COMPARISON OF EC7 DESIGN APPROACHES FOR NUMERICAL ANALYSIS OF DEEP EXCAVATIONS

Transcription

1 S C I E N C E P A S S I O N T E C H N O L O G Y COMPARISON OF EC7 DESIGN APPROACHES FOR NUMERICAL ANALYSIS OF DEEP EXCAVATIONS Helmut F. Schweiger Computational Geotechnics Group Institute for Soil Mechanics and Foundation Engineering Graz University of Technology

2 2 Introduction Eurocode 7 Design Approaches Benchmark Example Excavation in sand Excavation in soft clay - Comparison of constitutive model and design approaches Issues from simplified case histories Deep excavation in soft clay Deep excavation in stiff clay Wall with prestressed anchors NATM tunnel - Comparison of design approaches Summary and discussion

3 3 Application of numerical methods for ultimate limit state design in general and in accordance with Eurocode7 is a much discussed issue and work in progress what design approach is best suitable for numerical methods? at what stage should "partial factors" be introduced (if at all)? should we use the same design approach for numerical and conventional analysis (for a given type of problem)? should we use finite element analysis for ULS-design? see also (with emphasis mainly on deep excavations), e.g.: Schweiger (2009, 2010), Simpson (2007), Schweiger (2005), Lo (2003), Bauduin, De Vos & Frank (2003), Simpson (2000), Bauduin, De Vos & Simpson (2000) With respect to numerical modelling there is a significant difference between calculating a factor of safety performing a calculation with factored material parameters according to EC7

4 4 Goal of this presentation Demonstrate applicability of numerical methods for design in accordance with EC7 design approaches Address some important issues which have to be considered when using numerical methods for different design approaches Provoke some dicussion NOT Goal of this presentation Advocate the use of a particular design approach

5 5 PARTIAL FACTORS EC7 Design approach Actions F Permanent unfavourable 1) Variable 2) G Q DA1/ DA1/ DA DA3 Geot. 3) : 1.00 Struct. 4) : Partial factors for actions according to EC7 (can be changed in National Annex) for deep excavation and tunnelling problems this means that earth pressure has to be factored in numerical analysis not feasible alternatively effects of actions can be factored (e.g. bending moments, strut forces) > commonly referred to as DA2*

6 6 PARTIAL FACTORS EC7 Design approach Soil properties M Resistances tan c c u Unit weight Passive Anchor c cu F R;e a DA1/ DA1/ DA DA Partial factors for soil properties and resistances according to EC7 DA1/1 and DA1/2: two analysis required

7 7 EC7 design approaches in combination with numerical methods: DA2: Analysis is performed in terms of characteristic material parameters Partial factors applied to loads (feasible only for e.g. foundation problems) DA2*: Analysis is performed in terms of characteristic material parameters Partial factors applied to effects of actions (e.g. bending moments) DA3: Option 1: > This is straightforward for numerical analysis Analysis is performed in terms of design material parameters > perform all excavation steps with factored values for soil strength Option 2: Analysis is performed in terms of characteristic material parameters but for all construction steps a check with reduced strength parameters is made

8 8 Option 1 for DA3: perform all excavation steps with factored values for soil strength i.e. tan fact = tan unfact / excavation level 1 excavation level 2 final excavation level > if failure does not occur in one of the excavation steps > design criteria fulfilled N.B. No information on serviceability limit state

9 9 Option 2 for DA3: perform excavation step 1 with unfactored values for soil strength > reduce tan to tan unfact / > check for failure excavation level 1 excavation level 2 final excavation level

10 10 Option 2 for DA3: perform excavation step 1 with unfactored values for soil strength > reduce tan to tan unfact / > check for failure perform excavation step 2 with unfactored values for soil strength (start from results for excavation step 1 with unfactored properties) > reduce tan to tan unfact / > check for failure excavation level 1 excavation level 2 final excavation level

11 11 Option 2 for DA3: perform excavation step 1 with unfactored values for soil strength > reduce tan to tan unfact / > check for failure perform excavation step 2 with unfactored values for soil strength (start from results for excavation step 1 with unfactored properties) > reduce tan to tan unfact / > check for failure perform excavation step 3 with unfactored values for soil strength (start from results for excavation step 2 with unfactored properties) > reduce tan to tan unfact / > check for failure excavation level 1 excavation level 2 final excavation level N.B. Serviceability limit state obtained as well

12 12 EXCAVATION IN SAND Phases: 1: Initial stresses (K 0 = 1 - sin ') 2: Sheet pile wall (wished-in-place) > displacements set to 0 3: Excavation 1 to m 4: Activation of strut at m 5: GW-lowering to -6.0 m 6: Excavation 2 to m 7: Excavation 3 to m 8: Surcharge 15 kpa (variable load)

13 13 EXCAVATION IN SAND Constitutive models compared: Hardening Soil (small) model* Mohr-Coulomb model * MC failure criterion Secant modulus G [ kn/m²] HS-Small Hardin & Drnevich 1E Shear strain [-]

14 14 EXCAVATION IN SAND Parameters for HSS-model Parameter Meaning Value [kn/m³] Unit weight (unsaturated) 18 r [kn/m³] Unit weight (saturated) 20 [ ] Friction angle 41 c [kpa] Cohesion 0 [ ] Angle of dilatancy 15 ur [-] Poisson s ratio unloading-reloading 0.20 ref E 50 [kpa] Secant modulus for primary triaxial loading E oed ref E ur ref [kpa] Tangent modulus for oedometric loading [kpa] Secant modulus for un- and reloading m [-] Exponent of the Ohde/Janbu law 0.55 p ref [kpa] Reference stress for the stiffness parameters 100 [-] Coefficient of earth pressure at rest (NC) 1-sin( ) R f [-] Failure ratio 0.90 Tension [kpa] Tensile strength 0 G 0 [kpa] Small-strain shear modulus ,7 [-] Reference shear strain where G sec =0.7G K 0 nc

15 15 EXCAVATION IN SAND horizontal wall displacement [mm] bending moments [knm/m] HS HSS MC 1 HS HSS MC depth below surface [m] depth below surface [m]

16 16 EC7 PARTIAL FACTORS DA2*: Permanent loads: G = 1.35 Variable loads: Q = 1.50 All soil factors = 1.0 surcharge permanent = 10 kpa surcharge variable = 15 kpa Note: if an advanced model is used, where strength depends on e.g. density then this approach cannot be used. It becomes more complex but can still be done, see: Potts and Zdravkovic Accounting for partial material factors in numerical analysis, Geotechnique 2012 DA3: Permanent loads: G = 1.00 Variable loads: Q = 1.30 Strength: c = = 1.25 > ' = ( = 12 ) surcharge permanent = 10 kpa > surcharge variable = 15 kpa > 19.5 kpa Initial stresses (DA3): K 0c = 1 sin(41) = (based on characteristic ')

17 17 COMPARISON OF RESULTS bending moments [knm/m] M design, DA2* = M 1 x (M 2 M 1 ) x 1.5 M 1 bending moment excluding variable load M 2 bending moment including variable load Difference in maximum design bending moment between DA2 and DA3 smaller for HSS model than for MC model (in this particular example) HSS-DA3 MC-DA3 HSS-DA2 MC-DA depth below surface [m] 8 9

18 18 COMPARISON OF RESULTS design strut force [kn/m] MC HSS DA2 DA3 design approach DA2 Strut force after Strut force Design strut excavation due to load force MC HSS DA3 Strut force after Strut force Design strut excavation due to load force MC HSS

19 19 EXCAVATION IN CLAY Phases: 1: Initial stresses (K 0 = 1 - sin ') 2: Sheet pile wall (wished-in-place) > displacements set to 0 3: Excavation 1 to m 4: Activation of strut at m 5: Excavation 2 to m 6: Excavation 3 to m 7: Surcharge 15 kpa (variable load)

20 20 EXCAVATION IN CLAY Parameters for HSS-model Parameter Meaning Value [kn/m³] Unit weight (unsaturated) 15 sat [kn/m³] Unit weight (saturated) 16 ' [ ] Friction angle (Mohr-Coulomb) 27 c [kpa] Cohesion (Mohr-Coulomb) 15 [ ] Angle of dilatancy 0 ur [-] Poisson s ratio unloading-reloading 0.20 ref E 50 [kpa] Secant modulus for primary triaxial loading E oed ref E ur ref [kpa] Tangent modulus for oedometric loading [kpa] Secant modulus for un- and reloading m [-] Exponent of the Ohde/Janbu law 0.90 p ref [kpa] Reference stress for the stiffness parameters 100 [-] Coefficient of earth pressure at rest (NC) 1-sin( ) R f [-] Failure ratio 0.90 t [kpa] Tensile strength 0 G 0 [kpa] Small-strain shear modulus [-] Reference shear strain where G sec =0.7G K 0 nc Undrained analysis with "Method B" (undrained strength parameters): c u = 23.9 kpa at -2.0m c u = 2.1 kpa/m "Method A": undrained analysis with effective strength parameters

21 21 EXCAVATION IN CLAY horizontal wall displacement [mm] Comparison of constitutive models HS HSS MC SS 1 2 surface displacement [mm] distance from wall [m] HS HSS MC SS depth below surface [m]

22 22 EC7 PARTIAL FACTORS DA2*: Permanent loads: G = 1.35 Variable loads: Q = 1.50 All soil factors = 1.0 surcharge permanent = 10 kpa surcharge variable = 15 kpa DA3: Permanent loads: G = 1.00 Variable loads: Q = 1.30 Strength: c = = 1.25 > ' = 22.2 > c' = 12 kpa > surcharge variable = 15 kpa > 19.5 kpa Undrained strength: cu = 1.40 c u = 17.1 kpa at -2.0m, c u = 1.5 kpa/m Initial stresses (DA3): K 0c = 1 sin(27) = (based on characteristic ')

23 23 COMPARISON OF RESULTS design bending moments [knm/m] Difference resulting from choice of constitutive model much larger than difference between DA2 and DA3 Note: undrained strength for "Method B" is chosen such that c u is the same for Methods A and B for MC-model and this value is also used for the HSS analysis using Method B HSS_DA2-A MC_DA2-A HSS_DA2-B MC_DA2-B HSS_DA3-A MC_DA3-A HSS_DA3-B MC_DA3-B depth below surface [m]

24 24 Comparison of EC7 design approaches for numerical analysis of deep excavations EXAMPLE AK KLEI DA2 - DA3 / Method A - B COMPARISON OF RESULTS 250 design strut force [kn/m] DA2 DA3 design approach HSS-A MC-A HSS-B MC-B DA2 strut force after strut force design excavation due to load strut force MC HSS MC_B HSS_B DA3 strut force after strut force design excavation due to load strut force MC HSS MC_B HSS_B

25 25 CASE HISTORY - STIFF CLAY m m P m GWT m m P m P m P m P 5 Diaphragm Wall t = 46.7 m m m P 6 P 7 London Clay stiff clay d = 66.7 m m m 17.5 m 1.2 m Prop Level Excavation Level m Chalk

26 26 Comparison of EC7 design approaches for numerical analysis of deep excavations EXAMPLE STIFF CLAY - STAGE 3 DA2 / DA3 - HSS-Model CASE HISTORY - STIFF CLAY bending moments [knm/m] DA2 DA2 DA3 DA3 DA2*1.35 DA2* Partial factor on strength parameters does not influence bending moments significantly > higher design values for DA2* depth below surface [m]

27 27 DIAPHRAGM WALL WITH PRESTRESSED GROUND ANCHORS Prestressed ground anchors

28 28 DIAPHRAGM WALL WITH PRESTRESSED GROUND ANCHORS max. bending moment knm/m anchor force layer 1 (kn/m) anchor force layer 2 (kn/m) anchor force layer 3 (kn/m) factor of safety characteristic x 1.35 (DA2*) DA Only sligthly increased as compared to prestress forces Increase in anchor force due to factored soil strength < 10% Consequence: anchor forces DA2* >> DA3 bending moments are not so much different N.B. effect of water is fully factored in DA2* but not in DA3

29 29 CASE HISTORY - SOFT CLAY 10.0 m Strut levels (Prestress forces) -1.0 m (200) -4.0 m (550) Excavation steps -2.0 m -5.0 m surface 0.0 m GW-Table -4.0 m FILL K 0 = m (650) -8.5 m m (600) m (700) m (700) m (800) m (850) m m m m m MARINE CLAY K 0 = m (800) m m (700) m Final excavation m -36 m JGP 1: 2 m JGP 2: 3 m -40 m m 0.8 m OLD ALLUVIUM SW2 K 0 = m OLD ALLUVIUM CZ K 0 = 0.46

30 30 Comparison of EC7 design approaches for numerical analysis of deep excavations EXAMPLE MARINE CLAY EXAMPLE MARINE CLAY DA2 / DA3 DA2 / DA3 CASE HISTORY - SOFT CLAY wall deflection [mm] MC_DA2_A MC_DA2_B MC_DA3_A MC_DA3_B MC_DA3_A bending moments [knm/m] depth below surface [m] MC_DA2c MC_DA2c MC_DA2d MC_DA2d MC_DA3_A MC_DA3_A MC_DA3_B MC_DA3_B MC_DA3_A2 MC_DA3_A depth below surface [m] Note: Analysis A2 > partial factor on stiffness of soil layers 35 40

31 31 NATM TUNNEL Phases: Step 0: Initial stresses (K 0 = 1.25) Step 1: Pre-relaxation top heading (55%) Step 2: Full excavation top heading with lining in place (shotcrete "young") Step 3: Pre-relaxation bench (35%, shotcrete top heading > "old")) Step 4: Full excavation bench with lining in place (shotcrete bench "young") Step 5: Pre-relaxation invert (20%, shotcrete bench > "old")) Step 6: Full excavation invert with lining in place (shotcrete invert "young")

32 32 NATM TUNNEL Normal force in lining smaller for DA3? design normal force [kn/m] 1400 HSS MC HS 1200 SS DA2 DA3 maximum design bending moment [knm/m] HSS MC HS SS DA2 DA3 design approach design approach

33 33 NATM TUNNEL DA3 DA2 Vertical displacements DA3: possibly pre-relaxation factors have to be modified too

34 34 EC7 - ULS-design approaches using FEM: Different design approaches (DA2 / DA3) will lead to different design (true also for conventional analysis) Choice of constitutive model may have larger influence than choice of design approach It seems that difference between DA2 and DA3 is less pronounced for advanced constitutive models Application of numerical methods complying with EC7 requirements is in general possible, but results of numerical analysis depend on constitutive model and other modelling assumptions not all failure modes required to be checked by EC7 are easily covered, but is this really required? Structural elements have to be considered in a consistent manner

35 35 Arguments for DA2 (DA2*), against DA3 "Real" soil is considered "Limit state" of working load conditions are obtained, only one analysis required (not exactly true if variable loads are present) Unrealistic system behaviour (e.g. struts in tension) is avoided Arguments against DA2 (DA2*), for DA3 Partial factor should be placed where one of the uncertainty is > soil parameters Soil is load and resistance > not always clear cut, automatically taken into account in DA3/DA1 Some critical mechanisms may be missed in DA2*