1. Lecture 2
In situ Rock Stress

2. Why do we need to know the in situ stresses
How our structures will respond,
Other factors being equal, the direction in which the groundwater will flow.
To provide the boundary conditions necessary for stress analyses conducted in the design phase of rock tunnels and underground excavations.

3. In situ Vertical Stress
General relationship between depth and in situ vertical stress
sv = gz
Where g = unit weight overlying the rock mass
And z = depth

4. In situ Vertical Stress
After Hoek & Brown, 1980

5. Example
If we excavated a tunnel at a depth of m below ground level in a sandstone with a Uniaxial Compressive Strength (UCS) of 25 MPa, what is likely to happen to the walls of the tunnel?

6. In situ Vertical Stress
Vertical stress at a given point below ground level is a function of depth and the density of the overlying soil and rock.
Density of rock varies due to variations: in the mineralogy, percentage of porous space, volume of open fractures, volume of other voids.
Specific gravity of quartz = 2.65
Specific gravity of olivine = 3.3 to 3.5

7. In situ horizontal stresses
In situ horizontal stresses vary due to the following factors:
Tectonic activity – close to plate boundaries horizontal stresses are greater.
Topographic features – top of mountains have higher tensile stresses and in valley bottoms there are higher compressional stresses.
In folded strata higher compressional stress act towards the axes of synformal structures and higher tensile are present at the axes of antiformal structures.

8. In situ horizontal stress
The two major in situ horizontal stresses may not be equal.
Horizontal stresses are more difficult to estimate than vertical stress.
The ratio of the average horizontal stress to vertical stress is :
sh = k sv = kgz
Where g = unit weight of the rock mass
z = depth
where v = Poisson’s ratio

9. Worldwide in situ Stress Data
After Hoek & Brown, 1980

10. In situ horizontal stress
Sheorey (1994) developed an elasto-static thermal stress model of the earth. This model considers curvature of the crust and variation of elastic constants, density and thermal expansion coefficients through the crust and mantle.

11. In situ horizontal stress
where z (m) is the depth below surface and Eh (GPa) is the average deformation modulus of the upper part of the earth’s crust measured in a horizontal direction.
This direction of measurement is important particularly in layered sedimentary rocks, in which the deformation modulus may be significantly different in different directions.

13. Sheorey pointed out that his work does not explain the occurrence of measured vertical stresses that are higher than the calculated overburden pressure, the presence of very high horizontal stresses at some locations or why the two horizontal stresses are seldom equal. These differences are probably due to local topographic and geological features that cannot be taken into account in a large scale model. Where sensitivity studies have shown that the in situ stresses are likely to have a significant influence on the behaviour of underground openings, it is recommended that the in situ stresses should be measured.

14. World Stress Map

16. Global Horizontal Stresses
The World Stress Map demonstrates that tectonic activity is a significant factor in determining the amount of horizontal stress.
High horizontal stresses are seen at areas of:
Destructive (compressive) plate boundaries.
Past tectonic activity e.g. SW England where higher than expected horizontal stresses were discovered during the early research for the Camborne School of Mines Hot Dry Rock geothermal project.

17. World Stress Map
Each stress data record is assigned a quality between A and E, with A being the highest quality and E the lowest. A quality means that the orientation of the maximum horizontal compressional stress SH is accurate to within ±15°, B quality to within ±20°, C quality to within ±25°, and D quality to within ±40°. For the most methods these quality classes are defined through the standard deviation of SH. E-quality data records do not provide sufficient information or have standard deviations greater than 40°.

18. www-wsm. physik. uni-karlsruhe. de/pub/stress_data/stress_data_frame
www-wsm.physik.uni-karlsruhe.de/pub/stress_data/stress_data_frame.html

19. Measuring in situ stress
The representation of any stress state involves a minimum of six independent measurements.

20. Failure caused by high in situ stress and low strength rock
Practical_Rock_Engineering-Hoek

21. Induced Stresses

22. Induced Stresses

23. Induced Stresses

24. In situ stress measurement
There are three main methods of in situ stress measurement
Flatjack
Overcoring
Hydraulic

25. The Flatjack Test
Two pins are fixed into the excavation wall at a distance d apart. The distance is measured accurately. A slot is cut into the rock between the pins. If the normal stress is compressive, the pins will move together as the slot is cut. A flatjack is then grouted into the slot and pressurised with oil or water forcing the pins apart again. It is assumed that, when the distance d reaches the value it had before the slot was cut, the force exerted by the flatjack on the walls of the slot is the same as that exerted by the pre-existing normal stress.

26. The Flatjack Test
Major disadvantage with the system is that the necessary minimum number of six tests, at different orientations, have to be conducted at six different locations and it is therefore necessary to distribute these around the boundary walls of an excavation.

27. The Flatjack Test
For a successful in situ stress determination using flatjacks there are three prerequisites:
A relatively undisturbed surface of the opening constituting the test site.
An opening geometry for which closed-form solutions exist, relating the far-field stress and boundary stresses.
A rock mass which behaves elastically, in that displacements are recoverable when the stress increments inducing them are reversed.

28. The Flatjack Test
The items 1) and 3) in the list given above virtually eliminate the use of a test site of an excavation developed by conventional drilling and blasting.
Cracking associated with blasting and other transient effects may cause extensive disturbance in the stress distribution in the rock.
It may also give rise to non-elastic displacements in the rock during the measurement process.
Item 2) restricts suitable opening geometry to simple shapes, ideally a circular opening.

29. Overcoring

30. Overcoring
This method of in situ stress determination is based on the determination of strain in the wall of a borehole, or other deformations of the borehole induced by overcoring that part of the hole containing the measurement device.
If sufficient strain or deformation measurements are made during the stress-relief operation, the six components of the field stress tensor can be obtained directly from the experimental observations.

31. Overcoring Method

32. Overcoring Method

33. Disking in cored granite

34. Overcoring strain devices
A range of devices for direct and indirect determination of in situ stresses are used in over coring tests and include:
Photoelastic gauges
USBM borehole deformation gauges
Biaxial and triaxial strain cells
Triaxial strain (soft inclusion cell) developed by CSIRO is shown on the next slide.

35. Overcoring Stress Cell

36. Overcoring Stress Cell
The hollow cylinder on the left is filled with adhesive which is extruded when the piston, on the right, is forced into the cylinder. The cell is glued in the borehole prior to it being overcored.

37. Strain Measurements

38. The Hydraulic Fracturing Test
Hydraulic fracturing is a process where water is injected into a section of a borehole isolated by two packers.
When the pressure is increased, the state of stress around the borehole boundary is modified by the hydraulically-induced stresses.
If the field principal stresses in the plane perpendicular to the hole axis are not equal, application of sufficient pressure induces tensile circumferential stress over limited sectors of the boundary.

39. The Hydraulic Fracturing Test
When the tensile stress exceeds the rock material tensile strength, fractures initiate and propagate perpendicular to the hole boundary and parallel to the major principal stress.
As the fractures open, simultaneously the water pressure falls in the test section.
Typically the water pressure is applied to the test section in a series of cycles.

40. Hydraulic Fracturing Test
After B.C. Haimson, F.H. Cornet ISRM Suggested Methods for rock stress estimation—Part 3: hydraulic fracturing (HF) and/or hydraulic testing of pre-existing fractures (HTPF). International Journal of Rock Mechanics & Mining Sciences, 40, p1011–1020

41. The Hydraulic Fracturing Test
The two measurements taken are the water pressure when the fracture occurs and the subsequent pressure required to hold the fracture open, known, respectively, as the breakdown (PB) and shut-in (Ps) pressures. The pressure required to reopen the fracture (Pr) is assumed to differ from PB by the tensile strength of the rock. The shut-in pressure is assumed to give the minor principal stress, s3, whilst the major principal stress, s1, is given via the breakdown pressure, the value of s3 and the magnitude of the tensile strength of the rock (st).

42. The minimum boundary stress for a circular opening (from Kirsch equation) is,
smin = 3 sh - sH.
If a pressure (Po) is applied within the borehole, the tangential stress at the wall is given by, sqq = -P0
By superimposition, the minimum tangential boundary stress is, smin = 3 sh - sH - P0
At the point where the crack reopens, Pr = Po and smin = 0, hence sH = 3 sh – Pr
By inspection, sh = Ps and st = PB - Pr

43. Example
The following plot illustrates a typical set of data obtained from a hydraulic fracturing experiment. Determine the tensile strength of the rock and the in situ stress profile.

44. Solution
PB=20.5 MPa
Pr=8.5 MPa
Ps=6.5 MPa
MPa
MPa
MPa

45. Tell-tale indicators of the stress state…

46. Borehole breakouts - damage to a borehole indicating principal stress orientations;
Fault plane solutions - back analysis of principal stresses causing faults;
Acoustic emission - the rock emits low-intensity ‘noise’ when it is stressed;
An elastic strain relaxation - core exhibits expansion/contraction on removal from the borehole;
Differential strain analysis - pressurising a piece of rock indicates its previous stress state through differential strain effects;
Core discing - geometry of stress-induced core fracturing indicates stress components;
Observations of discontinuity states, e.g. open discontinuities are not transmitting stress across the gap.