Session 4. Risk and Reliability. Design of Retaining Structures. Slopes, Overall Stability and Embankments. (Blarney Castle)

Transcription

1 Session 4 Risk and Reliability Design of Retaining Structures Slopes, Overall Stability and Embankments (Blarney Castle) 1

2 2 Session 4a Risk and reliability

3 Complexity and Geotechnical Risk The complexity of a geotechnical design situation and the geotechnical risks involved are due to the geotechnical hazards and the vulnerability of the structure being designed When assessing the complexity of a design situation, the following factors related to geotechnical hazards should be considered (Clause 2.1(2)): Ground conditions Groundwater situation Regional seismicity Influence of the environment And the following factors relating to the vulnerability of a structure: Nature and size of the structure and its elements Surroundings The concept of three Geotechnical Categories is offered as a method to assess the complexity (Clause 2.1(10)) 3

4 Geotechnical Categories and Risk Factors Risk Factors Geotechnical Categories GC1 GC2 GC3 Geotechnical hazards Low Geotechnical Complexity Moderate High round conditions Known from comparable experience to be straightforward. Not involving soft, loose or compressible soil, loose fill or sloping ground. Ground conditions and properties can be determined from routine investigations and tests. Unusual or exceptionally difficult ground conditions requiring non routine investigations and tests roundwater ituation No excavations below water table, except where experience indicates this will not cause problems No risk of damage without prior warning to structures due to groundwater lowering or drainage. No exceptional water tightness requirements High groundwater pressures and except-ional groundwater conditions, e.g. multi-layered strata with variable permeability egional seismicity Areas with no or very low earthquake hazard Moderate earthquake hazard where seismic design code (EC8) may be used Areas of high earthquake hazard fluence of the nvironment Negligible risk of problems due to surface water, subsidence, hazardous chemicals, etc. Environmental factors covered by routine design methods Complex or difficult environmental factors requiring special design methods Vulnerability Low Moderate High ature and size of e structure and its lements Small and relatively simple structures or construction. Insensitive structures in seismic areas Conventional types of structures with no abnormal risks Very large or unusual structures and structures involving abnormal risks. Very sensitive structures in seismic areas urroundings Negligible risk of damage to or from neighbouring structures or services and negligible risk for life Possible risk of damage to neighbouring structures or services due, for example, to excavations or piling High risk of damage to neighbouring structures or services 4

5 Expertise, Investigations, Design Methods and Structural Types related to Geotechnical Categories xpertise required eotechnical vestigations GC1 Person with appropriate comparable experience Qualitative investigations including trial pits Geotechnical Categories GC2 Experienced qualified person Routine investigations involving borings, field and laboratory tests GC3 Experienced geotechnical specialist Additional more sophisticated investigations and laboratory tests esign rocedures Prescriptive measures and simplified design procedures, e.g. design bearing pressures based on experience or published presumed bearing pressures. Stability or deformation calculations may not be necessary. Routine calculations for stability and deformations based on design procedures in EC7 More sophisticated analyses xamples of ructures Simple 1 and 2 storey structures and agricultural buildings having maximum design column load of 250kN and maximum design wall load of 100kN/m Retaining walls and excavation supports where ground level difference does not exceed 2m Small excavations for drainage and pipes Conventional: Spread and pile foundations Walls and other retaining structures Bridge piers and abutments Embankments and earthworks Ground anchors and other support systems Tunnels in hard, non-fractured rock Very large buildings Large bridges Deep excavations Embankments on soft ground Tunnels in soft or highly permeable ground 5

6 Reliability All Eurocodes based on reliability analyses i.e. aim to achieve structures with a certain target probability of failure: 1x10-6 in 1 year for a ULS 2x10-3 for an SLS β = 3.8 Target reliability achieved through: Use of characteristic loads Selection of characteristic parameter values Choice of appropriate partial factor values Hence appropriate selection of characteristic values is essential to obtain the required reliability for geotechnical designs 6

7 Reliability Analyses The reliability of the ULS design of a spread foundation was investigated for: Different loading conditions Different failure mechanism Different characteristic values 5% fractile or 95% confidence in mean Auto-correlation length δv Correlated and uncorrelated c tanφ values 7

8 8 Example Details Loading conditions Results shown for Load Case 1 FORM analysis and β values

9 9 Failure Mechanism Choice of depth to select soil parameter values

10 Calculated β Values DA1 DA2 DA3 FOS = 2 FOS = DA1 DA2 DA3 FOS = 2 FOS = 3 β β φ' φ' Assumptions: Correlated c - tanφ δv = 2m V (tanφ ) = 15% φ k = 95% of mean Assumptions: Uncorrelated c - tanφ δv = 2m V (tanφ ) = 15% φ k = 5% fractile Result β generally > 3.8 Result β generally <

11 11 Discussion Any questions

12 Session 4b Design of Retaining Structures (Carton House) 12

13 Scope 13 Requirements in Section 9: Retaining Structures of Eurocode 7 apply to structures which retain ground comprising soil, rock or backfill and water at a slope steeper than it would eventually adopt if no structure were present Main types are gravity walls and embedded walls Eurocode 7 also covers composite walls which are defined in Eurocode 7 as walls as composed of elements from the above two types of wall. A large variety of such walls exists and examples include double sheet pile wall cofferdams, earth structures reinforced by tendons, geotextiles or grouting and structures with multiple rows of ground anchorages or soil nails Pressures in silos are not covered by Eurocode 7 but by EN1991-4

14 14 Relevant CEN Standards Eurocode 7 refers to the following CEN standards that are relevant to the design and construction (execution) of retaining walls EN : Part 53-Pt 5 Design of Steel Structures - Piling (EN :1997) Execution standard Execution of special geotechnical work EN Diaphragm Walls EN Sheet pile walls EN Bored Piles

15 Construction Considerations Items to be considered Checked The effects of constructing the wall including: Temporary support to the sides of the excavation Changes in in-situ stresses and resulting ground movements caused by the wall excavation and its construction Disturbance of the ground due to driving and boring operations Provision of access for construction The required degree of water tightness of the finished wall The practicality of constructing the wall to form a water cut-off The practicality of forming ground anchorages in adjacent ground The practicality of excavating beneath any propping of retaining walls The ability to carry vertical load The ductility of structural components Access for maintenance of the wall and any associated drainage measures The appearance and durability of the wall and any anchorages For sheet piling, their drivability without loss of interlock The stability of borings or slurry trench panels while they are open For fill, the nature of the materials available and the means used to compact them adjacent to the wall 15

16 16 Pressures and Forces on Retaining Walls The following five different types of earth pressure are considered in the sub-sections of Clause 9.5: At rest earth pressure (C9.5.2) Limiting values of earth pressure (C9.5.3) Intermediate values of earth pressure (C9.5.4) Earth pressure due to compaction (C9.5.5) Water pressure (C9.5.6) Backfill density estimated from knowledge of available material. GDR shall specify verification checks Use conservative backfill density values to avoid excessive site testing Surcharges consideration should be taken of increased surcharge due to repetition of load Wave and ice forces, seepage forces, collision forces, temperature effects

17 Determination of Earth Pressures At rest earth pressures K 0 values Factors to be considered Stress history May assume at rest conditions if wall movement is < 5 x 10-4 x h for normally consolidated soil (Clause 9.5.2(2)) For overconsolidated soil except for high OCR values (Clause 9.5.2(3)) Horizontal coefficient of earth pressure K 0 = (1-sinφ') OCR For sloping ground (Clause 9.5.2(4)) K 0;β = K 0 (1+sinβ) Limiting Values K a and K p values obtained from charts and equations in Annex C Equations for earth pressure in Annex C are useful for numerical analyses 17

18 18 Water Pressures For silts and clays - The ground water level shall be assumed to be at surface of retained material unless reliable drainage system or infiltration is prevented Effects of water filled tension cracks shall be considered where no special drainage or flow prevention measures are installed (principle)

19 Points to Note 19 Earth pressures include the pressure from soil and weathered rock and water pressures The single source principle applies to DA1 and DA3, although not expressly stated in Eurocode 7 i.e. the same partial action factors are applied to earth pressures on opposite sides of the wall DA3 is as DA1.C2 but with partial factors of 1.35 &1.5 on permanent and variable structural actions The partial factor is applied to the net water force, although this not expressly stated in EC7, this is very important for DA2 and to DA1.C1 in some design situations DA1.C1 may not apply a safety margin against overall stability of an retaining structure in particular design situations Need to demonstrate vertical equilibrium can be achieved

20 20 Wall Friction Mobilised wall friction δ Concrete or steel sheet pile: d d = k φ cv,d k 2/3 for precast concrete or steel sheet piling k =1.0 may be assumed for concrete cast to soil No adhesion or friction resistance for steel sheet pile in clay under undrained conditions immediately after driving.

21 21 Allowance for Unplanned Excavations For embedded cantilever walls, a = 10% of its height and for a supported wall a = 10% of the height beneath the lowest support with a limited to a maximum of 0.5m. Smaller values may be used where the surface level is specified to be controlled [C (3)] or larger values where the surface level is particularly uncertain (Clause (4)) No overdig allowance for SLS check

22 22 Design Methods and Considerations Design methods Calculation Prescriptive measures Experimental models and load tests Observational method Observational method specifically mentioned γ F and γ R are strictly applied to actions (forces) and not to pressures but in practice it is more convenient to apply factors to pressures Design should guard against brittle failure The SLS design values of the earth pressures at not necessarily the limiting values Deflection must not cause damage to adjacent structures (note: SLS not necessary in some circumstances) Drainage systems must have maintenance in place or demonstrated to work effectively without maintenance

23 Limit states to be Considered Limit states to be considered Loss of overall stability Failure of structural element e.g. wall, anchor, strut, connection Combined failure in ground and in structural element Movements of the retaining structure which may cause collapse or affect structure, nearby structures or services Unacceptable leakage through or beneath the wall Unacceptable change to the flow of groundwater Bearing resistance failure of the soil below the base Failure by sliding at the base of the wall Failure by toppling of the wall Failure by rotation or translation of the wall or parts thereof Failure by lack of vertical equilibrium Retaining structure type All types All types All types All types All types All types Gravity and composite Gravity and composite Gravity and composite Embedded Embedded Checked 23

24 24 Actions and Resistances Geotechnical Action Eurocode 7 defines a geotechnical action as an action transmitted to the structure by the ground, fill, standing water or ground-water (Clause ) Passive Earth Pressure The passive earth pressure, P P acting on resistance side of a gravity wall should be considered as an earth resistance (Table A.13) when considering base sliding and as a favourable geotechnical action (Table A3) when considering bearing failure Design water levels/pressures The design value of the water table is generally taken as the worst reasonable scenario. An alternative approach is to consider the variations in the water level as a variable action and the apply appropriate partial factor

25 25 Design Actions DA1.C1 & DA2 In DA1.C1 and DA2, design values of action are obtained by applying γ F to the characteristic values of non geotechnical actions e.g. self weight of the wall F d = γ F F k and to geotechnical actions obtained from the characteristic values of the ground parameters F d = γ F F(X k ) or alternatively to the effect of actions E d = γ E E(F k,x k, a d ) DA1.C2 & DA3 In DA1.C2 and DA3, design values are obtained by applying γ F to the characteristic values of non geotechnical actions F d = γ F F k and the design values of geotechnical actions are obtained by factoring the ground parameters F d = γ F F(X k / γ m ) Effects of actions Where the application of the partial values to geotechnical actions gives unreasonable results, the partial factors for actions can be applied directly to the effect of actions, e.g. BM or SF, calculated using representative values of the actions (Clause (2))

26 Embedded Wall 26 Need to find: The minimum length of wall penetration to prevent rotational failure and vertical equilibrium, and The distribution of effects of the actions (BMs, SF) and the magnitude of the support reactions (anchors, props) Analyse using limit equilibrium method (LEM) assuming free earth support for tied back (single) sheet pile wall O Σabout OBM = 0

27 27 Analysis of Tied-Back Sheet Pile Wall Tie Rod Surcharge = 20kPa 1.5m 1 2 Coarse gravel Tidal lag = 0.6m = 0.5m d 6.0m 4.0m Design level d Silty sand 5 Active Passive 8 a) Problem geometry b) Calculation model

28 arth Pressure Equations DA1.C1, DA1.C2 & DA3 UNIFORM SOIL c k ' φ k ' u a A B u b p a,d '+ u = γ Gunfav [K a,d (σ v u a ) - 2c k ' K a,d, / γ M + u a ] + γ Qunfav K a,d q p p,d '+ u = γ Gunfav [K p,d (σ v u b ) + 2c k ' K p,d / γ m + u b ] / γ R Single source princiiple used for DA1 and DA3 Use of net pressure not necessary when using single source principle as γ R = 1.0 Useful for FE analyses 28

29 Earth Pressure Equations DA2 Uniform Soil. c k ', φ k ' A u a - u b B Single source principle not used Net water pressure force used p ad ' = γ G,unfav [K a,k (σ v u a ) - 2c k ' K a,k /γ M + (u a -u b )] + γ Qunfav q p p,d ' = γ G,fav [K p,k (σ v u b ) +2c k ' K p,k / γ M ] / γ R 29

30 30 Calculation Stages Compute the design earth pressure Determine the sheet pile length by taking moments about the tie rod Determine the design tie rod force by balancing horizontal forces Determine the bending moments using the design earth pressure values.

31 31 Design φ values Granular Backfill φ d ' (γ φ' ) DA1.C1 atan(tan35/1.0) =35 o DA3 M3 γ cu =1.4; γ c' =1.25; γ φ' =1.25 DA1.C2 atan(tan35/1.25) = o Sandy Silt φ d ' (γ φ' ) atan(tan32/1.0) = 32 o atan(tan32/1.25) = o DA2 DA3 atan(tan35/1.0) = 35 o atan(tan35/1.25) = o atan(tan32/1.0) = 32 o atan(tan32/1.25) = o Design earth pressures are obtained using design φ values

32 Informative Annex C K a & K P 32

33 33 Design Parameters Soil Parameter Drained DA1.C1& DA2 DA1.C2 & DA3 Granular backfill (γ k = 22kN/m 3 ) φ d ' ( o ) K a K P - - Silty Sand (γ k = 18kN/m 3 ) φ d ' ( o ) K a K P

34 34 Approximation for Seepage Water Pressures H Gravel Silty sand L d γ w HL/(L+D) γ w d/(l+d)

35 35 Earth Pressure Equations DA1.C1 c k '=0 for both soils u a A u b d B p ad ' + u = 1.35 [K ad (σ v u a ) + u a ] q p Pd ' + u = 1.35 [K Pd (σ v u b ) + u b ]/1.0

36 DA1.C ID DA1:C * 0.25* *0.25* 22* * 0.25* *0.25* 22* * 0.25* *[0.25* (22*10-4.6*10)+4.6*10]+ 1.5* 0.25* *[0.28* (22*10-4.6*10)+4.6*10]+ 1.5* 0.28* *{0.28*[22*10+18*(d+0.5)-((d )*10-0.6*(d+0.5)*10/(2d+0.5))]+((d )*10-0.6*(d+0.5)*10/(2d+0.5))}+ 1.5* 0.28* (d=4.32m) *[10*4.5] *{6.1*[4.5*10+18*d-((d )*10-0.6*(d+0.5)*10/(2d+0.5))]+((d )*10-0.6*(d+0.5)*10/(2d+0.5))} (d=4.32m) 36

37 37 Vertical and Horizontal Equilibrium Vertical equilibrium Vertical downward force due to active pressure Σ{1.35 x K ad x (σ v '-q) + 1.5K ad q} x L x tanδ = kn/m Vertical upward force due to passive pressure Σ{1.35 x K Pd x (σ v ')} x L x tanδ = 243 kn/m If there were a significant difference, change δ, on generally the active side as sheet piles tends to move down [Frank et al., 2004] Horizontal equilibrium Design anchor force T d = P a;d -P P;d = kn/m

38 SHEAR FORCE kn/m TIED SHEET PILE RETAINING WALL Shear Force and BM DA1.C1 T d = kn/m DEPTH (m) BENDING MOMENT DIAGRAM BENDING MOMENT (knm/m) DEPTH (m) 38

39 DA1.C ID DA1:C * 0.31* *0.31* 22* * 0.31* *0.31 * 22* * 0.31* *[0.31* (22*10-4.6*10)+4.6*10]+ 1.3* 0.31* *[0.35* (22*10-4.6*10)+4.6*10]+ 1.3* 0.35* *{0.35*[22*10+18*(d+0.5)-((d )*10-0.6*(d+0.5)*10/(2d+0.5))]+((d )*10-0.6*(d+0.5)*10/(2d+0.5))}+ 1.3* 0.35* (d=6.56m) *10* *{4.2*[4.5*10+18*d-((d )*10-0.6*(d+0.5)*10/(2d+0.5))]+((d )*10-0.6*(d+0.5)*10/(2d+0.5))} (d=6.56m) 39

40 40 SHEAR FORCE kn TIED SHEET PILE RETAINING WALL DEPTH (m) Shear Force and BM DA1.C2 T d = kn/m BENDING MOMENT DIAGRAM BENDING MOMENT (knm DEPTH (m)

41 Summary DA1 DA1.C1 DA1.C2 DA1 Length (m) T d kn/m M d knm/m 1045* S d kn/m * If M d from DA1.C1 were > that from DA1.C2 could reduce it by carrying out a FE or other soil/structure analysis for longer length. 41

42 42 Earth Pressure Equations DA2 c k = 0 for both soils Net water pressure u a A u b B d p ad + u = 1.35[K ad (σ v u a )+(u a -u b ]+1.5q p Pd + u = 1.0[K Pd (σ v u b )]/1.4

43 Earth and Water Pressures DA Y X Net water pressure kpa Depth (m) 20

44 DA Y X ID DA * 0.25* *0.25* 22* * 0.25* *0.25* 22* * 0.25* X 1.35*(0.25*(22*6-0.6*10)+0.6*10)+1.5*0.25* *[0.25* (22*10-4.6*10)+ 0.6*10]+1.5* 0.25* *[0.28* (22*10-4.6*10)+ 0.6*10]+1.5* 0.28* Y 1.35*[0.28*{22*10+18*(0.5)-(( )*10-0.6*(0.5)*10/(2*d+0.5))}+(0.6*10-0.6*(0.5)*10/(2*d+0.5))]+1.5* 0.28* *[0.28*{22*10+18*(d+0.5)-((d )*10-0.6*(d+0.5)*10/(2*d+0.5))}]+1.5* 0.28* (d=6.74m) *[6.1*{4.5*10+18*d-((d )*10-0.6*(d+0.5)*10/(2*d+0.5))}]/ (d=6.74m) 44

45 45 SHEAR FORCE kn TIED SHEET PILE RETAINING WALL DEPTH (m) Shear Force and BM DA2 T d = 347 kn/m BENDING MOMENT DIAGRAM BENDING MOMENT (knm DEPTH (m)

46 DA ID DA * 0.31* *0.31* 22* * 0.31* *0.31 * 22* * 0.31* *[0.31* (22*10-4.6*10)+4.6*10]+ 1.3* 0.31* *[0.35* (22*10-4.6*10)+4.6*10]+ 1.3* 0.35* *{0.35*[22*10+18*(d+0.5)-((d )*10-0.6*(d+0.5)*10/(2d+0.5))]+((d )*10-0.6*(d+0.5)*10/(2d+0.5))}+ 1.3* 0.35* (d=6.56m) *10* *{4.2*[4.5*10+18*d-((d )*10-0.6*(d+0.5)*10/(2d+0.5))]+((d )*10-0.6*(d+0.5)*10/(2d+0.5))} (d=6.56m) 46

47 47 SHEAR FORCE kn TIED SHEET PILE RETAINING WALL DEPTH (m) Shear Force and BM DA3 T d = kn/m BENDING MOMENT DIAGRAM BENDING MOMENT (knm DEPTH (m)

48 48 Summary of Results DA1 DA2 DA3 Length (m) T d kn/m M d knm/m S d kn/m

49 49 Reinforced Cantilever Gravity Retaining Wall Surcharge = 20kPa A A 1 5.0m 1.6m 0.4m Coarse grained backfill 0.3m Design level 2.0m 1.0m 5.2m Water level Glacial till B 0.5m B Uplift a) Problem geometry b) Calculation model Design against bearing and sliding failure as for a spread foundation

50 50 Discussion Any Questions

51 51 Session 4c Slopes, Overall Stability and Embankments

52 Slopes and Overall Stability Eurocode 7 has no separate section on the design of slopes Instead there is a separate Section 11 on Overall Stability - Overall stability situations are where there is loss of overall stability of the ground and associated structures or where excessive movements in the ground cause damage or loss of serviceability in neighbouring structures, roads or services - Typical structures for which an analysis of overall stability should be performed (and mentioned in relevant sections of Eurocode 7): - Retaining structures - Excavations, slopes and embankments - Foundations on sloping ground. natural slopes or embankments - Foundations near an excavation, cut or buried structure, or shore It is stated that a slope analysis should verify the overall moment and vertical stability of the sliding mass. If horizontal equilibrium is not checked, interslice forces should be assumed to be horizontal This means that Bishop s method is acceptable, but not Fellenius method 52

53 Overall Stability Failure Modes 53 - Examples of overall failure modes involving ground failure around retaining structures presented in Section 11

54 Comments on Overall Stability Centre of rotation Favourable weight Surcharge Slip surface W f W u Unfavourable weight Typical slope stability design situation No specific inequality to be satisfied is given in Eurocode 7 It could analysed be in terms of forces or moments or both No calculation model is given Finite elements can be used but no guidance given DA2 is generally not used for slopes 54

55 Design of Slopes Using DA1 55 Both DA1.C1 and DA1.C2 should be considered, but DA1.C2 normally controls if no structural element or soil reinforcement is involved For undrained conditions: DA1.C1 γ G = 1.35, γ Q = 1.5, γ cu = 1.0 DA1.C2 γ G = 1.0, γ Q = 1.3, γ cu = 1.4 Drained conditions In DA1.C1 an increase in the vertical load generally increases the resistance, leaving the margin of safety relatively unchanged. Thus DA1.C2, where γ G = 1.0, γ Q = 1.3, γ c, γ φ, = 1.25, governs Single source principle is applied i.e. both unfavourable and favourable components of the same load, e.g. soil weight, are treated as if they act as a single load

56 DA1 Design Example 56 W = 150kN β = 20 ο L = 1.75m Interface properties c u,k = 40 kpa c k = 5 kpa φ k = 35 o Sliding stability of a block on a slope Design sliding resistance, R d Undrained: ( c u,k /γ M ) x L Drained: (c k /γ M ) x L + N tan φ k /γ M ) Undrained Conditions DA1.C1 F d = 1.35x150xsin20 = 69.3 kn/m; R d = (40/1.0)x1.75 = 70 kn/m F d < R d OK DA1.C2 F d = 1.0x150xsin20 = 51.3 kn/m; R d = (40/1.4)x1.75 = 50 kn/m F d > R d Fail Drained Conditions DA1.C1 F d = 1.35x150xsin20 = 69.3 kn/m R d = (5/1.0)x x150xcos20x(tan35/1.0) = = 142kN/m OK DA1.C2 F d = 1.0x150xsin20 = 51.3kN/m R d = (5/1.25)x x150xcos20x(tan35/1.25) = =105.7kN/m OK

57 57 Sliding Stability of an Infinite Slope Design situation: - Hard stratum resting on a weak layer 30 0 Ground surface Hard s tratum S d 1.8m Equilibrium requirement: Weak clay layer c = 25kPa uk R d Slip plane - Design sliding force, S d Design resisting force, R d

58 58 Infinite Slope with Seepage b h z Slip plane β bcosβ For water table at the surface: Traditional design F = γ ' γ sat tanφ ' tan β If F = 1.25 γ sat tan β γ (tanφ / 1.25) i.e Eurocode 7 condition

59 Slope Stability Analysis Using Method of Slices y Axis Centre of rotation Radius, r x Axis Eurocode 7 requirements when using the method of slices: - Both vertical and moment equilibrium should be checked, and - If horizontal equilibrium is not checked, then the interslice forces shall be assumed to be horizontal - This means some simpler methods not acceptable 59

60 60 Details of different methods of slices from SLOPE/W ote: Not acceptable methods Acceptable methods

61 Bishop s Simplified Method of Slices c Tanφ ' ' ' ' τ mob = + N = + F F γm;mob c N' Tanφ γ ' k m;mob γ = Design Procedure: ' ' 1 [ c + kb ( γ GW γ Gub) Tanϕk ] Secα γ Tan Tan GWSinα α φ k 1+ γ m; mob ' m; mob DA1.C1 DA1.C2 Apply γ G = 1.35 to permanent actions, incl. soil weight force via the soil weigh density and γ Q = 1.5 to variable actions and check that γ m;mob = F 1.0 Apply γ G = 1.0 to permanent actions, incl. soil weight force via the soil weight density and γ Q =1.3 to variable actions and check that γ m;mob = F

62 62 Slope Stability Analysis Example Using Method of Slices y Axis Radius, r Centre of slip circle at: X=28 Y= x Axis 6 slices

63 63 Stability Analyses Using DA1.C1 F= Slice h b W r u α γ G Wsinα c'b A B A/B Sum F= F = γ M, mob 1.0 so OK according to DA1.C1 A = [c'b + W (1 - r u )tanφ') ] secα B = 1 + tanφ tanα /F

64 64 Stability Analyses Using DA1.C2 F= Slice h b W r u α Wsinα c'b A B A/B Sum F= A = [c'b + W (1 - r u )tanφ') ] secα B = 1 + tanφ tanα /F F = γ M, mob 1.25 so OK according to DA1.C2

65 Stability of an Anchored Excavation 65 In this situation the anchor imposes a stabilizing action on the excavation Hence DA1.C1 should be checked It may control the design

66 Slope Design Using DA3 66 Slope design using DA3 is the same as DA1.C2 since actions on the soil (e.g. structural actions G k, Q k, traffic loads, etc.) are treated as geotechnical actions, like the soil weight W k, and the A1 partial action factors γ G =1.0; γ Q =1.3 are applied. However, in a bearing analysis of the foundations the structural loads are treated as structural actions and the A2, i.e. DA1.C1 partial action factors γ G =1.35; γ Q =1.5, are used G k, Q k Is this slope stability or bearing resistance? W k

67 67 Design of Embankments Section 12: Embankments of EN 1997 provides the principles and requirements for the design of embankments for small dams and for infrastructure projects, such as road embankments No definition is given for the word small but Frank et al. state that it may be appropriate to assume small dams include dams (and embankments for infrastructure) up to a height of approximately 10m A long list of possible limit states, both GEO and HYD types, that should be checked is provided including: Loss of overall stability Failure in the embankment slope or crest Failure by internal erosion Failure by surface erosion or scour Excessive deformation Deformations caused by hydraulic actions Limit states involving adjacent structures, roads and services are included in the list

68 68 Particular Aspects Regarding Embankment Design Since embankments are constructed by placing fill and sometimes involve ground improvement, the provisions in Section 5 should be applied For embankments on ground with low strength and high compressibility, EN states that the construction process shall be specified, i.e. in Geotechnical Design Report, to ensure that the bearing resistance is not exceeded or excessive movements do not occur during construction Since the behaviour of embankments on soft ground during construction is usually monitored to ensure failure does not occur, it is often appropriate to use the Observational Method for design The importance of both supervision and monitoring in the case of embankments is demonstrated by the fact that there is a separate sub-section on the supervision of the construction of embankments and the monitoring of embankments during and after construction in Section 12 The only other section of Eurocode 7 that has provisions for both supervision and monitoring is the section on ground anchorages

69 69 Conclusions Sections 11 and 12 set out the provisions for designing against overall stability and for the design of embankments The focus is on the relevant limit states to be checked No calculation models are provided When using method of slices for slope stability, some simplified methods not acceptable The relevance and importance of other sections of EN is demonstrated, for example: The section on Fill and Ground Improvement The sub-section on the Observational Method The sub-section on the Geotechnical Design Report The section on Supervision and Monitoring

70 70 Discussion Any questions

71 71 Tomorrow - Special Features of Soi - Geotechnical Design Triangle - Associated CEN Standards - Implementation and Future Development - Tutorial Examples