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Safety demonstration and verification concept - Principle and application examples -

Technical Report

Translated extraction from (Kudla et al., 2013 – chapter 2)

Philipp Herold & Nina Müller-Hoeppe

DBE TECHNOLOGY GmbH, Eschenstraße 55, D-31224 Peine, Germany

December 2013

Background The primary objective of repository research is to establish a scientific and technological ba-sis for a safe disposal of high-level radioactive waste. In addition to the technical feasibility, one major goal is the feasibility of suitable safety assessments. In this context, the safety assessments of the multi-barrier system, which consists of the geologic barrier and the nec-essary geotechnical barriers, e.g., containers and drift or shaft seals, are of major im-portance. These individual components of the sealing concept, which often are arranged in parallel, are to ensure the safe long-term isolation of the radioactive waste. Regarding design and safety assessment, the use of a uniform concept for all types of ge-otechnical barriers is considered to yield the best results. In accordance with the state of technology established internationally, this is to be effected by means of the partial factors method. (Müller-Hoeppe & Krone, 1999) used limit states and partial factors for an initial safety assessment of a geotechnical barrier using a drift seal as an example. The following sections give an introduction into the partial factor concept. The methodology as relevant to a safety analysis is described quantitatively using a sealing element and an abutment for a shaft seal concept recently developed within the scope of the preliminary safety analysis for the Gorleben site (VSG) as examples. The research work related to this study was funded by the German Ministry of Economics and Tech-nology (“Bundesministerium für Wirtschaft und Technologie”; BMWi). However the authors are re-sponsible for all the content.

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Table of contents

1 Description of the partial factor method ..................................................................... 3

2 Modifications to demonstrate the effectiveness of a shaft seal .................................. 6

2.1 Tightness .................................................................................................................. 7

2.2 Filtration stability ....................................................................................................... 7

2.3 Structural stability ..................................................................................................... 7

2.4 Crack limitation ......................................................................................................... 8

2.5 Long-term stability .................................................................................................... 8

3 Example for applying the safety assessment concept to elements of a shaft

seal ........................................................................................................................... 8

3.1 Shaft sealing concept according to VSG ................................................................... 9

3.2 Demonstration of deformation stability using the hard rock gravel abutment at

a depth between 460 and 650 m as an example ..................................................... 11

3.2.1 Requirements ......................................................................................................... 11

3.2.2 Actions on the abutment ......................................................................................... 12

3.2.3 Resistances ............................................................................................................ 13

3.2.4 Results and Assessment ........................................................................................ 14

3.3 Safety assessment concept using the salt concrete sealing element as an

example .................................................................................................................. 15

3.3.1 Permeability estimates ............................................................................................ 15

3.3.2 Flow time ................................................................................................................ 20

3.3.3 Results and Assessment ........................................................................................ 21

3.4 Summary ................................................................................................................ 22

4 References ............................................................................................................. 23

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1 Description of the partial factor method

The semi-probabilistic, reliability-oriented safety assessment concept using partial factors is based on the internationally recognized Eurocodes (DIN EN 1990). In engineering, it can thus be considered as state of the art for demonstrating the load bearing capacity (re-sistance) of a structure. The actual safety case for the system as a whole and for the individual barriers consists of a number of individual safety assessments for various limit states that also include, e.g., the mechanical properties of the construction material. As a first step, the requirements for the multi-barrier system as a whole and for the individual subsystems need to be derived from the safety goals. Whether specific requirements are met is demonstrated by means of “as-sessment cases“(load cases). The term "assessment cases" was chosen analogous to the term used in long-term safety assessments as in addition to the load, other parameters need to be taken into account as well. The assessment cases are derived from the combinations of actions (impacts) and from the specific system characteristics. The respective states of the structure, e.g., the stress states, are to be determined by means of equilibrium considera-tions. The proper demonstration is carried out by means of a limit value evaluation of the opposing actions and resistances, e.g. the (existing) stresses determined in the equilibrium considerations are compared with the nominal design stresses which can be calculated, e.g., from the material strengths. The actions on the structure are compared with the resistances of the structure by means of limiting criteria which are allocated to the combinations of ac-tions. The analyses by means of assessment cases have to be carried out for all relevant combinations of actions as well as for their limit states. The reference to a limit state makes sense because both actions and resistances are deter-mined from typical distribution functions. Because of the dispersion (variability) of the two parameters, a number of states are possible. The limit state describes the state of the struc-ture where it just barely meets the requirements. If this state is exceeded, the structure no longer complies with the design requirements. Accordingly, in order to meet the design re-quirements, the resistances need to be higher than the actions. According to (Kreienmeyer et al., 2008) and (Müller-Hoeppe et al., 2007), the following indi-vidual assessments are essential for a safety assessment according to the state of the art in technology:

Demonstration of sufficient hydraulic resistance (demonstration of tightness)

Demonstration of sufficient load bearing capacity (structural integrity) o Demonstration of structural stability o Demonstration of crack limitation o Demonstration of deformation limitation o Deformation of filter stability o Demonstration of durability

These assessments are essential for demonstrating the effectiveness of the shaft seal. Fur-thermore, the

Feasibility needs to be assessed and demonstrated. Figure 1 shows the individual assessments and their connections to the overall demonstration of functionality. In addition to applying the method of partial factors, a reliability assessment based on empirical data needs to be car-ried out in order to quantify the reliability of using probabilistic methods. Methods to assess reliability are also used in risk analyses (Müller-Hoeppe & Krone, 1999).

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Fig. 1: Connection of hydraulic long-term calculations in a long-term safety assessment with the individual,

function-related assessments using the example of a shaft seal (Müller-Hoeppe et al., 2013a)

The design values for the individual assessments are derived from the characteristic values of the actions on and the properties of the barrier combined with the related partial factors. When applying the method of partial factors, actions and resistances, i.e. the parameters of the targeted relation, are allocated partial factors. The effects of actions (Ed) are multiplied by partial safety factors and, thus, increased, whereas resistances (Rd) are divided by partial factors and, thus, decreased. This method and the application of partial factors generally account for uncertainties in the representative values of the actions and uncertainties in the properties of the structure. Depending on model generation, any uncertainties in the model regarding actions and resistances are accounted for by the choice of specific model parame-ters, if necessary. Generally, if the models are very precise, model parameters covering the uncertainties are not taken into account (Müller-Hoeppe & Eberth, 2009). Thus, the initial requirement

Ed ≤ Rd (1) is divided into specific calculations for both terms. For the effects of actions, Ed, the following applies:

Ed = YEd · E (Fdi ; adi ; Xdi) (2) With: γEd partial factor for model uncertainty in the actions model Fdi design values for actions adi design values for the geometric parameters Xdi design values for the construction material properties

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The design values for the action Fd are calculated by multiplying the characteristic individual value (Fc) by the partial factor of the (γf) action.

Fd = Yf · Fc (3) In accordance with the above, the following applies for the design values of the construction material properties Xd:

Xd = (η · Xc) / Ym (4) With: η conversion factor for duration of loading, moisture, etc. Xc characteristic value for the building material properties γm partial factor of the construction material property In contrast to actions, there is no partial factor assigned to geometric parameters. The design value of a geometric parameter (ad) is calculated by adding the nominal value (anom) and the deviation from the nominal value (Δa) that has been taken into account. Taking the deviation (Δa) into account is particularly important for geometric parameters that react sensitively. The deviation is determined from the expected changes in the respective parameter. An example is the effective length (buckling length) of a steeply inclined rock layer. Changes in length directly affect the buckling behaviour. Thus, a deviation Δa needs to be taken into account as well.

ad = anom + Δa (5) The design value for the resistance is calculated as follows:

Rd = 1/YRd · R·(adi ; Xdi) (6) γRd partial factor for model uncertainty in the resistance model The various factors influencing the system can be determined by both, deterministic and probabilistic methods. For example, the geometry of the structure is a result of the design draft and the stress model. Actions can be determined based on statistics and on limit value assessments and building material properties can also be determined based on statistics (Müller-Hoeppe & Krone, 1999). If the applicable standards and regulations do not contain suitable partial factors, the latter can also be determined by means of probabilistic methods or calibration (Kreienmeyer et al., 2008). Figure 2 illustrates the methods for determining partial factors.

Fig. 2: Reliability methods for determining partial factors (DIN EN 1990)

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The individual assessments of the limit states are to be carried out “at the level of ultimate limit state verifications”, i.e. they have to have the same reliability level as a verification of ultimate limit states. This safety concept is necessary in order to ensure that the design com-plies with the requirements. In the structures considered, the demonstration of tightness is thus to be considered at the level of a verification of ultimate limit states, because a loss of tightness would result in “danger to life and limb” (DAfStb 1997). Unlike in the Eurocodes, the term “resistance” includes more than just mechanical stability. The term is used synonymous for the prevention of a danger to life and limb and can also be used, e.g., for the hydraulic resistance. Compliance with the reliability level for resistance in the corresponding assess-ment ensures the functional integrity of the structure. As mentioned above, the assessments give information on the reliability of a structure. To demonstrate reliability, a corresponding confidence level or failure probability needs to be met. In an ultimate limit state verification, a failure probability pf of 10-4 for the intended life-time of the structure is sufficient (Müller-Hoeppe & Krone, 1999). Thus, the verification of the effectiveness of the safety function indicates that the probability that a barrier does not fail prematurely during its expected lifetime is pf = 10-4, i.e., the survival probability ps of the bar-rier is ps = 1 - pf (Müller-Hoeppe & Krone, 1999). 2 Modifications to demonstrate the effectiveness of a shaft seal

As already explained in the general description of the partial factors' method, the correspond-ing assessments need to be carried out for all relevant combinations of actions as well as for all subsystems and the shaft seal as a whole. The following will concentrate on the demon-stration of reliability of a shaft seal. According to (Sitz, 2001), the following basic requirements apply to shaft seals:

Prevention of fluid flow into the mine

Prevention of fluid flow out of the mine

Complete backfilling of shafts in salt formations after closure

Settlement in the filling column to be as small as possible

Measures to prevent emptying of the filling column

De-installation of existing installation to the largest possible extent

All installed structures have to be maintenance-free and stable in the long term For the design of the shaft seal to meet the requirements, the individual elements are as-signed different functions. To put it simply: The sealing elements of the shaft seal have a sealing function while the abutments restrict deformation of the seals (position stability). Type and number of sealing elements and abutments depend on the requirements on the shaft seal and on the boundary conditions. The sealing elements in a shaft seal can be designed to be redundant and diverse. The same applies to abutments. The corresponding verifica-tions need to be carried out for all subsystems. In accordance with Figure 1, the safety of a shaft seal is considered to be demonstrated when it can be constructed according to high standards and when the design assessment cases meet the following requirements:

tightness (specification of the hydraulic resistance of the sealing element and of the contact zone and excavation damaged zones

demonstration of integrity, i.e. filtration stability, structural stability, crack limitation (de-sign-related), deformation limitation, chemical long-term stability

In the following, the individual assessments as related to the shaft seal and its subsystems will be considered in more detail. In preparation of the exemplified safety assessment in the

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following sections, this general explanation outlines the specifics of a safety demonstration of a shaft seal. Issues specific to the host rock are not considered at this point. 2.1 Tightness

As with drift seals, the assessment of the tightness of the individual sealing elements and, thus, of the sealing construction as a whole has to take into account not only the sealing body but the hydraulically effective contact and excavation damaged zones that are located in parallel as well. The integral hydraulic permeability of the sealing location needs to be as-sessed from the combination of all three subsystems. Due to gravitation and the related inherent properties of the shaft sealing system, the evolu-tion of roof clefts, which affect the tightness of the sealing elements and which can occur in drift seals, can be excluded. The sealing of the shaft cross section is affected in a horizontal plane. Unlike in drifts seals, settlement in a sealing element or between two subsystems does not necessarily diminish the sealing properties or cause a complete loss of the sealing function. 2.2 Filtration stability

The filtration stability of the subsystems of a shaft seal may have to be checked. This filtra-tion stability can be described as the avoidance of erosion and suffusion processes. Due to

high hydraulic gradients caused by fluid inflow from the aquifers in the surrounding rock mass, the risks for erosion and suffosion may be high-er, especially in the saturation phase. This has to be counteracted by design measures and suitable analyses. Figure 3 illustrates the basic erosion and suffosion pro-cesses. A lack of filtration stability may, e.g., cause the loss of tight-ness of a sealing element. Fig. 3: Basic erosion and suffosion processes (DGGT 1997)

2.3 Structural stability

The vertical arrangement of the subsystems contributes to the system reliability. To ensure the position stability of the seals, it needs to be demonstrated that settlement in the abut-ments and filter layers is sufficiently low (restriction of deformation). The demonstration that settlement is sufficiently low is part of the demonstration of integrity. For abutments made of cohesive material, the demonstration of mechanical resistance is covered by the demonstration of restriction of crack formation. Mechanical failure causes mechanical damage to or failure of the structure. If cohesive material is used, mechanical damage is always preceded by crack formation. Cohesive construction materials are those that – through a cohesive agent – develop tensile or adhesive tensile strengths. Among these are salt concrete and sorel concrete. If a restriction of crack formation can be demon-strated for these materials, mechanical damage can be excluded and, thus, mechanical re-sistance is verified.

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2.4 Crack limitation

The demonstration of limited crack formation is relevant both to sealing elements and to abutments made of cohesive material. Crack formation is induced by excessive mechanical stress on the individual subsystems or by thermo-mechanical/chemical processes during installation. An example for crack formation due to changes in volume and/or temperature is the cooling process of seals made of bitumen or asphalt and installed while hot where the volume of the sealing material shrinks during cooling. As observed in practise, this volume shrinkage can lead to a decrease in effective sealing length (of the sealing element) due to contraction in the upper part of the sealing element and detachment from the contour. As a further example, crack formation due to setting processes in salt concrete or magnesia binder when constructing corresponding abutments or seals can be mentioned. Additional crack formation when the fluid pressure criterion (minimum normal stress, low fluid pressure) in the sealing element and in the contact zone is exceeded can be possible, depending on the material used and the corresponding limit states (Müller-Hoeppe & Krone, 1999). An ex-ample for this is the large-scale experiment to construct a shaft seal in Salzdetfurth. In this case, the pressure increase in a sealing element made of bentonite was too fast and thus damaged the seal (Teichmann et al., 2002). 2.5 Long-term stability

Shaft seals are to prevent access to the repository. Due to their location in the geologic bar-rier and to their probable contact with fluids from above, shaft seals have particular long-term safety functions. For this reason, they can only be constructed of material with long-term per-formances that have been verified by natural analogues or advanced studies on their chem-ism. For the subsystems abutment and sealing element, only sealing material that is charac-teristic or mostly characteristic to the host rock can be used, e.g. salt concrete and sorel con-crete or long-term stable material like clay (i.e. bentonite), asphalt, bitumen or natural rock. In addition to the above, subsection 2.4.1 (2) of (DIN EN 1997-1) generally applies to the demonstration of the various properties and assessment cases of a shaft seal for a reposito-ry for radioactive waste: „It should be considered that knowledge of the ground conditions depends on the extent and quality of the geotechnical investigations. Such knowledge and the control of workmanship are usually more significant to fulfilling the fundamental require-ments than is precision in the calculation models and partial factors.” 3 Example for applying the safety assessment concept to elements of a shaft

seal

To clarify the above, the assessment and demonstration concept based on the partial factor method will be explained using a shaft seal as an example. The draft design of the sealing concept which was developed within the scope of the preliminary safety analysis for the Gorleben site (VSG) and whose safety function and reliability has been assessed will serve as an example. First, the design of the shaft seal and the material proposed will be de-scribed. Then, the assessment concept will be illustrated on a representative sealing element and a representative abutment. The exemplary demonstration will contain selected, simplified individual assessments of the reference scenario and is not considered to be comprehensive and complete. The simplifica-tions are to facilitate understanding of the partial factor method and of the general methodol-ogy. For this reason, the functional draft design will be used as the basis for the following

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simplified safety assessment. A more detailed and complete description of the sealing con-cept developed within the scope of the VSG and of the corresponding safety assessment concept can be found in (Müller-Hoeppe et al., 2013a) and (Müller-Hoeppe et al., 2013b). 3.1 Shaft sealing concept according to VSG

With the Gorleben exploration mine, the corresponding salt diapir is to be investigated on its suitability to host a repository for radioactive waste. Within the scope of the preliminary safety assessment of the Gorleben site, a sealing concept was designed for the existing shaft Gorleben 1, and a concept to assess its reliability and effectiveness was developed. As the geologic environment, depth, and construction of shaft Gorleben 2 of the twin-shaft installa-tion are similar to those of shaft Gorleben 1, it was assumed that the same sealing concept can be used for both shafts. The locations of the individual components of the shaft construc-tions and of the intended sealing systems vary due to the geology of the respective shaft sites. In the overburden, both shafts are furnished with a lining, i.e., an outer liner, which is con-nected to the rock mass, and an inner liner. The liners are separated from each other by means of a hydrostatic asphalt seal. The outer liner extends to a depth of 260 m, below which it is supported by a foundation. The inner liner extends to a depth of 340 m and is also supported by a foundation (to a depth of 345 m). Inner liner and foundation are separated by a Teflon layer. Below the foundation, down to a depth of 349.5 m, a supporting ring consist-ing of several steel rings is located (Müller-Hoeppe et al., 2012c). In the draft design, the shaft seal is situated below the supporting rings of the waterproof lining. The shaft diameter below the supporting rings is 7.63 m. Within the lining, the shaft diameter is 7.53 m. The upper part of the waterproof lining will be backfilled with suitable material. The shaft seal itself consists of three sealing elements, which are made of different materials, and of various abutments and further components. Figure 4 shows a schematic of the prelim-inary design of the shaft seal. At the top, between the shaft seal and the bottom of the supporting rings at a depth of 386 m, a filter layer made of hard rock gravel or gravel and sand is planned. Beneath the 1st sealing element, a similar filter layer is planned down to a depth of 460 m. The two filter layers sandwiching the bentonite seal are to ensure the filtration stability of the seal. The first seal-ing element has a total height of 60 m and is positioned between 386 and 446 m below sur-face. Like the two other sealing elements it will, thus, be positioned in the so-called Gorlebenbank. The Gorlebenbank is a narrowly stratified Anhydrite bank in the rock salt. It has been folded due to salt tectonics and is penetrated by the reference shaft several times. It is known that brine inclusions are present in the Gorlebenbank and, as the Gorlebenbank could not be excluded as a potential migration path for fluids at the draft design stage, it will also be sealed by the sealing elements so that it does not have any direct connection with the reservoir elements. Upon dimensioning, the effective length of the sealing element will be shortened by 10 m in order to take into account the Gorlebenbank. To remove the highly damaged parts of the excavation damaged zone, approximately 0.5 m of the contour adjoin-ing the sealing element are to be trimmed off (Müller-Hoeppe et al., 2012b). The exact depth of the layer to be trimmed off will be determined based on geotechnical measuring results. Beneath the second filter layer, down to a depth of 650 m, an abutment made of hard rock gravel ensures the positioning stability of the subsystem, which consists of bentonite sealing element and filter layers (Müller-Hoeppe et al., 2013a).

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Fig. 4: Schematic of the shaft seal according to VSG (1st draft). The elements considered in the exemplary

safety assessment are framed in red (Müller-Hoeppe et al., 2013a)

As long-term sealing element of the seal, it is intended to use wetted and technically com-pacted crushed salt in the zone between 650 and 680 m below ground. The crushed salt, which in the long term will have similar characteristics as the surrounding host rock, will be technically compacted during installation as far as possible. To facilitate compaction, it is necessary to wet the crushed salt. In the long term, the compaction of the long-term sealing element – combined with the convergence of the surrounding rock – leads to a healing of the rock mass that has been damaged by the shaft excavation. This prevents brine intrusion to the waste and brine emergence from the closed repository. The 2nd sealing element is located beneath the long-term sealing element. This sealing ele-ment is to be made of salt concrete. It is 60 m long and extends to a depth of 740 m. 0.6 m of the contour adjoining the sealing element will be trimmed off. Beneath the sealing element, down to a depth of 780 m, a 40-m-long abutment made of salt concrete is planned. Both subsystems will be made of the same construction material. The contour adjoining the abut-

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ment will not be trimmed off. The lower part of the abutment is to ensure the position stability of the sealing element. The two components have to meet different requirements. While the sealing element has to have sufficient hydraulic resistance, the abutment has to have suffi-cient mechanical resistance. For the latter, demonstration of sufficient resistance also covers the demonstration of deformation stability (Müller-Hoeppe et al., 2013a). Between a depth of 780 and 846 m, a further abutment, made of hard rock gravel, is planned. In accordance with the sealing concept, the infrastructural areas of the mine that are connected to the shafts will be backfilled with hard rock gravel. An additional depository of technical bischoffite will be placed in those parts of the infrastructural area that are close to the shaft. This is to convert any brine solutions from above into solutions rich in MgCl2 so that brines not rich in MgCl2 are prevented from progressing to the succeeding seal made of sorel concrete to prevent corrosion. According to the sealing concept, the infrastructural areas of the exploration and emplace-ment level that are connected to the shaft are to be backfilled with hard rock gravel as well. The third sealing element is positioned between the two entrances at a depth between 846 and 876 m. It is made of sorel concrete. At the position of the sealing element, it is intended to trim off 0.8 m of the contour. This sealing element will be joined cohesively with the shaft contour and can also act as an abutment. The filling stations of the entrances to the em-placement and to the exploration level will also be backfilled with sorel concrete and act as a further abutment. Like the 3rd sealing element, the shaft sump will be backfilled with sorel concrete. To illustrate the safety assessment concept, the top hard rock gravel abutment, which is located at a depth between 460 and 650 m, and the 2nd sealing element, which is located at a depth between 680 and 740 m, will be described in more detail. Both elements are highlighted in Figure 4 (red frame). 3.2 Demonstration of deformation stability using the hard rock gravel abutment at

a depth between 460 and 650 m as an example

The main function of the hard rock gravel abutment beneath the first sealing element is to ensure its own long-term stability and the position stability of the sealing element. The posi-tion stability of the sealing element is ensured by the high settling stability of the hard rock gravel column. Potential design situations for the hard rock gravel abutment are the construc-tion phase, the temporary saturation phase, the permanent phase where the gravel column is saturated, and the special event of an earthquake. In the following, an exemplary demonstra-tion that the abutment has a low tendency to settlement during the temporary saturation phase will be carried out. 3.2.1 Requirements

According to equation (1), the resistance of the abutment to the existing actions has to be high enough so that the maximum permissible amount of settlement is not exceeded. This describes the limit state. Adherence to the permissible amount of settlement limits distortion or disruption of parts of the bentonite sealing element so that it maintains its required proper-ties regarding hydraulic conductivity and swelling pressure. According to (Wagner, 2005), the permissible amount of settlement (Δlper) is calculated by:

(

) (7)

With: L effective length of the sealing element ρtr dry density ρcrit critical dry density

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According to Wagner (2005) the following settlement limit is valid:

Settlement of the bentonite sealing element in question may not exceed 3% of the seal’s length.

Within the scope of this permissible settlement, the density of the bentonite remains suffi-ciently high to retain the required swelling pressure and the hydraulic conductivity. Any set-tlement will occur in the abutment made of hard rock gravel and in the lower filter layer. The abutment is, thus, to be considered a layered construction. The effective total length of the bentonite sealing element is 50 m (60 m total length minus the part enclosed by the Gorlebenbank). Thus, the maximum permissible settlement of the gravel column is Δlper ≤ 1.5 m. 3.2.2 Actions on the abutment

According to (Müller-Hoeppe & Eberth, 2009), the resulting settlement can be described in accordance with the silo theory as follows:

( )

[

] (8)

With: Δl settlement p0 load λ stress ratio (horizontal load) 𝜈 Poisson’s ratio E elasticity modulus U circumference A cross-section L length of gravel column The actions on the abutment are characterized by the load p0 which is made up as follows: stress from the backfill column above; stress due to the structural load (dead load) of the sealing element; stress due to the structural load of the filter layers. Stress from the backfill column above

As mentioned above the shaft sealing system is situated directly below the shaft lining. The part of the shaft that is furnished with a shaft lining, i.e. between ground level and shaft seal, will be backfilled after the seal has been constructed. The inner liner, which is not connected to the rock mass, does not transfer any load to the surrounding rock so that the complete load (weight) of the backfill column acts on the hard rock gravel abutment. The backfill con-sists of various types of sand and gravel as well as of mineral mixtures. Between the overly-ing rock mass and the surface, the density of the shaft backfill is considered to be homoge-neous with 2240 kg/m³. The pressure of the overlying backfill column is calculated as follows:

pb = ρb·g·h = 2240 kg/m3 · 9.81 m/s2 · 349.5 m = 7.68 MPa (9) With ρb = density of backfill column, g = gravitational acceleration, and h = height of backfill column. Due to the overlying backfill column, an additional load of pb = 7.68 MPa acts on the hard rock gravel abutment. The material in the backfill column will be as tightly packed as possible. Its geometry is determined by the shaft lining and the depth. Due to the limitation of the parameters, a significant increase of the load from the overlying backfill column is not

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plausible, i.e. physically not possible. According to (DIN EN 1997-1), a partial factor of γF,1 = 1.0 is, thus, sufficient for the permanent action. Dead load of the sealing element As it is conservatively assumed that sealing element and filter layer do not transfer any load, the complete dead load of the sealing element acts on the abutment. The bentonite sealing element is assumed to have a density of 1750 kg/m³. This is the maximum density technical-ly feasible. As a further compaction of the bentonite is physically not plausible, a partial factor of γF,2 = 1.0 as permanent and favourable action can be used for the structural load of the sealing element. The sealing element (SE) has a total thickness of 60 m. The extra load from the bentonite sealing element is:

pSE = ρSE·g·h = 1750 kg/m3 · 9.81 m/s2 · 60 m = 1.03 MPa (10) Dead load of the filter layers The two filter layers consist of various types of sand, gravel, and chippings and have a densi-ty of ρf = 1900 kg/m³. The upper filter layer is 36.5 m thick while the bottom filter layer has a thickness of 14 m. The sum of the additional load resulting from both layers is:

pf = ρf·g·h = 1900 kg/m3 · 9.81 m/s2 · (36.5m + 14m) = 0.94 MPa (11) The maximum construction density for the filter layers, i.e. the technically and physically fea-sible upper limit, cannot be specified here. To take into account possible variation in the con-struction density, its action is allocated a partial factor of γF,3 = 1.35 (DIN EN 1997-1). Total actions The actions on the abutment can be summarized as follows: Tab. 1: Overview of actions

Action Load [MPa] Partial factor

Upper backfill column 7.68 1.0

Bentonite sealing element 1.03 1.0

Upper filter layer 0.68 1.35

Bottom filter layer 0.26 1.35

The total action or total additional load on the abutment is calculated as follows:

ED = ∑ ( ) = pb·YF,1 + pSE·YF,2 + pf·YF,3 = 9.98 MPa (12)

For the demonstration of deformation stability, possible fluid pressure and the resulting uplift need not be taken into account. The load acting on the bottom filter layer is 9.1 MPa and is the sum of the loads from the upper backfill column, the upper filter layer, and the bentonite sealing element. 3.2.3 Resistances

The abutment’s resistances opposing the actions result from the properties of the construc-tion material used and the geometry of the abutment. There is a high level of knowledge about the design of silos. The properties of the stored particulate solids relevant for the de-sign can be determined by means of (DIN EN 1991-4). Resistances in the bottom filter layer Annex E of (DIN EN 1991-4) contains characteristic values of the properties of various types of particulate solids. The respective mean values of the wall friction coefficient (μ) and of the horizontal stress ratio (λ) are adapted by means of conversion factors (aμ, aλ). For both char-acteristic values, the lower limit value is used, thus, the mean values have to be divided by

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the conversion factors. As reference material for the filter layer, the bulk solid “aggregate” as listed in (DIN EN 1991-4) is selected. The contour at the location of the abutment is specified to belong into wall friction category D3. The resulting partial factors are compiled in Table 2. For both characteristic values it is not necessary to take a further partial factor into account. Tab. 2: Determination of particulate solids‘ properties according to (DIN EN 1991-4)

Characteristic value Mean value Conversion factor Design value

Wall friction coefficient μ [-] 0.59 1.12 0.53

Horizontal stress ratio λ [-] 0.52 1.15 0.45

According to (Müller-Hoeppe & Eberth, 2009), an elasticity modulus E = 150 MPa and a Poisson’s ratio of v = 0.33 are taken into account. The length of the filter layer is L = 14 m. It is not necessary to additionally take into account a variation of the geometric parameter as per equation 5. During construction, the filling height is continuously monitored to ensure a correct height. Resistances in the gravel column The necessary characteristic values for the gravel column can also be determined by means of (DIN EN 1991-4). For the gravel, an elasticity modulus E = 200 MPa and a Poisson’s ratio of v = 0.32 are taken into account. The length of the gravel column is L = 190 m. A horizontal stress ratio λ of 0.41 and a wall friction coefficient μ of 1.04 are taken into account. These characteristic values are based on empiric values from previous projects (Müller-Hoeppe & Eberth, 2009), (Teichmann et al., 2002). It is not necessary to additionally take into account a variation of the geometric parameter as per equation 5. During construction, the filling height is continuously monitored to ensure a correct height. The geometric parameter “shaft diameter” in the unlined part of the shaft is d = 7.63 m. Due to additional excavation activities, shaft circumference and cross-section may vary slightly. As these slight variations in shaft geometry do not indicate an additional hazard, the respec-tive nominal values for the shaft circumference and cross-section without taking into account any variation may be used. The results are: Shaft circumference Ud = URef = 23.9 m Shaft cross-section Ad = ARef = 45.7 m² 3.2.4 Results and Assessment

Based on the parameters determined and equation (9), the following settlement can be cal-culated for the bottom filter layer:

( 𝜈)

[

]

( )

[

]

And for the gravel column:

( 𝜈)

[

]

( )

[

]

The total settlement to be expected is the sum of the settlements to be expected in the bot-tom filter lay and in the abutment. In total, the settlement of Δltot = Δl1 +Δl2 = 0.45 m is below the permissible settlement of Δlper ≤ 1.5 m (3% settlement of the effective length of the seal). The simple addition of the settlements of both components is a conservative assumption. It can actually be expected that the most of the stress in the filter layer will be transferred to the

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15 TEC-12-2013-AP

shaft wall. The additional load acting on the gravel column is decreased and causes only little settlement. The conservative assumption can be used to demonstrate the deformation stabil-ity of the abutment (Müller-Hoeppe et al., 2013a). 3.3 Safety assessment concept using the salt concrete sealing element as an ex-

ample

The 2nd sealing element at a depth between 685 and 775 m is to be constructed of salt con-crete with a composition of the type “Asse”. This reference composition has already been tested in the construction of the “Asse-Vordamm" (seal). It consists of 18 Ma.-% blast furnace cement, 72 Ma.-% crushed rock salt and 10 Ma.-% NaCl solution (sodium chloride solution) (Müller-Hoeppe et al., 2012b). At the location of the seal, the contour is trimmed off for 0.6 m so that the final diameter at the location is 8.83 m. The total length of the sealing element is 60 m, however, as this location includes the Gorlebenbank, the effective length of the sealing element is assumed to be only 50 m (Müller-Hoeppe et al., 2013a). In the case of a repository in a salt formation, the requirements on the sealing properties and functional life of the shaft seal and the individual components are based on the compaction properties of the crushed salt used as backfill in the repository. In the long term, the permea-bility of the backfill material, which has similar characteristics as the host rock, will be the same as that of the host rock due to the convergence of the surrounding rock mass and the creep properties of the salt. This leads to a healing of the cavities that were excavated to construct the repository. Strictly speaking, the functional life of the shaft seal, which has to include the sealing function, is thus limited to the compaction phase of the crushed salt. The long-term safe confinement of the radioactive waste is effected by the rock mass and – after its healing – by the compacted backfill. Based on current knowledge, the minimum functional life of shaft seals in rock salt is esti-mated to be approximately 1,000 years (Müller-Hoeppe et al., 2013b). An assessment for a comparable shaft seal in clay formations is still pending. A seal is demonstrated to be tight when the integral permeability at the seal’s location is sufficiently low and when the delay of brine flow through the sealing element is sufficiently long. 3.3.1 Permeability estimates

Tightness needs to be demonstrated for the integral permeability at the seal’s location. This assessment has to include the three sub-systems sealing element (SE), contact zone (CZ), and excavation damaged zone (EDZ), which act parallel to each other. At the location of the seal, a maximum mean integral permeability of kreq = 7·10-19 m2 is required (Müller-Hoeppe et al., 2013a). This means that under the existing conditions, the sealing element has to have at least this mean permeability in order to be able to delay brine intrusion into the repository for a sufficiently long period. This permeability is the integral permeability of the construction, calculated as mean over the cross-section including contact zone and EDZ. During construc-tion, this has to be demonstrated by structural analysis verifications. Within the scope of the safety case, possible limit states and failures cases are investigated by means of a long-term safety analysis. This analysis takes into account the real/to be expected distribution of the permeability in the sealing element. The integral permeability that has to be demonstrated on the resistance side consists of the individual permeabilities of the components, related to the surface:

As in equation 1, this mean permeability (kint) is compared with the required limit value (kreq = 7·10-19 m2). At this point, we refrain from equipping the individual components of the

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16 TEC-12-2013-AP

design value of the resistance with partial factors. The salt concrete sealing element is part of the overall shaft seal, which is to delay potential brine intrusions. As already mentioned above, the assessment of the hydraulic system as a whole is carried out in a final, probabilis-tic long-term safety analysis which takes into account the distribution functions. This covers model uncertainties. The analysis also covers failure cases. Partial factors for individual rep-resentative characteristic values are not taken into account. The representative characteristic values listed in the following section, especially of the permeability, were used as design val-ues. For the permeability, the values used are the means of the existing distribution. In accordance with Figure 2, (DIN EN 1990), and (DIN EN 1997-1), design values can be determined by empirical/deterministic methods as well as by statistical methods. The 95% confidence interval for the mean value is considered to be a conservative estimate of the mean. Depending on the individual case, the characteristic value can also be calculated as 5% fractile. Both are possibilities to determine the design value of the resistance using the characteristic value. In addition to this, a direct determination of the design value for ultimate limit state verifications is possible. In the following, the three methods according to (DIN EN 1990), (DIN EN 1997-1), and (Mül-ler-Hoeppe & Eberth, 2009) are outlined. As an example, the mean permeabilities for the sealing element, the contact zone, and the EDZ are determined using selected test series. Determining the design value using the characteristic value

The design values Xd of a quantity X should be determined as follows:

[ ]

With Xd design value Xc characteristic value ηd design value of the conversion factor used to scale laboratory tests up to in-situ

conditions, unless the conversion is already included in γm. Often: ηd = 1.0 γm partial factor for sample properties (material properties)

mx mean value of the properties of n samples,

∑( )

√ with the variance

∑( )

Vx variation coefficient for X, ⁄

kn value from table 3

Tab. 3: Values of kn for the 5% characteristic value (5% fractile), corresponds with Table D1 in (DIN EN 1990)

n 1 2 3 4 5 6 8 10 20 30 ∞

Vx known 2.31 2.01 1.89 1.83 1.80 1.77 1.74 1.72 1.68 1.67 1.64

Vx unknown - - 3.37 2.63 2.33 2.18 2.00 1.92 1.76 1.73 1.64

This method is based on the following assumptions: the distribution is based on the normal (Gaussian) distribution there is no advance information about the mean value in the case of „Vx unknown”, there is no advance information about the variation coeffi-

cient in the case of „Vx known”, there is full advance information about the variation coefficient

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17 TEC-12-2013-AP

Direct determination of the design value for ultimate limit state verifications

The design value Xd of a quantity X should be determined as follows, where ηd should take into account all uncertainties that were not covered by the tests. The values of kd,n should be determined by means of Tab.

[ ] With Xd design value ηd design value of the conversion factor used to scale laboratory tests up to in-situ

conditions. Often: ηd = 1.0

mx mean value of the properties of n samples (

∑( ) )

kd,n value from Table 4

Vx variation coefficient for X, ( ⁄ )

Tab. 4: Values of kd,n for the ultimate limit state design value, corrsponds with Table D.2 in (DIN EN 1990)

n 1 2 3 4 5 6 8 10 20 30 ∞

Vx known 4.36 3.77 3.56 3.44 3.37 3.33 3.27 3.23 3.16 3.13 3.04

Vx unknown - - - 11.4 7.85 6.36 5.07 4.51 3.64 3.44 3.04

The non-exceedance probability is approximately 0.1%. The method is based on the follow-ing assumptions: the distribution is based on the normal (Gaussian) distribution there is no advance information about the mean value in the case of „Vx unknown”, there is no advance information about the variation coeffi-

cient in the case of „Vx known”, there is full advance information about the variation coefficient Determining a conservative estimate of the mean value (95% confidence level)

As mentioned above, Eurocode 7 (DIN EN 1997-1) allows the use of cautious estimates of mean values in geotechnical contexts. A cautious estimate of the mean value is a selection of the mean value with a confidence level of 95%. It is determined as follows (DIN EN 1990):

[ ]

√

In this case – if the variation coefficient is unknown – the t-distribution according to Student with (n-1) degrees of freedom can be used. Properties of the sealing element

The initial diameter in the unlined part of the shaft is 7.63 m. At the location of the seal, the excavation damaged zone of the contour is trimmed off for 0.6 m. Thus, the diameter of the salt concrete sealing element is 8.83 m, which corresponds to a cross-section area of the sealing element of ASE = 61.24 m². An additional deviation needs not be taken into account. The type “Asse” salt concrete composition to be used is described in (Müller-Hoeppe et al., 2012b). This type of salt concrete was used in the Project “Asse-Vordamm” (Müller-Hoeppe & Eberth, 2009). Based on this experience, the producibility of a vertical sealing element made of salt concrete can be demonstrated. As a result of tests on the structure, characteris-tic values concerning the fluid and gas permeability of the salt concrete as well as character-istic values of the contact joint and the surrounding excavation damaged zone are known. According to (Müller-Hoeppe et al., 2012b), only three characteristic values were determined in-situ for the seal’s permeability to fluid. It is between 4·10-20 and 9·10-21 m².

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18 TEC-12-2013-AP

There is a large database for the gas permeability of the material. Table 5 summarizes measured gas permeability values of a structure made of salt concrete. Tab. 5: Example of measured gas permeabilty values of a structure; (Müller-Hoeppe & Eberth, 2009)

Floor drillings Roof drillings Wall drillings, South Wall drillings, North

8·10-23

m² 3·10

-23 m²

6·10-23

m²

1.3·10-22

m² 3.5·10

-22 m²

5·10-23

m² 2·10

-23 m²

4.4·10-24

m² 1.5·10

-23 m²

1.3·10-22

m²

8·10-24

m² 6·10

-24 m²

7·10-24

m²

As explained above, by means of statistical methods, these measuring data can be used to determine characteristic values of the permeability. mean (for comparison) 3·10-23 m² 5% fractile 3·10-22 m² 95% confidence interval 5·10-23 m² Directly determined design value 3·10-21 m² Properties of the contact zone

The contact zone between sealing element and surrounding rock mass is characterized by the material properties, the installation conditions, and the grain size distribution in the rock mass. The wet salt concrete is compacted during installation. It spreads evenly within the space designated for the seal and adheres to the rock mass after settling. Based on (DAfStb 2004), the expansion of the contact zone is assumed to be two-times the maximum opening diameter. As the exact properties of the rock mass at the location of the seal are not suffi-ciently known, the contact joint is assumed to have a thickness of 30 mm as specified in (DAfStb 2004). Due to its small extent compared with the system as a whole, it is not neces-sary to additionally take into account a geometric deviation. The annular contact joint has a surface area of ACZ = 0.84 m². Exemplary permeability properties of the contact joint are derived from the project “Asse Vordamm”. Measurements in the contact zone between salt concrete and rock salt taken at the walls and the floor yielded permeabilities between K = 1·10-23 and 7·10-23 m² (Müller-Hoeppe & Eberth, 2009), (Müller-Hoeppe, 2010), cf. Table 6. Using a similar method as the one used to determine the design value of the permeability of the salt concrete structure, the mean permeability of the contact joint can be determined. The roof is not taken into account. Tab. 6: Example of measured gas permeabilties of the contact joint between salt concrete/rock salt; (Müller-Hoeppe & Eberth, 2009)

Floor drillings Roof drillings Wall drillings, South Wall drillings, North

1·10-24

m² 1·10

-24 m²

1.4·10-14

m² 2.1·10

-13 m²

6.5·10-19

m² 3.3·10

-14 m²

7·10-23

m² 2.5·10

-23 m²

4·10-23

m² 6·10

-23 m²

The significantly increased permeability values in the roof of the sealing element are due to the sealing element’s construction and are not relevant for a vertical sealing element. They are not taken into account in the following illustration. Nevertheless, it should be pointed out that a permeability in the range of the required mean value is feasible. This is indicated by the individual value 6.5·10-19 m². Based on the three statistical methods mentioned above, the following characteristic or design values are derived from the data measured in the floor and wall drillings: mean value (for comparison) 1·10-23 m² 5% fractile 4·10-22 m² 95% confidence interval 7·10-23 m² Directly determined design value 1·10-20 m²

19 TEC-12-2013-AP

Properties of the excavation damaged zone

While the shaft is open, an EDZ develops in the rock mass close to the contour. The charac-teristics of the EDZ are site-specific and are influenced by the existing stress and defor-mation states, the geometry and size of the cavity, the duration the cavity remains open, the mineralogical composition of the rock, and by thermal aspects. The latter include, e.g., natu-ral ventilation. According to the calculations, the plastic zone of the EDZ caused by excava-tion at the location of the 2nd sealing element expands for 0.66 m from the shaft contour into the rock. Variations due to seasonal or thermal aspects are not taken into account at this point as they can be controlled by technical measures. After the EDZ has been trimmed off for 0.6 m (Müller-Hoeppe et al., 2013a), an EDZ of 0.06 m remains. This is based on the additional assumptions that trimming off is carried out with as little damage to the rock as possible and that the sealing element is installed as soon as possible so that re-damage of the rock mass close to the contour is kept to a minimum. The newly developed damage should be estimated prior to installation and should be taken into account in the permeability calculations. In this case, we refrain from doing so. From this new contour (rN = 4.415 m), the remaining EDZ, which is assumed to be perfectly circular, ex-tends 0.06 m into the rock. Taking into account the contact zone, an EDZ area of AEDZ = 0.84 m² remains. In addition to the actual depth of the EDZ, the permeability of the damaged zone needs to be determined. As both depend on a number of different and site-specific factors, it is essential that they are determined by means of in-situ measurements. Due to inhomogeneities in the rock mass, for example, the EDZ may not expand in a perfect annulus around the contour. Characteristically, the region close to the contour has the highest permeability. The greater the distance to the contour, the more approaches the permeability the initial permeability of the rock mass (Hunsche et al., 2003). This is the reason why – according to (Wagner, 2005) – it is reasonable to identify a limit permeability to be able to differentiate between permeable and technically impermeable re-gions and to determine the exact characteristics of the EDZ. In (Wagner, 2005), a limit per-meability is identified for the rock salt in question. However, this value cannot necessarily be considered as universally valid. In fact, it is rec-ommended to define a limit value that takes into account the site-specific parameters that influence the permeability. The effective or integral permeability of the EDZ can be deter-mined by means of extrapolation using existing series of measurements. The measurement series used as an example for the permeability can also be used to derive estimated mean values for the excavation damaged zone (see Table 7). Tab. 7: Example of measured gas permeabilty values in the EDZ; (Müller-Hoeppe & Eberth, 2009)

Floor drillings Roof drillings Wall drillings, South Wall drillings, North

3·10-24

m² 1·10

-23 m²

1·10-23

m² 2·10

-24 m²

6.5·10-21

m² 5.2·10

-23 m²

2.5·10-24

m²

1·10-23

m² 24.6·10

-22 m²

8·10-24

m² 1.2·10

-22 m²

Based on the three statistical methods mentioned above, the following characteristic or de-sign values are derived from the data measured in the floor and wall drillings:

The limit permeability to differentiate between permeable and tech-nically impermeable regions is set to klimit = 10-19 m²

20 TEC-12-2013-AP

Mean value (for comparison 2·10-23 m² 5% fractile 2·10-21 m² 95% confidence interval 1·10-22 m² Directly determined design value 8·10-20 m² Over time, the creep behaviour of the surrounding rock salt mass leads to a healing of the remaining EDZ. The permeability of the EDZ changes and – in the long term – reaches the level of the intact rock mass. This effect, which has a positive influence on the sealing prop-erties of the salt concrete element, will not be taken into account in this simplified safety analysis. As a conservative assumption, only the increased permeability at the beginning of the lifetime of the sealing element will be considered. Determining the integral permeability

The characteristic values derived in the previous section will be used in equation 15 to de-termine the integral permeability. Table 8 summarizes all relevant data. Tab. 8: Summary of the design data of the mean integral permeabiltiy relevant to the calculations

Element Surface area Ai[m²]

Xk as 5% fractile [m²]

Xk as 95% confi-dence interval [m²]

Xd as directly determined design value [m²]

Structure 61.24 3·10-22

5·10-23

3·10-21

Contact zone 0.84 4·10-22

7·10-23

1·10-20

EDZ 0.84 2·10-21

1·10-22

8·10-20

For the three calculation methods used, this leads to an integral permeability Kint calculated as mean over the cross-section: 5% fractile 3.3·10-22 m² 95% confidence interval 5.2·10-23 m² Directly determined design value 4.2·10-21 m² A comparison with the limit criterion selected for the permeability of kreq ≤ 7·10-19 m² shows that – based on the assumption made in this context – the integral permeability to be ex-pected at the location of the seal is sufficiently lower that the targeted limit criterion. This demonstrates that – based on the assumptions made and provided they are implemented correspondingly – a sufficiently low integral permeability can be achieved. However, the integral permeability alone is not sufficient to demonstrate tightness but rather the resistance the sealing element opposes any actions or its delay effect which both result from the integral permeability and other properties of the sealing element. 3.3.2 Flow time

In the previous section it is shows that the sealing element and, thus, the shaft seal as a whole is not completely tight. Complete tightness is practically not feasible. Instead, the aim is to achieve a state where the sealing element and, thus, the shaft seal as a whole can be considered to be technically tight. This means that during the lifetime of the shaft seal, there is no complete flow through the structure. The long-term safe containment of the radioactive waste is to be effected by the rock mass of the salt diapir that surrounds the repository. Based on these requirements, the lifetime or functional life of a shaft seal in a salt formation depends on the compaction properties of the backfill material in the repository. Only after the crushed salt in the drift has compacted in such a way that its permeability is lower than that of the drift seals and approximates that of the surrounding intact rock, the barrier function of the shaft seal is no longer absolutely nec-essary. According to current calculations, this process takes approx. 1,000 years (Müller-Hoeppe et al., 2013b). This is, thus, the minimum period for which the shaft seal has to delay

21 TEC-12-2013-AP

brine intrusion. A premature brine flow into the backfill material would influence the further compaction and thus, the evolving pore pressures and may even stop the latter process. In this case, a formation of migration paths could not be excluded. The second sealing element considered here, is located in the middle of the shaft seal. Brine at the top of the sealing element would mean that there is brine flow through the upstream sealing and buffer elements of the shaft seal or that their retention capacity has been ex-hausted. These brines are assumed to have a density of ρ = 1200 kg/m³. Based on these assumptions, it is further assumed that the load on the salt concrete sealing element is the result of a hydrostatic pressure caused by a brine column that extends to the ground level.

p = ρ·g·h = 1200 kg/m3 · 9.81 m/s2 · 680m = 8.0 MPa (19) The flow time through the sealing element is calculated as follows:

( ( ) )

With porosity n = 10% saturation S = 85% viscosity η = 1.5·10-3 Pa·s permeability k = 2.3·10-19 m² effective sealing length L = 50 m hydrostatic pressure p = 8.0 MPa height of brine column h = 680 m seal cross section ASE= 61.2366 m² According to equation 1-20, the flow time is t = 485 years. When the sealing element is com-pletely saturated, the flow through it is stationary. The resulting volumetric flow V is calculat-ed as follows:

The calculated volumetric flow is thus V = 0.05 m³/a. Beneath the salt concrete sealing ele-ment and the following salt concrete abutment, a further section of the shaft column is back-filled with hart rock gravel. This section is 66 m long and upon instalment has a porosity of 38% and a pore volume of about 1150 m³. It is calculated that the volumetric flow determined above would take approx. 23,000 year to fill this reservoir below the 2nd sealing element. The resistance of the sealing element is sufficient to prevent premature flow of brine to the downstream barriers and repository areas. 3.3.3 Results and Assessment

The calculations above show that the delay effect of the second sealing element of salt con-crete can be considered to be sufficient. The delay of brine intrusion by this component of the shaft seal is sufficiently long. Thus, the sealing element is considered to be technically tight. In addition to hydraulic tightness, it is demonstrated that the functional life is sufficiently long. This simplified safety assessment does not take into account the sealing and buffer effects of the upstream and downstream elements. The combination of subsystems is part of the long-term safety analysis. The lifetime or functional life of the shaft seal as a whole can, thus, be estimated to be significantly longer. In the previous sections, the integral permeability of the sealing element as characteristic value of the resistance was determined as an example in a simplified way. To simplify the

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22 TEC-12-2013-AP

presentation, the various characteristic permeability values were taken from literature. A real safety analysis would require a reliable data base which allows statistically verified state-ments about characteristic values, e.g., of the permeability of the EDZ, and the application of suitable variability factors. As the integral permeability would be part of a subsequent proba-bilistic long-term safety analysis, we refrained from using partial factors. However, when di-rectly determining design values according to the standard “partial factors”, the latter are in-cluded. For the sealing element as well as for the abutment, only individual assessments of the com-plete analysis shown in Figure 1 were carried out. The aim was to illustrate the general methodology using individual assessments as examples. The assessment of the settlement stability of the gravel column was carried out using corresponding partial factors. When as-sessing the tightness, we refrained from doing so. Tightness and functionality were verified by means of calculations. A final probabilistic analysis of the long-term safety of the shaft seal as a whole investigates the system’s behaviour at various limit states and is, thus, con-servative. The application of additional partial factors to determine tightness and functionality is thus not necessary at this point. 3.4 Summary

The methodology of applying partial factors in a safety analysis was illustrated. It can be stated that it is generally possible, to apply the partial factor method in a safety assessment for a geotechnical sealing structure. Due to particularities based in the design, construction, and function of drift and shaft seals, however, it is necessary to make specific adjustments when demonstrating their safety. Shaft seals are engineered structures. Prior to their construction, it has to be demonstrated that they are reliable during their intended functional life and that they meet the required safety functions. In accordance with the international state of the art in science and technolo-gy in the fields of construction engineering and earthwork and foundation engineering, the rules and standards of the EUROCODE are used. At the centre of the standards is the appli-cation of the partial factor method. This is a semi-probabilistic, reliability-oriented safety as-sessment concept. The assessments to demonstrate compliance with the safety functions and reliability of the system as a whole and of the individual components consist of a number of individual safety assessments for various properties or limit states. The corresponding states or existing stresses in the structure are to be determined by means of equilibrium con-siderations. The actual assessment is carried out by a consideration of the limit states of the opposing actions and resistances. The actions on the structure are compared with the re-sistances of the structure using limit state criteria that are allocated to the combinations of actions. The analyses for action combinations to be considered and for their limit states are to be carried out by means of assessment cases. Following the general introduction to the safety assessment concept, the individual assess-ments required for a shaft seal and system-specific particularities were described. Based on a draft shaft sealing concept designed within the scope of the preliminary safety analysis of the Gorleben site, two individual assessments were carried out to illustrate the methodology. This allows an eventual safety assessment within the scope of – as yet unplanned – large-scale experiments that is based on established methods.

23 TEC-12-2013-AP

4 References

(DAfStb 1997) Deutscher Ausschuss für Stahlbeton: Sicherheitskonzept für Bauten des Umweltschutzes, Beuth Verlag, Berlin, 1997.

(DAfStb 2004) Deutscher Ausschuss für Stahlbeton: Betonbau beim Umgang mit wassergefährdenden Stoffen Teil 1: Grundlagen, Bemessung und Konstruktion unbeschichteter Betonbauten, Berlin, 2004.

(DGGT 1997) Deutsche Gesellschaft für Geotechnik e.V. 1997: GDA-Empfehlungen Geotechnik der Deponien und Altlasten, Verlag Ernst und Sohn, 3. Auflage, 1997.

(DIN EN 1990) Eurocode: Grundlagen der Tragwerksplanung, Deutsche Fassung EN 1990:2010, Beuth Verlag, 2010.

(DIN EN 1991-4) Eurocode 1: Einwirkungen auf Tragwerke – Teil 4: Einwirkungen auf Silos und Flüssigkeitsbehälter, Deutsche Fassung EN 1991-4:2006, Beuth Verlag, 2006.

(DIN EN 1997-1) DIN EN 1997-1, Eurocode 7: Entwurf, Berechnung und Bemessung in der Geotechnik –Teil 1: Allgemeine Regeln, Deutsche Fassung 1997-1:2009, Beuth Verlag, 2009

(Hunsche et al., 2003)

Hunsche, U., Schulze, O., Walter, F., Plischke (2003): Projekt Gorle-ben, Thermomechanisches Verhalten von Steinsalz, Abschlussbericht (9G2138110000), BGR Hannover.

(Kreienmeyer et al., 2008)

Kudla et al., 2013

Kreienmeyer, et al: ISIBEL. AP5 Nachweiskonzept zur Integrität der einschlusswirksamen technischen Barrieren, DBE TECHNOLOGY GmbH, Peine , 2008

Kudla, W., Schreiter, F., Gruner, M., Jobmann, M., Bollingerfehr, W., Müller-Hoeppe, N., Herold, P., Freyer, D., Wilsnack, T., Grafe, F. (2013). Schachtverschlüsse für Endlager für hochradioaktive Abfälle – ELSA Teil 1–, TU Bergakademie Freiberg und DBE TECHNOLO-GY, Freiberg, Peine (in German).

(Müller-Hoeppe, 2010)

Müller-Hoeppe, N.: Untersuchung der Kontaktzone am ASSE-Vordamm – Gesamtinterpretation, DBE TECHNOLOGY GmbH, Pei-ne, 2010

(Müller-Hoeppe et al., 2007)

Müller-Hoeppe, N. et al.: The Role of Structural Reliability of Ge-otechnical Barriers of an HLW/SF Repository in Salt Rock within the Safety Case, Peine, 2007

(Müller-Hoeppe et al., 2012b)

Müller-Hoeppe, N. et al.: vorläufige Sicherheitsanalyse Gorleben: AP 9.1, Materialspezifikationen für Dichtelemente für die Planung von Strecken- und Schachtverschlüssen, unveröffentlicht, Peine, 2012

(Müller-Hoeppe et al., 2012c)

Müller-Hoeppe,N. et al.: vorläufige Sicherheitsanalyse Gorleben: AP 9.1, Ermittlung von Einwirkungen aus dem Deckgebirge auf die Schachtverschlüsse Gorleben 1 und Gorleben 2 - Grundlagen zur Zusammensetzung der einwirkenden Deckgebirgswässer, unveröf-fentlicht, Peine, 2012

(Müller-Hoeppe et al., 2013a)

Müller-Hoeppe, N. et al.: vorläufige Sicherheitsanalyse Gorleben Ab-schlussbericht Arbeitspaket 9b Integrität geotechnischer Barrieren -

24 TEC-12-2013-AP

Teil 1: Vorbemessung, GRS-Bericht, Köln, 2013, in Vorbereitung

(Müller-Hoeppe et al., 2013b)

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