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A new coupling concept for the hydro-mechanical interaction of clay stone and rock salt in underground waste repositories
Paper 2B 40 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
A NEW COUPLING CONCEPT FOR THE HYDRO-MECHANICAL INTERACTION OF CLAY STONE AND ROCK SALT IN UNDERGROUND WASTE REPOSITORIES Z. Hou¹, K.-H. Lux² ¹) Disposal Technology and Geomechanics, TU Clausthal, Germany [email protected] ²) Disposal Technology and Geomechanics, TU Clausthal, Germany [email protected]
Abstract: For the simulation of the hydraulic and mechanical behaviour of clay stone and rock salt as well as the hydro-mechanical interaction in the excavation disturbed zone (EDZ) around sealing systems in underground radioactive or toxic waste repositories, a new hydro-mechanical coupling concept has been developed, which includes the Hou/Lux constitutive model formulated with effective stresses, the Darcy flow model as well as several coupling models. An exemplary drift in clay stone and an exemplary drift sealing in rock salt have been investigated. Following the calculation results, the construction of a drift dam can noticeably reduce or even heal the EDZ of ∆r≈1.5m in a 1000m deep drift over a period of approx. 20 years, due to the creep behaviour of rock salt and the supporting effect of the dam. To improve the design for the construction of sealing systems, the drift should be expanded shortly before constructing the dam, and the dam should be constructed as early as possible in order to heal damage in time and in order to reduce the permeability and porosity in the EDZ around the dam prior to a possible brine entry. Keywords: Hydro-mechanical coupling, radioactive waste repository, rock salt, clay stone, excavation disturbed zone (EDZ), sealing system.
1. INTRODUCTION Through sealing systems, e.g. drift or shaft sealing systems, direct influx of brine or water in disposal cavities of the underground radioactive or toxic waste repositories is initially ruled out. However, secondary micro cracks in the EDZ around the sealing systems build networked hydraulic pathways, which make axial seepage flow along the sealing direction possible. The hydraulic pathways in the EDZ have additional impacts through the present pore pressure as well as hydrodynamic and hydrostatic forces with the development of further secondary micro cracks as a result in case of flooding. This process can continue itself progressively: Micro cracks build-up ⇒ Additional creep deformations ⇒ Deterioration of the load bearing capacity ⇒ Intensification of the strain softening and loosening ⇒ Increase of the porosity and permeability ⇒ Intensification of the seepage flow ⇒ Increase of the hydraulic impacts induced by seepage flow and so on. This accumulated damage and dilatancy of the EDZ can be removed, if the healing boundary is undershot as a result of convergence and the redistribution of stresses around the sealing
systems (passive or active contact pressure). Then the opposing process is activated: Closing and healing of the micro cracks and pores ⇒ Regression of the creep deformation ⇒ Improvement of the load bearing capacity ⇒ Reduction of the strain softening and loosening ⇒ Reduction of the porosity and permeability ⇒ Decrease of the seepage flow ⇒ Reduction of the hydraulic impacts induced by seepage flow and so on.
Figure 1. Hou/Lux hydro-mechanical coupling concept for rock salt and clay stone. The above description illustrates the interactions between the mechanical and hydraulic fields in the
1
Paper 2B 40 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
case of flooding in underground repositories. Although the two fields will be described using different models, they must be jointly investigated due to interactions. Therefore a coupling concept is necessary that has the task of bringing together the mechanical and the hydraulic field in a plausible as well as mechanically and hydraulically compatible manner allowing for interaction. Based on the poroelesticity theory, e.g. Charlez (1991), and on the concept following Cosenza & Ghoreychi (1996) for rock salt, the Hou/Lux hydromechanical coupling concept has been developed, e.g. Hou (2002), which includes the Hou/Lux constitutive model formulated with effective stresses, the Darcy flow model as well as several coupling models (e.g. permeability model, α-model for the determination of Biot’s coefficient α, fh model for the determination of the hydrodynamic force fhd and the hydrostatic force fhs , strength model, damage and healing model), figure 1.
interval ∆t. During the numerical analysis the seepage process at time interval ∆t will be regarded as stationary. The solutions are found from a successive execution of stationary flow processes in the time interval ∆t. From interval to interval the hydraulic properties of the rock salt or clay stone change alongside the mechanical properties and over the implemented Hou/Lux coupling models for the description of the interactions, among other things porosity-dependant permeability and a damage-dependant Biot’s coefficient follow. Therefore the flow equation, which contains of incorporated in the Darcy flow model as well as of which the mass balance equation, can be described through equation 2. Thereby p, ηFl and Kx/Ky /Kz are respectively the pore pressure in MPa, the dynamic viscosity of the fluid in MPa⋅s and the direction-dependant permeability in m2 : ∂ K x ∂p ∂ K y ∂p ∂ K z ∂p ⋅ + ⋅ + ⋅ =0 ∂x η Fl ∂x ∂y η Fl ∂y ∂z η Fl ∂z
(2)
2. HOU/LUX CONSTITUTIVE MODEL The Hou/Lux constitutive model, which describes the effects of the different deformation mechanisms (diffusion and dislocation, strain hardening and recovery, damage and healing) mainly integrally, was developed based on the Lubby2 model and on the fundamentals of continuum damage mechanics. Details concerning the Hou/Lux constitutive model can be found in Hou (2002, 2003) and Hou & Lux (2002). Considering that in a saturated porous medium only those forces actually acting inside the rock matrix are responsible for the matrix deformation, the effective stresses σ' instead of the total stresses σ have been introduced into the Hou/Lux constitutive model: σ ij' = σ ij − α ⋅ p ⋅ δ ij
4. INTERFACES AND COUPLING MODELS FOR THE DESCRIPTION OF THE HYDRO-MECHANICAL INTERACTIONS The interfaces between the mechanical process and the hydraulic process are summarised in figure 1. Every interface will be described by a corresponding coupling model as well as integrated in the computational FEM program MISES3 for both fields.
4.1 Permeability model after Hou (2002)
(1)
3. DARCY FLOW MODEL Basically from a quasi-stationary laminar flow (at time interval ∆t) and a saturated pore space with water or brine, and therefore a single-phase flow in clay stone or rock salt without imbibitions can be assumed. This is due particularly to the long-term behaviour of the rocks (no simulation of the imbibitions or drainage process). The mechanical and hydraulic properties can however spatially and/or temporally change, as quasi-stationary behaviour will only be assumed for the time
Figure 2. Maximal permeability after Hou (2002). The permeability of rock salt is mainly dependant on the dilatancy and the effective
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Paper 2B 40 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
principal stress. To describe this dependency there are many models that can be used. After a comparison the permeability model, which takes into consideration the direction dependency after Hou (2002), will be chosen as the coupling model for the description of the effect of the mechanical field on the hydraulic field. Figure 2 shows the maximal permeability in the direction of the maximal principal stress.
4.2 α-Model for the determination of the Biot’s coefficient after Hou (2002)
Basically the Biot’s coefficient α is dependant on the material type, the material behaviour, the damage, the porosity and the volumetric strain, the stress states and the load rate as well as the saturation level, Charlez (1991). Therefore it can only be determined in connection with the specified coupling model. The most known equation 3 is only valid for rocks, which have elastic behaviour. Thereby KB and KM are the bulk module and the matrix module of the rocks: α = 1−
KB KM
(3)
The relation between the Biot’s coefficient and the material properties of rock salt and clay stone, which behave viscose-plastic-elastic , has not yet been intensively researched. Hou (2002) theoretically derived a α-model in connection with the Hou/Lux constitutive model as well as with damage and healing. Details could not be described here because of space limit.
4.3 fh-Model for the description of the geohydraulical forces (= hydrodynamic and hydrostatic force) As the permeability K and the Biot’s coefficient α can change spatially and temporally, their effects on the mechanical field must be researched. Thereto the equilibrium conditions for a rock element must be considered. Out of the equilibrium conditions, the hydraulic forces fh,i , which is made up of the hydrodynamic force fhd,i and the hydrostatic force fhs,i , was derived by Hou (2002): f h ,i = −
∂ (α ⋅ p ) ∂p ∂α = −α ⋅ − p⋅ = f hd ,i + f hs,i ∂xi ∂xi ∂x i
(4)
The conclusions below can be drawn from the fh -model (equation 4): • Mechanical effects of the flow process on very low permeable rocks like rock salt or clay stone are dependant not only on the pore
•
•
•
pressure gradient dp/dxi , but also on the changes of the Biot’s coefficient dα/dxi . If the pore pressure remains spatially constant despite temporal changes, the pore pressure gradient must be equal to zero (dp/dxi = 0) and therefore the hydrodynamic force must also be equal to zero (fhd,i = 0). In this case there is still the hydrostatic force fhs,i , as a result of the specially different Biot’s coefficient α. If the Biot’s coefficient changes temporal, but is spatially constant, it’s gradient must be equal to zero (dα/dxi =0) and therefore the hydrostatic force must also be equal to zero (fhs,i =0). In this case there is still a hydrodynamic force fhd,i due to the temporarily different pore pressure p. Therefore it is ascertained, that the well known seepage force (fs =dp/dxi ), which is valid for porous soft rocks with a constant Biot’s coefficient of α = 1, can only represent a special case and not the far more complicated general case of a spatial and temporal changing Biot’s coefficient 0≤α≤1, which results from a varying intensity of the EDZ and a varying distribution of the pore pressure in the EDZ with the surrounding very low permeable rock salt or clay stone (e. g. K<10-20m2 ).
5. HYDRAULIC AND MECHANICAL BEHAVIOR OF CLAY STONE IN THE EDZ OF A HORIZONTAL DRIFT An exemplary horizontal drift in clay stone at a depth of z=600m is numerically analyzed with the Hou/Lux constitutive model and the permeability model after Hou (2002), figure 3. The results of the calculation in the horizontal section of the drift in clay stone are summarized in the following, according to the figures 4 and 5: • It is clearly visible that the expansion of the EDZ increases spatially and temporally (t=30d, 1a and 5a: ∆r≈2.3m, 2.75m and 4.0m) and the strain softening intensifies, which leads to the reduced von Mises stresses as well as to the increased permeability in the EDZ. • Consequently, the stresses distribution is rearranged. The von Mises stress on the boundary of the drift and the maximal von Mises stress at the end of the EDZ are reduced respectively from σv ≈13,0/20,3MPa at t=30d to σv ≈10.6/19.1MPa at t=1a and σv ≈8.8/16.2MPa at t=50a, figure 4.
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Paper 2B 40 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
6. HYDRAULIC AND MECHANICAL BEHAVIOR OF ROCK SALT IN THE EDZ AROUND A DRIFT DAM An exemplary sealing system in rock salt is numerically analyzed with the Hou/Lux coupling concept in consideration of creep, damage, healing and hydro-mechanical interactions, Hou (2002). This sealing system is a simple parallel dam, where the sealing element and the static abutment are identical. Figure 6 shows the calculation model, which has been simplified to a rotational model. The parallel dam is located in a horizontal straight drift with a circular cross-section. The drift has a radius of r1 =4m and is located at a depth of z=1,000m.
von Mises stress [MPa]
Figure 3. Calculation model for a horizontal drift in clay stone. 22 20 18 16 14 12 10 8 6 4 2 0
t = 30d t = 1a t = 50a
Figure 6. Rotation-symmetrical calculation model for a parallel dam in rock salt. 4
6
8
10
x [m]
12
14
Figure 4. Spatial development of the von Mises stress in the horizontal section.
permeability[m 2 ]
1.0E-15
t = 30d
1.0E-16
t = 1a t = 50a
1.0E-17 1.0E-18 1.0E-19 1.0E-20 4
4.5
5
5.5
6
6.5
7
7.5
8
x [m]
Figure 5. Spatial development of the maximum permeability in the horizontal section.
The numerical calculation is divided into the following phases: + • t = 0 a: excavation of the drift + • t = 50 a: construction of the drift dam + • t = 60 a: entry of salt solution on the left side • t = 110a: end of the calculation In general, the permeability of the rock salt is at its smallest above the drift dam due to the supporting effect and due to the increased minimum stress. The calculated but not shown relatively high permeability of the rock salt on the air and fluid side, however, must not be overrated. The permeability of the rock salt directly above the drift dam determines the amount of seepage flow through the EDZ around a drift sealing system. Some calculation results in the symmetry plane of the dam are shown in figures 7-10: • The damage in the rock mass increases continuously until the construction of the dam (t=50a), but the expansion of the ∆r=1.5m EDZ remains the same order of magnitude as of t=1a, figures 7 and 8.
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Paper 2B 40 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
according to the calculation results, figure 8. In the course of another 9 years (t=60a) the maximum damage of maxD ≈ 0.11 has been reduced to maxD≈2.10-4, figure 8.
t = 10d t = 50a t = 51a t = 60a t = 110a
.
12
1,0E-14
permeability [m2 ]...
6
1,0E-13
3
0 0
4
8
12
16
x [m]
20
24
28
drift boundary
9
1,0E-15 1,0E-16 1,0E-17 1,0E-18 1,0E-19
32 1,0E-20 1,0E-21
Figure 7. Spatial development of the von Mises stress in the middle vertical section.
1,0E-22 3,5
0,4
.
5,5
6,0
51a 60a 61a 70a
0,05 0 4,0
4,5
x [m]
5,0
5,5
6,0
1,0E-18 drift boundary
0,1
3,5
5,0
x [m]
1,0E-17
2
0,15
permeability [m ]....
0,2
4,5
1,0E-16
drift boundary
damage parameter [-]...
0,3
4,0
Figure 9. Spatial development of the direction dependant permeability in the middle vertical section.
10d 1a 50a 51a 60a
0,35
0,25
radial (50a) axial (50a) tangential (50a) radial (51a) axial (51a) tangential (51a)
1,0E-12
drift boundary
von Mises stress [MPa]...
15
1,0E-19 1,0E-20 1,0E-21
Figure 8. Spatial development of damage in the middle vertical section until t = 60a. •
1,0E-22 3,5
The dam constructed at the time t=50a has a supporting effect on the surrounding rock mass. This prevents any further development of the damage and the dilatancy of the rock in EDZ. Over time, the state of stress returns to the state of primary stress, figure 7. At increased minimum stress or reduced von Mises stress, the pathways will be reduced as well as closed and the secondary permeability of the rock mass in the direct vicinity of the dam will slowly decrease again, figures 9 and 10. As early as one year after the construction of the dam, the damage can be distinctly healed
4,0
4,5
5,0
5,5
6,0
x [m]
Figure 10.Spatial development of maximum permeability in the middle vertical section. •
The permeability shows additionally a clear dependence upon the direction. At the time t=50a the maximum tangential permeability (K=2.6.10-13m2 ) is about 137 times higher than the value in axial direction as well as four orders of magnitude higher than in radial direction, figure 9. One year after the
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Paper 2B 40 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
•
•
construction of the dam, the permeability can be drastically reduced. In view of the direction of seepage flow in the EDZ above the dam, the axial permeability is the decisive reference value. Therefore, one year after the construction the maximum permeability of the dam, maxK≈1.7. 10-20m2 , in the axial direction is of special importance. As a consequence of healing the hydraulic properties in this area are further improved. Before brine entry (t=60a +) the maximum permeability is only marginally higher than the primary value of K0 =10-22 m2 . At the time t=70a this primary permeability is achieved again, i.e. the EDZ has disappeared. The determined results allow improved design for the building of sealing systems and thus a more realistic long-term proof of stability for permanent repositories. For example, a drift expansion should be done shortly before constructing the dam to improve the efficiency of the dam and the dam should be constructed as early as possible to heal damage in time and to reduce permeability in the EDZ around the dam prior to a possible water or brine entry, Hou (2002). It must be pointed out, that the numerical results are strongly dependant on the martial parameters. Therefore, the above shown results should be considerate exemplarily.
7. CONCLUSIONS A new coupling concept was developed for the numerical simulation of the hydro-mechanical interactions in the EDZ around a sealed system. The advantage of this concept in comparison to other available concepts is shown in the timedependant coupling of both processes under simultaneous consideration of the changes in the material properties and state variables, so that an investigation of the mechanical and hydraulic behaviour of the sealed system, which is at least in principle close to reality, is possible. Among the coupling models, the permeability model, the αmodel and the fh -model were newly by Hou (2002) developed. The results of calculated EDZ of a drift in clay stone and around a drift dam in rock salt allow the following conclusions: • The spatial development of the EDZ can be described qualitatively and quantitatively with the Hou/Lux constitutive model.
• •
•
•
The EDZ in clay stone is normally larger than in rock salt. The EDZ of ∆r≈1.5m in a 1000m-deep drift in salt rock could be reduced or even healed over a period of approx. 20 years by constructing a drift dam, due to the creep behavior of rock salt and the supporting effect of the dam. The primary permeability of rock salt is more or less recovered. The high permeability of the rock salt on the air and fluid side, however, must not be overrated, because the permeability of the rock salt directly above the dam construction determines the amount of flow through the EDZ around a drift sealing system. To improve the design for the construction of sealing systems, the drift should be expanded shortly before constructing the dam, and the dam should be constructed as early as possible in order to heal structural damage in time and in order to reduce permeability and porosity in the EDZ around the dam prior to a possible solution entry.
8. REFERENCES Charlez, P.A. 1991. Rock mechanics, Vol.1Theoretical fundamentals. Paris: Editions Technip. Cosenza, P. & Ghoreychi, M. 1996. Coupling between mechanical behavior and transfer phenomena in salt. In M. Ghoreychi et al., Proc. of the 3rd conf. on the mechanical behavior of salt, Ecole Polytechnique, 14-16 Sept. 1993. Clausthal-Zellerfeld: Trans Tech Publications. Hou, Z. 2002. Geomechanische Planungskonzepte für untertägige Tragwerke mit besonderer Berücksichtigung von Gefügeschädigung, Verheilung und hydromechanischer Kopplung. Clausthal-Zellerfeld: Papierflieger, ISBN 389720-099-6. Hou, Z. 2003. Mechanical behaviour of salt in the excavation disturbed zone around underground facilities. Int. J. of Rock Mechanics and Mining Sciences, Vol. 40/Issue 5: pp. 727-740. Hou, Z. & Lux K.-H. 2002. A material model for rock salt including structural damages as well as practice-oriented applications: In N.D. Cristescu et al. (ed.), Basic and applied salt mechanics; Proc. of 5th conf. on mechanical behavior of salt, Bucharest, 9-11 August 1999. Lisse: Balkema.
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A NEW COUPLING CONCEPT FOR THE HYDRO-MECHANICAL INTERACTION OF CLAY STONE AND ROCK SALT IN UNDERGROUND WASTE REPOSITORIES Z. Hou¹, K.-H. Lux² ¹) Disposal Technology and Geomechanics, TU Clausthal, Germany [email protected] ²) Disposal Technology and Geomechanics, TU Clausthal, Germany [email protected]
Abstract: For the simulation of the hydraulic and mechanical behaviour of clay stone and rock salt as well as the hydro-mechanical interaction in the excavation disturbed zone (EDZ) around sealing systems in underground radioactive or toxic waste repositories, a new hydro-mechanical coupling concept has been developed, which includes the Hou/Lux constitutive model formulated with effective stresses, the Darcy flow model as well as several coupling models. An exemplary drift in clay stone and an exemplary drift sealing in rock salt have been investigated. Following the calculation results, the construction of a drift dam can noticeably reduce or even heal the EDZ of ∆r≈1.5m in a 1000m deep drift over a period of approx. 20 years, due to the creep behaviour of rock salt and the supporting effect of the dam. To improve the design for the construction of sealing systems, the drift should be expanded shortly before constructing the dam, and the dam should be constructed as early as possible in order to heal damage in time and in order to reduce the permeability and porosity in the EDZ around the dam prior to a possible brine entry. Keywords: Hydro-mechanical coupling, radioactive waste repository, rock salt, clay stone, excavation disturbed zone (EDZ), sealing system.
1. INTRODUCTION Through sealing systems, e.g. drift or shaft sealing systems, direct influx of brine or water in disposal cavities of the underground radioactive or toxic waste repositories is initially ruled out. However, secondary micro cracks in the EDZ around the sealing systems build networked hydraulic pathways, which make axial seepage flow along the sealing direction possible. The hydraulic pathways in the EDZ have additional impacts through the present pore pressure as well as hydrodynamic and hydrostatic forces with the development of further secondary micro cracks as a result in case of flooding. This process can continue itself progressively: Micro cracks build-up ⇒ Additional creep deformations ⇒ Deterioration of the load bearing capacity ⇒ Intensification of the strain softening and loosening ⇒ Increase of the porosity and permeability ⇒ Intensification of the seepage flow ⇒ Increase of the hydraulic impacts induced by seepage flow and so on. This accumulated damage and dilatancy of the EDZ can be removed, if the healing boundary is undershot as a result of convergence and the redistribution of stresses around the sealing
systems (passive or active contact pressure). Then the opposing process is activated: Closing and healing of the micro cracks and pores ⇒ Regression of the creep deformation ⇒ Improvement of the load bearing capacity ⇒ Reduction of the strain softening and loosening ⇒ Reduction of the porosity and permeability ⇒ Decrease of the seepage flow ⇒ Reduction of the hydraulic impacts induced by seepage flow and so on.
Figure 1. Hou/Lux hydro-mechanical coupling concept for rock salt and clay stone. The above description illustrates the interactions between the mechanical and hydraulic fields in the
1
Paper 2B 40 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
case of flooding in underground repositories. Although the two fields will be described using different models, they must be jointly investigated due to interactions. Therefore a coupling concept is necessary that has the task of bringing together the mechanical and the hydraulic field in a plausible as well as mechanically and hydraulically compatible manner allowing for interaction. Based on the poroelesticity theory, e.g. Charlez (1991), and on the concept following Cosenza & Ghoreychi (1996) for rock salt, the Hou/Lux hydromechanical coupling concept has been developed, e.g. Hou (2002), which includes the Hou/Lux constitutive model formulated with effective stresses, the Darcy flow model as well as several coupling models (e.g. permeability model, α-model for the determination of Biot’s coefficient α, fh model for the determination of the hydrodynamic force fhd and the hydrostatic force fhs , strength model, damage and healing model), figure 1.
interval ∆t. During the numerical analysis the seepage process at time interval ∆t will be regarded as stationary. The solutions are found from a successive execution of stationary flow processes in the time interval ∆t. From interval to interval the hydraulic properties of the rock salt or clay stone change alongside the mechanical properties and over the implemented Hou/Lux coupling models for the description of the interactions, among other things porosity-dependant permeability and a damage-dependant Biot’s coefficient follow. Therefore the flow equation, which contains of incorporated in the Darcy flow model as well as of which the mass balance equation, can be described through equation 2. Thereby p, ηFl and Kx/Ky /Kz are respectively the pore pressure in MPa, the dynamic viscosity of the fluid in MPa⋅s and the direction-dependant permeability in m2 : ∂ K x ∂p ∂ K y ∂p ∂ K z ∂p ⋅ + ⋅ + ⋅ =0 ∂x η Fl ∂x ∂y η Fl ∂y ∂z η Fl ∂z
(2)
2. HOU/LUX CONSTITUTIVE MODEL The Hou/Lux constitutive model, which describes the effects of the different deformation mechanisms (diffusion and dislocation, strain hardening and recovery, damage and healing) mainly integrally, was developed based on the Lubby2 model and on the fundamentals of continuum damage mechanics. Details concerning the Hou/Lux constitutive model can be found in Hou (2002, 2003) and Hou & Lux (2002). Considering that in a saturated porous medium only those forces actually acting inside the rock matrix are responsible for the matrix deformation, the effective stresses σ' instead of the total stresses σ have been introduced into the Hou/Lux constitutive model: σ ij' = σ ij − α ⋅ p ⋅ δ ij
4. INTERFACES AND COUPLING MODELS FOR THE DESCRIPTION OF THE HYDRO-MECHANICAL INTERACTIONS The interfaces between the mechanical process and the hydraulic process are summarised in figure 1. Every interface will be described by a corresponding coupling model as well as integrated in the computational FEM program MISES3 for both fields.
4.1 Permeability model after Hou (2002)
(1)
3. DARCY FLOW MODEL Basically from a quasi-stationary laminar flow (at time interval ∆t) and a saturated pore space with water or brine, and therefore a single-phase flow in clay stone or rock salt without imbibitions can be assumed. This is due particularly to the long-term behaviour of the rocks (no simulation of the imbibitions or drainage process). The mechanical and hydraulic properties can however spatially and/or temporally change, as quasi-stationary behaviour will only be assumed for the time
Figure 2. Maximal permeability after Hou (2002). The permeability of rock salt is mainly dependant on the dilatancy and the effective
2
Paper 2B 40 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
principal stress. To describe this dependency there are many models that can be used. After a comparison the permeability model, which takes into consideration the direction dependency after Hou (2002), will be chosen as the coupling model for the description of the effect of the mechanical field on the hydraulic field. Figure 2 shows the maximal permeability in the direction of the maximal principal stress.
4.2 α-Model for the determination of the Biot’s coefficient after Hou (2002)
Basically the Biot’s coefficient α is dependant on the material type, the material behaviour, the damage, the porosity and the volumetric strain, the stress states and the load rate as well as the saturation level, Charlez (1991). Therefore it can only be determined in connection with the specified coupling model. The most known equation 3 is only valid for rocks, which have elastic behaviour. Thereby KB and KM are the bulk module and the matrix module of the rocks: α = 1−
KB KM
(3)
The relation between the Biot’s coefficient and the material properties of rock salt and clay stone, which behave viscose-plastic-elastic , has not yet been intensively researched. Hou (2002) theoretically derived a α-model in connection with the Hou/Lux constitutive model as well as with damage and healing. Details could not be described here because of space limit.
4.3 fh-Model for the description of the geohydraulical forces (= hydrodynamic and hydrostatic force) As the permeability K and the Biot’s coefficient α can change spatially and temporally, their effects on the mechanical field must be researched. Thereto the equilibrium conditions for a rock element must be considered. Out of the equilibrium conditions, the hydraulic forces fh,i , which is made up of the hydrodynamic force fhd,i and the hydrostatic force fhs,i , was derived by Hou (2002): f h ,i = −
∂ (α ⋅ p ) ∂p ∂α = −α ⋅ − p⋅ = f hd ,i + f hs,i ∂xi ∂xi ∂x i
(4)
The conclusions below can be drawn from the fh -model (equation 4): • Mechanical effects of the flow process on very low permeable rocks like rock salt or clay stone are dependant not only on the pore
•
•
•
pressure gradient dp/dxi , but also on the changes of the Biot’s coefficient dα/dxi . If the pore pressure remains spatially constant despite temporal changes, the pore pressure gradient must be equal to zero (dp/dxi = 0) and therefore the hydrodynamic force must also be equal to zero (fhd,i = 0). In this case there is still the hydrostatic force fhs,i , as a result of the specially different Biot’s coefficient α. If the Biot’s coefficient changes temporal, but is spatially constant, it’s gradient must be equal to zero (dα/dxi =0) and therefore the hydrostatic force must also be equal to zero (fhs,i =0). In this case there is still a hydrodynamic force fhd,i due to the temporarily different pore pressure p. Therefore it is ascertained, that the well known seepage force (fs =dp/dxi ), which is valid for porous soft rocks with a constant Biot’s coefficient of α = 1, can only represent a special case and not the far more complicated general case of a spatial and temporal changing Biot’s coefficient 0≤α≤1, which results from a varying intensity of the EDZ and a varying distribution of the pore pressure in the EDZ with the surrounding very low permeable rock salt or clay stone (e. g. K<10-20m2 ).
5. HYDRAULIC AND MECHANICAL BEHAVIOR OF CLAY STONE IN THE EDZ OF A HORIZONTAL DRIFT An exemplary horizontal drift in clay stone at a depth of z=600m is numerically analyzed with the Hou/Lux constitutive model and the permeability model after Hou (2002), figure 3. The results of the calculation in the horizontal section of the drift in clay stone are summarized in the following, according to the figures 4 and 5: • It is clearly visible that the expansion of the EDZ increases spatially and temporally (t=30d, 1a and 5a: ∆r≈2.3m, 2.75m and 4.0m) and the strain softening intensifies, which leads to the reduced von Mises stresses as well as to the increased permeability in the EDZ. • Consequently, the stresses distribution is rearranged. The von Mises stress on the boundary of the drift and the maximal von Mises stress at the end of the EDZ are reduced respectively from σv ≈13,0/20,3MPa at t=30d to σv ≈10.6/19.1MPa at t=1a and σv ≈8.8/16.2MPa at t=50a, figure 4.
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Paper 2B 40 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
6. HYDRAULIC AND MECHANICAL BEHAVIOR OF ROCK SALT IN THE EDZ AROUND A DRIFT DAM An exemplary sealing system in rock salt is numerically analyzed with the Hou/Lux coupling concept in consideration of creep, damage, healing and hydro-mechanical interactions, Hou (2002). This sealing system is a simple parallel dam, where the sealing element and the static abutment are identical. Figure 6 shows the calculation model, which has been simplified to a rotational model. The parallel dam is located in a horizontal straight drift with a circular cross-section. The drift has a radius of r1 =4m and is located at a depth of z=1,000m.
von Mises stress [MPa]
Figure 3. Calculation model for a horizontal drift in clay stone. 22 20 18 16 14 12 10 8 6 4 2 0
t = 30d t = 1a t = 50a
Figure 6. Rotation-symmetrical calculation model for a parallel dam in rock salt. 4
6
8
10
x [m]
12
14
Figure 4. Spatial development of the von Mises stress in the horizontal section.
permeability[m 2 ]
1.0E-15
t = 30d
1.0E-16
t = 1a t = 50a
1.0E-17 1.0E-18 1.0E-19 1.0E-20 4
4.5
5
5.5
6
6.5
7
7.5
8
x [m]
Figure 5. Spatial development of the maximum permeability in the horizontal section.
The numerical calculation is divided into the following phases: + • t = 0 a: excavation of the drift + • t = 50 a: construction of the drift dam + • t = 60 a: entry of salt solution on the left side • t = 110a: end of the calculation In general, the permeability of the rock salt is at its smallest above the drift dam due to the supporting effect and due to the increased minimum stress. The calculated but not shown relatively high permeability of the rock salt on the air and fluid side, however, must not be overrated. The permeability of the rock salt directly above the drift dam determines the amount of seepage flow through the EDZ around a drift sealing system. Some calculation results in the symmetry plane of the dam are shown in figures 7-10: • The damage in the rock mass increases continuously until the construction of the dam (t=50a), but the expansion of the ∆r=1.5m EDZ remains the same order of magnitude as of t=1a, figures 7 and 8.
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Paper 2B 40 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
according to the calculation results, figure 8. In the course of another 9 years (t=60a) the maximum damage of maxD ≈ 0.11 has been reduced to maxD≈2.10-4, figure 8.
t = 10d t = 50a t = 51a t = 60a t = 110a
.
12
1,0E-14
permeability [m2 ]...
6
1,0E-13
3
0 0
4
8
12
16
x [m]
20
24
28
drift boundary
9
1,0E-15 1,0E-16 1,0E-17 1,0E-18 1,0E-19
32 1,0E-20 1,0E-21
Figure 7. Spatial development of the von Mises stress in the middle vertical section.
1,0E-22 3,5
0,4
.
5,5
6,0
51a 60a 61a 70a
0,05 0 4,0
4,5
x [m]
5,0
5,5
6,0
1,0E-18 drift boundary
0,1
3,5
5,0
x [m]
1,0E-17
2
0,15
permeability [m ]....
0,2
4,5
1,0E-16
drift boundary
damage parameter [-]...
0,3
4,0
Figure 9. Spatial development of the direction dependant permeability in the middle vertical section.
10d 1a 50a 51a 60a
0,35
0,25
radial (50a) axial (50a) tangential (50a) radial (51a) axial (51a) tangential (51a)
1,0E-12
drift boundary
von Mises stress [MPa]...
15
1,0E-19 1,0E-20 1,0E-21
Figure 8. Spatial development of damage in the middle vertical section until t = 60a. •
1,0E-22 3,5
The dam constructed at the time t=50a has a supporting effect on the surrounding rock mass. This prevents any further development of the damage and the dilatancy of the rock in EDZ. Over time, the state of stress returns to the state of primary stress, figure 7. At increased minimum stress or reduced von Mises stress, the pathways will be reduced as well as closed and the secondary permeability of the rock mass in the direct vicinity of the dam will slowly decrease again, figures 9 and 10. As early as one year after the construction of the dam, the damage can be distinctly healed
4,0
4,5
5,0
5,5
6,0
x [m]
Figure 10.Spatial development of maximum permeability in the middle vertical section. •
The permeability shows additionally a clear dependence upon the direction. At the time t=50a the maximum tangential permeability (K=2.6.10-13m2 ) is about 137 times higher than the value in axial direction as well as four orders of magnitude higher than in radial direction, figure 9. One year after the
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Paper 2B 40 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
•
•
construction of the dam, the permeability can be drastically reduced. In view of the direction of seepage flow in the EDZ above the dam, the axial permeability is the decisive reference value. Therefore, one year after the construction the maximum permeability of the dam, maxK≈1.7. 10-20m2 , in the axial direction is of special importance. As a consequence of healing the hydraulic properties in this area are further improved. Before brine entry (t=60a +) the maximum permeability is only marginally higher than the primary value of K0 =10-22 m2 . At the time t=70a this primary permeability is achieved again, i.e. the EDZ has disappeared. The determined results allow improved design for the building of sealing systems and thus a more realistic long-term proof of stability for permanent repositories. For example, a drift expansion should be done shortly before constructing the dam to improve the efficiency of the dam and the dam should be constructed as early as possible to heal damage in time and to reduce permeability in the EDZ around the dam prior to a possible water or brine entry, Hou (2002). It must be pointed out, that the numerical results are strongly dependant on the martial parameters. Therefore, the above shown results should be considerate exemplarily.
7. CONCLUSIONS A new coupling concept was developed for the numerical simulation of the hydro-mechanical interactions in the EDZ around a sealed system. The advantage of this concept in comparison to other available concepts is shown in the timedependant coupling of both processes under simultaneous consideration of the changes in the material properties and state variables, so that an investigation of the mechanical and hydraulic behaviour of the sealed system, which is at least in principle close to reality, is possible. Among the coupling models, the permeability model, the αmodel and the fh -model were newly by Hou (2002) developed. The results of calculated EDZ of a drift in clay stone and around a drift dam in rock salt allow the following conclusions: • The spatial development of the EDZ can be described qualitatively and quantitatively with the Hou/Lux constitutive model.
• •
•
•
The EDZ in clay stone is normally larger than in rock salt. The EDZ of ∆r≈1.5m in a 1000m-deep drift in salt rock could be reduced or even healed over a period of approx. 20 years by constructing a drift dam, due to the creep behavior of rock salt and the supporting effect of the dam. The primary permeability of rock salt is more or less recovered. The high permeability of the rock salt on the air and fluid side, however, must not be overrated, because the permeability of the rock salt directly above the dam construction determines the amount of flow through the EDZ around a drift sealing system. To improve the design for the construction of sealing systems, the drift should be expanded shortly before constructing the dam, and the dam should be constructed as early as possible in order to heal structural damage in time and in order to reduce permeability and porosity in the EDZ around the dam prior to a possible solution entry.
8. REFERENCES Charlez, P.A. 1991. Rock mechanics, Vol.1Theoretical fundamentals. Paris: Editions Technip. Cosenza, P. & Ghoreychi, M. 1996. Coupling between mechanical behavior and transfer phenomena in salt. In M. Ghoreychi et al., Proc. of the 3rd conf. on the mechanical behavior of salt, Ecole Polytechnique, 14-16 Sept. 1993. Clausthal-Zellerfeld: Trans Tech Publications. Hou, Z. 2002. Geomechanische Planungskonzepte für untertägige Tragwerke mit besonderer Berücksichtigung von Gefügeschädigung, Verheilung und hydromechanischer Kopplung. Clausthal-Zellerfeld: Papierflieger, ISBN 389720-099-6. Hou, Z. 2003. Mechanical behaviour of salt in the excavation disturbed zone around underground facilities. Int. J. of Rock Mechanics and Mining Sciences, Vol. 40/Issue 5: pp. 727-740. Hou, Z. & Lux K.-H. 2002. A material model for rock salt including structural damages as well as practice-oriented applications: In N.D. Cristescu et al. (ed.), Basic and applied salt mechanics; Proc. of 5th conf. on mechanical behavior of salt, Bucharest, 9-11 August 1999. Lisse: Balkema.
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