Rock mechanics for engineering geology part 3
- 2. What Is Strain? • Increase (or decrease) in length resulting from a stress acting parallel to the longitudinal axis of the specimen. • strain is defined as extension per unit length. • Strain = extension / original length
- 3. Stress-Strain Curve for Textile Fibre
- 4. Typical regions that can be observed in a stress-strain curve are: • Elastic region, • Yielding, • Strain Hardening, • Necking and Failure Stress-Strain Curve for Textile Fibre
- 5. Elastic Behavior • If the specimen returns to its original length when the load acting on it is removed, it is said to response elastically
- 6. Yielding • A slight increase in stress above the elastic limit will result in permanent deformation. This behavior is called yielding • The stress that causes yielding is called yield stress sy. • The deformation that occurs is called plastic deformation
- 7. Strain Hardening • When yielding has ended, a further load can be applied to the specimen, resulting in a cure that rises continuously but becomes flatter until it reaches a maximum stress referred to as ultimate stress, su. • The rise in the curve is called Strain Hardening
- 8. Necking & Fracture • After the ultimate stress, the cross- sectional area begins to decrease in a localized region of the specimen, instead of over its entire length. The load (and stress) keeps dropping until the specimen reaches the fracture point.
- 9. Initial stress Stress state in rock mass without artificial disturbances. One of the basic data in designing rock structure. Competence factor = Uniaxial compressive stress / initial vertical stress is a good index for stability of an opening in rock mass Initial stress
- 10. Stress state near opening is disturbed Disturbed zone is avoided for measurement of initial stress Disturbed stress is also measured in some cases where investigating deformation and failure behavior around the opening
- 11. Primitive Estimation σ V = γ h stress σV is weight of rock Initial vertical equal to the overburden (overburden pressure) γ is unit volume weight (ex. 27 kN /m3） h is the depth (m) Ex. Initial vertical stress at 500 m deep is 13.5 MPa σ V = γ h σ h = k2σ V σ H = k1σ V Initial stress value
- 12. Initial horizontal stress σH at a shallow depth. Horizontal stress ε is assumed to be zero.H Eε H = σ H −ν (σ H σ H = kσ V + σ V ) = 0 ν k = 1−ν E is Young's modulus. ν is Poisson's ratio k is the coefficient for horizontal stress k is assumed to be 1 at great depth. σ V = γ h σ h = k2σ V σ H = k1σ V
- 13. Measured initial stress values Initial vertical stress is roughly equal to the primitive estimation Initial horizontal stress is different from the primitive estimation
- 14. Average initial horizontal stress σHavLower limit of (2.7 + 0.0081 h) σHavUpper limit of (40.5 + 0.0135 h) 0 200 Average initial horizontal stress = depth independent value + depth proportional value for 0.25 - 0.33 of poisson's ratio 400 600 800 1000 0 10 20 30 40 50 60 Stress (MPa) Depth(m) σV
- 15. Depth independent value? Movement of the tectonic plates Spherical shell subsidence model "Reprinted from http://pubs.usgs.gov/gip/earthq1/fig1.gif with permission from USGS".
- 16. Orientation of the maximum horizontal stress measured by hydraulic fracture method (Goodman, 1980) Average focal mechanism of deep earthquakes in and around Japan projected on the upper hemisphere. Arrows show tension and compression axes (Kasahara, 1983)
- 17. Spherical shell subsidence model The earth shrinks by gravity force. Compressive strain appears by the spherical geometry.
- 18. Need for initial stress measurement Initial stress can roughly estimated by the primitive method Measurement is required for precise values Initial stress can be affected by such geological phenomena as fold, faults, intrusion of magma etc. Method to measure initial stress
- 19. Method Description Feature Stress relief method A borehole is drilled to desired depth. A probe is installed in the hole. Stress around he probe is relieved by usually overcoring. Three dimensional stress state can be estimated by one overcoring in most methods. It takes costs and time. There are many results. The hole is drilled usually from a roadway. Stress compensation method Stress is relieved measuring displacement or strain. Stress is applied until the displacement or strain recovers to the values before the stress relief. Necessary stress is regarded as initial stress. Measurement is usually carried out at rock surface. It is difficult to estimate three dimensional stress state. Elastic constants are not required to estimate rock stress. Hydraulic fracturing method A borehole is drilled from the ground surface or a roadway. Initial stress is estimated from hydraulic fracturing data. Only horizontal stresses are usually estimated. It can be apllied up to several km deep. There are any results. Methods using oriented core Material tests in laboratory are carried out for rock cores. Initial stress is estimated from such data as stress-strain curves. Results similar to other methods are often obtained although the mechanisms are not well understood. Method based on fault earthquake data Orientation of initial stress is estimated based on the focal mechanism of fault earthquakes. Enormous data can be used although the stress magnitude can't be estimated.
- 20. Stress relief method (1) A borehole is drilled usually from a roadway. The borehole should be longer than the roadway width to avoid areas where stress concentrates. A pilot hole is drilled from the borehole top. A probe is installed in the pilot hole. Overcoring is carried out measuring deformation and/or strains. (2) (3) (4) Stress relief methods
- 21. Principle of stress relief method No stress exists in the hollow cylinder formed by overcoring. Magnitude of strain and/or deformation with overcoring are equal to that when the pilot hole is drilled under the initial stress state with an inverted sign. The strains and/or deformations can be obtained by analytical methods or numerical methods assuming an elastic medium. Initial stress can be estimated by solving the simultaneous equations.
- 22. Example 2 y 1 Overcoring σ α = σ cos2 α+ σ sin 2 α + 2τ xycosα sinα x y x 3 A rosette gage was atacched to a rock surface and overcoring was carried out around the gage. Represent change in strains of the gauges 1, 2 and 3 by E, ν, σx, σy τxy. Conical bottom strain method (Sakaguchi et al., 1994)
- 23. Hydraulic fracturing method Often used method. Originally developed for wells for petroleum and geothermal energy to measure stress and to enhance the prodcution Fracture There are some cases in which hydraulic fracturing p is carried out from an existed roadway. Packer Hydraulic fracturing
- 24. Hydraulic fracturing A borehole is drilled. Packer and a water pipe is installed. Water is injected measuring Fracture pressure and flow rate. p Packer
- 25. Hydraulic fracturing Water valve is closed after breakdown which is a decrease of water pressure and represents that a fracture appears at the borehole wall. Breakdown The pressure at the breadown is called pb. Water is injected again. Decrease of the slope of the water pb pr Down-hole pressure ps pressure-time curve represent reopening, namely, the fracture is opened again. The pressure at re- opening pressure pr. is called re-opening Injection and then pressure is continued for a while the valve is shut.Water Flow rate will converge. The converged pressure is called shut-in pressure ps. Time
- 26. Hydraulic fracturing Packer etc. are removed and fracture orientation is observed by a borehole Breakdown camera or impression packer. pb pr Down-hole pressure ps Flow rate Time
- 27. Principle of hydraulic fracturing Tangential stresses σA, σB at points A and B when internal pressure p acts to a circular hole under maximum principal stress σH and minimum principal ignored for convenience). σh σ stress (pore pressure is H A σ A σ = 3σ h − σ H − p σh = 3σ −σ − pB H h p B
- 28. principle of hydraulicfracturing σA is smaller than σB. A fracture initiate and grows from point A when the following criterion satisfied. T0 is tensile strength. is σH A T0 ≤ −σ A = −3σ h + σ H + p σh The following equation is derived for the breakdown pressure pb. T0 = −3σ h +σ H + pb p B
- 29. Principle of hydraulic Fracturing Reopening occurs when the tangential stress at point A becomes tensile. 0 ≥ 3σ h − σ H − p σH A Consequently, for reopening pressure, σh 0 = 3σ h − σ H − pr p B
- 30. Principle of hydraulic fracturing It is said that shut-in pressure is roughly σh. σ h = ps equal to σH A σh p B
- 31. Procedure to estimate initial stress Minimum principal stress is estimated from the shut-in pressure σ h = ps Maximum principal stress is estimated from the minimum principal stress and the re-opening pressure. 0 = 3σ h − σ H − pr Orientation of the maximum principal stress is equal to that of the fracture observed by a borehole camera or an impression packer.
- 32. Vertical fracture (left) and horizontal fracture (right)
- 33. Criterion for horizontal fracture Vertical stress σv at borehole wall is σ v = σ V − 2 p Criterion for horizontal fracture is σ v < 3σ h − σ H Another method has to be used in fracture occurs. he case where horizontal
- 34. More detail Consideration on pore pressure and fracture mechanics （Nihon Kikai Gakkai, 1989) Determination of three dimensional stress state based on data from one borehole (Nihon Kikai Gakkai, 1989) Statistical consideration (Shin & Okubo, 1999) Estimation of initial stress measuring strains (Sato et 1999b、Itoh et al., 2001) Detailed consideration on re-opening pressure (Ito et 1999b) al., al.,
- 35. Estimation of initial stress from laboratory test on oriented cores (Ex. Nihon Kikai Gakkai, 1989) AE mehod (Lavrov, 2003) DSCA method (Oikawa et al.,1995, Yamaguchi et al., 1991, Matsuki et al., 1995) DRA mehod ASR method Mehod utilizing P-wave velocity Results similar to such reliable methods as stress relief method and hydraulic fracturing method are often obtained. Principle is not well known. There are many points which should be clarified. For example, how long rock core maintain the stress memory is not well known. Methods using oriented cores
- 36. Example of DRA method b3 b3 6040 Loading30 40 20 20 10 0 0 0 0.1 0.2 0 10 20 30 40 Strain (10-2 ) Stress (MPa) Stress-strain curves Strain difference function Stress(MPa) Straindifference(10-6 ) Unloading
- 37. Sign and amplitude of elastic wave from fault slip depends on orientation to the observatory. Compressional and dilatational wave can be observed for P-wave, for example. Compressional wave Dilatational wave Method based on fault earthquakes
- 38. Compression and tensile axes can be obtained by projecting polarity of P-wave on the direction of observatory. Directions of compression and tension axes are sometimes regarded as those of the maximum and minimum principal stress, respectively.
- 39. Compression and tension axes represents stress change due to fault slip and their directions should not be always coincides to those of initial stress. However, similar results to stress relief method and hydraulic fracturing method are often obtained. The directions of initial stress can be easily estimated from enormous fault earthquake data although the magnitude of initial stress can't be estimated.
- 40. Borehole breakout Failure phenomena which are observed at sidewall of petroleum and geothermal wells Failure zones of dog ear-shape grow in the direction of the minimum principal stress Initial stress magntude can be estimated from the shape of the failure zone. For detail, refer Brudy & Zoback (1999), Cuss et al. (2003), Haimson & Lee (2004) σH σh Other methods
- 41. Core discing Rock core breaks in a many discs when a borehole is drilled to a high pressure zone. Relationship between stress state and disc shape is investigated (ex. Obara et al., 1998). Initial stress state can be roughly estimated. Core discing which was observed at Kamaishi Mine
- 42. Other other other Calcite twins （Kang et al., 1999） Sub-crater of volcano (Karino and Murata, 1998） Electric resistivity (Ito et al., 1999a） etc.........................
- 44. Magnitude and orientation of Insitu stresses vary considerably within geological systems. 2. The pre-existing stress state changes dramatically due to excavation/construction therefore load must be redistributed. 3. Stress is not familiar – it is a tensor quantity and tensors are not encountered in everyday life. 4. It is a means to analyze mechanical behaviors of rock. 5. It serves as boundary conditions in rock engineering problems as a stress state is applied for analysis and design. 6. It helps in understanding groundwater fluid flow. 7. At large scale shed some light on the mechanism causing tectonic plates to move or fault to rupture with the added uncertainty in that there is no constraint on the total force, as is the case with gravity loads.
- 45. Insitu Stress
- 55. A section, normally less than 1m in length, of a borehole is sealed off with a straddle packer. The sealed-off section is then slowly pressurized with a fluid, usually water. This generates tensile stresses at the borehole wall. Pressurization continues until the borehole wall ruptures through tensile failure and a hydro fracture is initiated. The fracture plane is normally parallel to the borehole axis, and two fractures are initiated simultaneously in diametrically opposite positions on the borehole periphery. The hydro fracture will initiate at the point, and propagate in the direction, offering the least resistance. The fracture will therefore develop in a direction perpendicular to the minimum principal stress. The orientation of the fracture is obtained from the fracture traces on the borehole wall –it coincides with the orientation of the maximum horizontal stress, in a vertical or subvertical hole where it is assumed that one principal stress is parallel to the borehole. The fracture orientation may be determined either by use of an impression packer and a compass or by use of geophysical methods such as a formation micro-scanner or a borehole televiewer.
- 56. In its conventional form, the method is 2D: only the maximum and minimum normal stresses in the plane perpendicular to the borehole axis are established. For a vertical borehole, these components are the maximum and minimum horizontal stresses. Since the principal stress directions in tectonically passive and topographically at areas areusually close to horizontal and vertical, it can often be assumed that the components measured in a vertical borehole are two of the principal stresses. Hydraulic fracturing is an efficient method for determining the 2D stress field, normally inthe horizontal plane, and is therefore suitable at the early stages of projects when no underground access exists. Due to its efficiency, it is especially advantageous for measurements at great depth. . The method is also not significantly affected by the drilling processes. Hydraulic fracturing normally includes large equipment, which requires space. Furthermore,the theoretical limitations normally imply that the measurements should be done in vertical holes. Hence, the method is most suited for surface measurements in vertical or subvertical boreholes. Applied packer pressure – 2-4 MPa