Eurocode 7 from soil mechanics to rock mechanics Luís Lamas, LNEC, Lisbon, Portugal Didier Virely, CEREMA, Toulouse, France
Contents 1. The discontinuous nature of rock mass 2. Design methods 3. Calculation models 4. Partial factors and geotechnical engineering 5. Examples 6. Summary and conclusions 2
1. The discontinuous nature of rock mass Radio interview of Leopold Müller and Franz Pacher on the eve of the foundation of the ISRM, in Salzburg, 1962: Reporter: International Society for Rock Mechanics. What is Rock Mechanics? Pacher: The scientific discipline that studies the response of jointed rock when subject to forces. Reporter: Do we know the strength of rock? Müller: For rock specimens, tested in the laboratory, yes. For a rock mass, no. This is what we need to determine. This is why we need an International Society for Rock Mechanics. 3
1. The discontinuous nature of rock mass Continuous versus discontinuous rock mass behaviour Small discontinuity spacing Discontinuous behaviour (AFTES GT30 recommendation, preliminary) Large discontinuity spacing High stress Low stress 4
1. The discontinuous nature of rock mass (Poisel, 2017) Statistical description Probabilistic analysis versus deterministic analysis 5
1. The discontinuous nature of rock mass Powerhouse design 1 Fixed (mean) orientation of 5 discontinuity sets Maximum trace length = 10 m (except set 2 = ) Characteristic (mean) values: k = 34, c k = 138 kpa Design values: tan = 1.25 d = 28 c = 1.60 c d = 90 kpa Support system: rock bolts and reinforced shotcrete Without support system (EDP, 2010) With support system 6
1. The discontinuous nature of rock mass Powerhouse design 2 7 discontinuity sets mean dip direction mean dip, +5, -5 Largest tetrahedral block (no size limitation) Design values d = 25, c d = 10 kpa Support system: rock bolts and reinforced shotcrete (COBA, EDP, 2012) 7
1. The discontinuous nature of rock mass Powerhouse design 3 Fixed orientation (mean) of 4 discontinuity sets 3 zones with decreasing spacing closer to the cavern 3 faults Design values d = 24-30, c d = 80-130 kpa fault: d = 28, c d = 0 kpa (Itasca, Iberdrola, 2016) 8
1. The discontinuous nature of rock mass Powerhouse design 3 Support system: rock bolts and reinforced shotcrete 3DEC global model for bolt design Individual verification of wedges between bolts Without support system Without support system (Itasca, Iberdrola, 2016) 9
1. The discontinuous nature of rock mass Powerhouse design 4 Major discontinuities represented in the global model 3DEC global model Global model used for calculation of the support (Renault, Vinci, 2017) 10
1. The discontinuous nature of rock mass The issue of the discontinuities in the revised EN1990 Definition of geometrical data in EN1990 doesn t include discontinuities in rock masses a d = a nom a (deviation from a nominal value) Note proposed for inclusion in the revised version: For geotechnical design, [ ] geometrical data [ ] such as [ ] the orientation of discontinuities within geotechnical units, should/may be [ ] catered for in a probabilistic way, as specified in EN1997. This opens the possibility for statistical description of discontinuities and for the use of probabilistic methods of analysis. 11
2. Design methods (EC7 4.4) Question: calculation or empiricism in rock mechanics design? Design by geotechnical analyses: Actions Ground properties Geometrical data Calculation models Analytical models Empirical models Numerical models Can charts, such as Grimstad and Barton s (1993), be considered here? 12
2. Design methods (EC7 4.4) Design by prescriptive measures: Nothing is written about this in the current revised version of EC7 Limitations and application given in National Annexes; Recommendations in EC7-part 3. Design assisted by testing: Typically for piles Pull-out tests of rock bolts? Exploratory tunnels? Experimental slope cuts? 13
2. Design methods (EC7 4.4) Design by the observational method: Requires an initial design (using a calculation model) based on the most probable geotechnical behaviour. Foreseeable deviations shall be assessed. Variants of the design shall be established. Monitoring plan: to verify/reject assumptions about geotechnical behaviour made in the initial design. 14
3. Calculation models 7.1.1(2) Calculation models may be used for both semi-probabilistic [using partial factors] or reliability based design. 7.1.2(1) Empirical models may be used for verification of Ultimate Limit States, unless otherwise specified in EC7-part 3. 8.3 Verification of ULS by the partial factor method: E d R d design value of the effect of actions design value of the corresponding resistances E d partial factors are applied to actions and action effects R d partial factors are applied to material properties or to resistance 15
3. Calculation models 8.3 Verification of ULS by the partial factor method: The concept of partial factor is intrinsically linked to that of characteristic value. The partial factor method is merely a simplification of reliability based methods. It can be easily used in practice, in a large number of problems where reliability based methods cannot. P E μ E E E k R, E 16
3. Calculation models 8.3 Verification of ULS by the partial factor method: The concept of partial factor is intrinsically linked to that of characteristic value. The partial factor method is merely a simplification of reliability based methods. It can be easily used in practice, in a large number of problems where reliability based methods cannot. P E μ E E E k R k R μ R R R, E 17
3. Calculation models 8.3 Verification of ULS by the partial factor method: The concept of partial factor is intrinsically linked to that of characteristic value. The partial factor method is merely a simplification of reliability based methods. It can be easily used in practice, in a large number of problems where reliability based methods cannot. P E μ E E P f = P(R<E) E k R k R μ R R R, E 18
3. Calculation models 8.3 Verification of ULS by the partial factor method: The concept of partial factor is intrinsically linked to that of characteristic value. The partial factor method is merely a simplification of reliability based methods. It can be easily used in practice, in a large number of problems where reliability based methods cannot. P E μ E E P f = P(R<E) E k R k R μ R R R, E E d = R d R d = R k / γ R E d = E k γ E 19
4. Partial factors and geotechnical engineering 4.1. Known difficulties of Limit State Design and partial factors in geotechnical engineering (soil and rock masses) E and R are not always independent variables (namely when the structural material and the source of the actions is the ground). Material properties and actions may be difficult to describe by statistical distributions. Tolerable probabilities of failure are difficult to specify. Partial factors are limited to linear failure envelopes (c, tan ), while non-linear failure envelopes are widely used in soil mechanics and rock mechanics problems. But: These issues are known and are of the same nature for soils and for rock masses. They cannot be ignored in the analyses and are addressed in several sections in EC7. 20
4. Partial factors and geotechnical engineering 4.2. Additional issues to consider in rock mechanics Geometrical data of discontinuities. Its uncertainty and variability need to be catered for. Discontinuity location, orientation, frequency, etc., are not included in the field of application of partial factors. This means that the concern of having to apply partial factors to geometrical data of discontinuities does not have a reason to exist. 4.3. EC7 brought structural safety concepts to geotechnical engineering The uniformity of the design philosophy now followed by geotechnical engineers represents a clear progress in situations where interaction of ground and structure exists. Partial factors may be an oversimplification of reality, but they are better than the rule of thumb of a dum engineer 21
5. Example, securing a rock mass with rock bolts Some first assessments (EC7 revision): Geotechnical complexity class (GCC) : GCC2 One of the following applies : variable ground conditions and standard construction technique based on sufficient local experience uniform ground conditions and advanced construction techniques related local experience available Consequences of failure (CC) : CC2 moderate, the tunnel entrance below is protected Tunnel entrance in the French Alpes 22
5. Example GCC2 + CC2 Oneway Level of monitoring (4.1.2.6.2) Robustness (4.1.3) Durability (4.1.4) Everything is a result of the pre-defined GCC and CC 23
5. Examples, rock bolting, collecting data (Ground investigation) French guide for design and execution of rock bolts (2017) Rock structure (or geometry) Rock properties and resistances: unit weight of the rock mass / unit lateral friction for bolts / friction, cohesion and dilatancy on the rock s joints Rock bolt properties: see EN 1992 (concrete structures) or EN 1993 (steel structures) 24
5. Examples Design approach (cases) Design approach 2 : A1 «+» M1 «+» R2 Ponderation on actions and effects of the actions, A 1 No ponderation on rock properties (mostly epistemic uncertainties), M 1 Ponderation on resistances, R 2 Design by geotechnical calculation (analysis) Characteristic value for joint shearing : tan φ dis;k = 1/ξ dis. tan φ mes with ξ dis = 1.0 or as chosen by engineering judgment idem for dilatancy and cohesion Unit shaft friction as defined by EN 1997-1 (7 and 8) with Investigation tests or at least suitability tests. Ponderation as described for pile in tension ξ 1 applied on the mean value and ξ 2 applied on the minimum value during pull-out test Unit shaft resistance as for pile in tension EN 1997-1, table A.7 : γ s;t = 1.15 [R2] Shear resistance of joints: γ R;dis doesn t exist in EN 1997. With some back calculations the French guide on rock bolts design give γ R;dis = 1.15 (R2) or 1.10 (R3 global stability) 25
5. Examples characteristic values Geometry : Volume (V) = 100 m 3 Discontinuity area = 16 m 2 Bolts Diameter (d) = 40 mm Corrosion (Δ d ) = 4 mm Elastic limit (σe) = 500 MPa Borehole diameter (φ) = 110 mm Rock mass Unit weight (γ r ) = 27.5 kn/m 3 Shear strength of rock joints (ISRM recommended method or French standard) : φ mes = 43 / δ mes = 4 / c mes = 0, 012 MPa Pull-out test : Rt = 565 kn / 480.25 kn / 565 kn / 565 kn giving R t;k = 480,3 kn 26
5. Examples characteristic values (2) Tension resistance for a bolt Shear strength on the discontinuity R t;k = min R t;m moyen ξ 1 R t;d = R t;k /γ s;t = 480.3 1.15 ; R t;m min ξ 2 = 417.7 kn = 480.3 kn Traditional factor of safety (no bolts) Static Partial factors tan φ dis;k = 1 ξ φdis tanφ mes = 1 1.0 tan(43 ) Seismic Partial factors γ R;dis = 1.1 Static traditional Seismic traditional F 0.16 0.01 0.16 0.02 Desired value 1.00 1.00 1.50 1.50 Calculated factor of safety F 1.05 1.06 1.62 1.59 Number of bolts 9 12 10 12 27
6. Summary and conclusions In some rock mechanics problems the rock mass exhibits discontinuous behaviour. In other problems the adoption of continuous behaviour is correct. In geotechnical analyses, whenever possible, discontinuity geometrical properties should be catered for in a probabilistic way. However, in many problems, a deterministic analysis is the only possibility and is reasonable. Sensitivity analyses are recommended. Empiricism in rock mechanics is an important aspect in the design. Empirical calculation models are allowed in the revised version of EC7. The observational method is specific of geotechnical engineering. It requires an initial design, with the corresponding geotechnical analysis and calculation model. 28
6. Summary and conclusions The partial factor method is merely a simplification of reliability based methods. It can be easily used in practice, in a large number of problems where reliability based methods are not applicable in practice. Due to the concept behind partial factors, they are not applicable to discontinuity geometrical properties. In view of the difficulties associated to recommend values for partial factors of material properties, it may be beneficial to use the design approaches that factor resistances. Upgraded methodologies for obtaining partial factors values should be encouraged. 29
6. Summary and conclusions The ongoing discussion regarding the applicability of EC7 principles namely of LSD, of probabilities and of partial factors to rock engineering, comes several decades after similar discussions started among soil mechanics engineers, namely among those involved in drafting and applying the EC7. Many arguments are repeated, but some are new, because they have to do with the discontinuous nature of rock masses and the greater empiricism used in rock design. This discussion is stimulating and, once again, questions the very basic principles used in Eurocode 7, in a field of application with increased difficulties. This is healthy, necessary and enriching! 30
6. Summary and conclusions However, time has arrived to be focused and objective. We must find out what effective contributions we can give to the Eurocode 7 (with all its positive and negative aspects) that have the chance to be included in the revised code and that are essential to rock engineering design. 31