to the overburden, σv = γ × true vertical depth, and solve directly for σNS, σEW and τNS/EW. This yields σH, σh, the azimuth of σH, KH = σH/σv and Kh = σh/σv. It is exact for vertical holes and well conditioned for steep holes, but it becomes unreliable as the hole flattens.

Because one component is assumed rather than measured, a 2D result is inherently less complete than a 3D result. It should be ranked and reported with that assumption stated.

4  Factors affecting reliability

The largest errors in overcoring rarely come from the least-squares solution itself. They come from the strain record and the elastic properties fed into it. Table 1 summarises the main issues, how they affect the result, and how to control them.

Table 1. Main issues affecting the reliability of overcoring results

Stress-induced fracturing during overcoring is the issue most often overlooked. Discing and fractures in recovered overcores (Figure 4) show that the transient stress path at the drill bit can damage the core while strains are being recorded. Numerical modelling of the overcoring stress path (Figure 5) indicates that, in Hawkesbury Sandstone, the axial tensile stress can exceed the rock tensile strength once the in-situ stress is above about 3 to 4 MPa.

Figure 4. Stress-induced fracturing and discing of overcores (Kang et al., 2006; Akesson, 2008; Siren et al., 2017; as compiled in Zoorabadi, 2022).

Figure 5. Modelled transient stress around the measurement point during overcoring, and maximum axial tensile stress against major horizontal in-situ stress for Hawkesbury Sandstone (Suchowerska McQueen and Zoorabadi, 2018).

Microcracking also produces axial gauge readings that do not represent elastic stress relief. These are often reduced in analysis with an "axial compensation factor". It should be noted that there is no theoretical and physical basis for quantifying the amount of compensation, so raw must be used in stress back analysis.

Heat generated during drilling, glue curing in cold holes, air bubbles under the strain rosettes and pilot-hole damage before installation are installation-stage issues (Figure 6). They are controlled through water circulation, curing time, gauge checks in the biaxial test and an ATV log of the pilot hole before the cell is installed.

Figure 6. Installation-stage quality issues: cell and glue installation, air bubbles under a strain rosette, and pilot-hole damage before installation (Zoorabadi, 2022).

Two further checks are useful. The vertical stress from a 3D test should be compared with the overburden weight; a ratio far from 1 needs explanation. The calculated stress concentration around the pilot hole should also be compared with the strength of intact rock, since it may have caused damage before or during overcoring.

5  Reliability ranking of overcoring tests

Each test should be ranked high, acceptable or low before its result is used in design. A "successful" test should not mean only that a tensor was calculated. Service providers generally follow the ISRM suggested methods (Sjöberg et al., 2003), but tests are sometimes reported as successful despite broken cores, noisy records or joints near the gauges (Figures 7 and 8). Zoorabadi (2022) introduced the ranking criteria in Table 2 after reviewing 2D and 3D overcoring results from several mining and civil infrastructure projects. A test takes the lowest rank met by any criterion.

Figure 7. Requirement for intact rock at the measurement location: the gauges must be clear of joints by a minimum intact rock radius and pilot-hole length (Hakala et al, 2003).

Figure 8. Examples of tests claimed as successful despite a broken core and unstable or noisy strain records (Zoorabadi, 2022).

Table 2. Reliability ranking criteria for overcoring tests (Zoorabadi, 2022)

6  Reporting recommendations

A test report should let an independent reviewer repeat the calculation and apply the ranking above. It should include:

1.       Raw strain-time (or displacement-time) records for every gauge or pin, including those excluded.

2.       Biaxial test records and the E and ν values adopted, with the range considered.

3.       Any compensation or correction applied, with raw and corrected values side by side.

4.       The gauges or pins used in each solution and the reason for each exclusion.

5.       The stress tensor with 95% confidence limits, principal stresses with trend and plunge, and fit statistics.

6.       For 2D tests, the assumed vertical stress, unit weight and plane condition.

7.       Photographs of the overcore and the pilot-hole televiewer log, if taken.

8.       The reliability rank of each test against the criteria above.

9.        

6.1  Selecting the test method

Most of the issues described in Section 4, particularly tensile stress developing ahead of the drill bit and heat generated during drilling, have their greatest effect in deep overcoring. There the overcoring diameter is limited, so the annulus around the cell is thin. Numerical modelling and field experience indicate that these effects are much smaller with a thick annulus, such as the overcoring diameters commonly used with HI cells. In deep exploration boreholes, however, a thick annulus is rarely practicable.

Based on the author's experience, the following approach is recommended:

•      Overcoring: use it mainly in shallower holes drilled from underground excavations, where a much larger overcoring diameter, and therefore a thicker annulus, is possible. This reduces the likelihood of tensile damage to the core and limits the effect of drilling heat on the strain gauges.

•      Deep exploration boreholes: use hydraulic fracturing or hydraulic jacking instead. These methods can give more reliable results at much lower cost, provided enough tests are carried out to support a reliability assessment.

7  Overcoring stress analysis tool

Despite a well-established and published theoretical basis, overcoring stress analysis has remained a black box for most clients. The calculation tools are rarely made available with test reports, so the results are usually accepted without independent verification. This tool was developed to remove that barrier.

I have developed a browser-based tool that applies the methods and checks in this document to both 3D and 2D overcoring tests (Figure 9). It turns the reliability ranking from a judgement made after the fact into checks the analyst can see while selecting gauges.

For 3D cells, the analyst can select 18 cells or less gauges to include, any set of six or more independent directions, and the tool solves the stress tensor by least squares. It reports the six stress components with 95% confidence limits, R², adjusted R² and the standard deviation of the residuals, and gives the principal stresses as eigenvalues with trend and plunge on a stereonet. It also projects the tensor onto the horizontal plane to give σH, σh, the azimuth of σH, KH and Kh, and compares the measured vertical stress with the overburden. For 2D cells, it accepts three to six radial strain readings, solves the in-plane tensor in plane strain or plane stress, and derives σH, σh and the K ratios with the vertical-principal assumption.

Figure 9. Results view of the overcoring stress analysis tool for a 3D cell, with illustrative data: principal stresses on a stereonet, horizontal stresses and stress ratios.

The tool also tests how far each result can be trusted:

•      Sensitivity sweep: varies E, ν, hole orientation, cell factors, depth or unit weight across a range and plots the effect on every output.

•      Tornado charts: rank which inputs, or which individual gauge or pin readings, control each result.

•      Drop-one analysis: re-solves without each gauge or pin in turn and flags readings with high leverage or studentised residuals beyond ±2.

•      Monte Carlo simulation: samples uncertainty in E, ν, orientation and strains, and reports distributions and P5 to P95 ranges of the principal and horizontal stresses.

Results can be compared against a pinned baseline, printed as a report for each analysis and exported to CSV. These outputs map directly onto the ranking criteria in Section 5: the number of operational gauges or pins, confidence limits, correlation and the vertical stress check. The 3D solution reproduces independent least-squares spreadsheet solutions to machine precision, and the 2D solution reproduces the analysis in a field-test report.

References

Amadei, B. and Stephansson, O. (1997). Rock Stress and Its Measurement. Chapman and Hall, London.

Ask, D. (2003). Evaluation of measurement-related uncertainties in the analysis of overcoring rock stress data from Äspö HRL, Sweden. International Journal of Rock Mechanics and Mining Sciences, 40.

Hakala, M., Hudson, J.A. and Christiansson, R. (2003). Quality control of overcoring stress measurement data. International Journal of Rock Mechanics and Mining Sciences, 40.

Hooker, V.E., Aggson, J.R. and Bickel, D.L. (1974). Improvements in the three-component borehole deformation gage and overcoring techniques. US Bureau of Mines RI 7894.

Leeman, E.R. and Hayes, D.J. (1966). A technique for determining the complete state of stress in rock using a single borehole. Proceedings, 1st ISRM Congress, Lisbon.

Merrill, R.H. (1967). Three-component borehole deformation gage for determining the stress in rock. US Bureau of Mines RI 7015.

Mills, K.W. and Pender, M.J. (1986). A soft inclusion instrument for in situ stress measurement in coal. Proceedings, International Symposium on Rock Stress and Rock Stress Measurements, Stockholm.

Mills, K.W., Zoorabadi, M. et al. (2016). Axial strain compensation in overcoring stress measurements (as cited in Zoorabadi, 2022).

Sjöberg, J., Christiansson, R. and Hudson, J.A. (2003). ISRM suggested methods for rock stress estimation, Part 2: overcoring methods. International Journal of Rock Mechanics and Mining Sciences, 40.

Suchowerska McQueen, A.M. and Zoorabadi, M. (2018). Numerical modelling of the transient stress path during overcoring (as cited in Zoorabadi, 2022).

Worotnicki, G. and Walton, R.J. (1976). Triaxial hollow inclusion gauges for determination of rock stresses in situ. Proceedings, ISRM Symposium on Investigation of Stress in Rock, Sydney.

Zoorabadi, M. (2022). Reliability Assessment and Ranking of Rock Stress Measurements. EAGCG Seminar: Ground Support for Underground and Surface Mines, Melbourne.