Circular and Toppling failure 1.pdf
- 2. La Conchita, California-a small seaside community along Highway 101 north of Santa Barbara. This landslide and debris flow occurred in the spring of 1995. Many people were evacuated because of the slide and the houses nearest the slide were completely destroyed. Fortunately, no one was killed or injured. Photograph by R.L. Schuster, U.S. Geological Survey.
- 3. Victoria, Australia: An aerial view of a coal mine that collapsed, washing away a road and railway lines http://images.google.com.my/imgres?imgurl=http://stormwater.files.wordpress.com/2007/
- 5. COMMON FEATURES OF SLOPE STABILITY ANALYSIS METHODS Safety Factor: F = S/Sm where S = shear strength and Sm = mobilized shear resistance. F = 1: failure, F > 1: safety Shape and location of failure is not known, a priori** but assumed (trial and error to find minimum F) Static equilibrium (equilibrium of forces and moments on a sliding mass) Two-dimensional analysis **relating to what can be known through an understanding of how certain things work rather than by observation; relating to or derived by reasoning from self-evident propositions ; presupposed by experience ; being without examination or analysis
- 6. Granular materials Sand and gravel exhibit friction component of strength Most soil exhibit cohesive and frictional strength. N W T Force parallel to slope = W sin Force perpendicular to slope = W cos For stability or safetyfact gforce restrainin ce slidingfor = F W W tan cos sin = tan tan = F • Weight of material does not affect the stability of slope • Safe angle for slope is same whether the soil is submerge or dry. • Embankment can be at any height = angle of shearing resistance
- 7. Seepage forces in a granular slope subjected to rapid drawdown W.L. G. W.L. b l z The river level dropped suddenly due to tidal effect. In soil, permeability effect → water cannot flow fast→ seepage occurs Water flow from high level to low level of slope Flow net can be drawn
- 8. Seepage forces in a granular slope subjected to rapid drawdown b l z Assume potential failure plane parallel to slope occurs at a depth of z and weight is W Excess pore water pressure induced by seepage, u at the mid point of the base of the element. Normal reaction N = W cos Normal stress = = = cosβ b 1 b β Wcos l Wcosβ 2 where Normal effective stress ’= u β γzcos u b β Wcos 2 2 − = − Tangential shear stress, = γzsinβcosβ = β W sin l
- 9. Ultimate shear strength of soil = ’ tan = F tan tan ) cos 1 ( 2 u r F − = Where z u ru = Pore pressure ratio = the pore water pressure to the weight of material acting on unit area above it.
- 10. Flow parallel to the surface and at the surface b l z Equipotential line A B hz Excess water head = Hw AB = z cos Hw=z cos2 Excess pore water pressure = wzcos2 tan tan tan tan ) ( tan tan ) 1 ( ' sat w w F = − = − =
- 11. A granular soil has a saturated unit weight of 18.0kN/m3 and angle of shearing resistance of 300. A slope is to be made of this material. If the factor of safety is to be 1.25, determine the safe angle of the slope 1. When the slope is dry or submerge 2. If seepage occurs at and parallel to the surface of slope. 1. When dry or submerge tan tan = F 0 25 462 . 0 25 . 1 30 tan tan = = = Example
- 12. 2. seepage occurs at and parallel to the surface of slope tan tan ' sat F = 0 5 . 11 205 . 0 18 25 . 1 30 tan 8 tan = = = x x 18 x 25 . 1 30 tan ) 0 . 10 0 . 18 ( tan − =
- 13. Soils with two strength components Tends to be rotational, the actual slip surface approximating to be arc of a circle crack Slip surface Heave of material at toe Method of investigating slope stability •Assuming a slip surface and a center about which it rotates •Study the equilibrium of the forces acting on this surface •Repeat the process until the worst slip surface is found
- 14. Total stress analysis Often called the = 0 analysis Intended to give the stability of embankment immediately after its construction. Assumed that the soil in embankment has no time to drain. Strength parameter used – undrain strength of soil - unconfined compression test - undrain triaxial test. r A B W We r c moment disturbing gmoment restrainin F 2 = = G e O 2 . . . . . . . cr r r c r l c e W = = = At equilibirium, As ϕ=0°, Ƭmax=σ tan ϕ+C = 0, e=eccentricity
- 15. Effect of tension crack r ’ A B hc c hc 2 = In pure cohesive soil, depth of crack Tension crack depth Fig: Tension crack in a cohesive soil O B’
- 16. Example Figure below gives details of an embankment of made cohesive soil with = 0 and C = 20 kN/m3. The unit weight of the soil is 19 kN/m3. For the trial circle shown, determine the factor of safety against sliding. The weight of sliding sector is 346 kN acting at the eccentricity of 5m from the center of rotation. What would be if the shaded portion of the embankment were removed? In both cases assume that no tension crack develops. 700 R=9m W 1.5m 3m 3m 1.1 1 e=5m
- 17. Solution Disturbing moment = 346 x 5 = 1730 kNm Restraining moment = 14 . 1 1730 1980 1980 7 22 180 70 9 20 2 2 = = = = F kNm x x x cr Area of portion removed = 1.5 x 3 =4.5m2 Weight of portion removed = 4.5 x 19 = 85.5 kN Eccentricity from 0 = 3.3 + (3.3+1.5)/2 = 5.7 m Relief of disturbing moment = 5.7 x 85.5 = 490 kNm 6 . 1 490 1730 1980 = − = F
- 18. INTRODUCTION TO SLOPE INSTABILITY:- 1. Rotational: This type of failure surface may be either circular or non-circular. Consists of a movement of rock or debris, about an axis that is parallel to the slope contours, involving shear displacement along a concave upward – curving failure 2. Translational : Consists of a non – circular failure which involves motion on a near – planar slip surface 3.Compound Slip
- 23. Causes of Slope Failure 1
- 24. Causes of Slope Failure 2
- 25. To Be Considered in Assessment of Stability ✓ Ground Investigation ✓ Most Critical Slip Surface ✓ Tension Cracks ✓ Submerged Slopes ✓ Factor of Safety ✓ Long and Short-Term Stability ✓ Effective or Total Stress Parameters? ✓ Progressive Failure ✓ Pre-Existing Failure Surfaces ✓ Assumptions in Limit Equilibrium Methods of Analysis for Circular Failure extra reading articles : 05 Circular failure.pdf 1. Granular Soils: (the simplest method) 1.1 The C'=0 Method 2. Cohesive Soils: 2.1 Circular Failure Surface 2.1.1 The Basic Idea 2.1.2 Method of Slices 2.1.3 Bishop's Method 2.2 Non-Circular Failure Surface 2.2.1 Janbu's Method 2.2.2 Infinite Slope Method 2.2.3 Stability Charts
- 26. 1. GRANULAR SOILS 1.1 The C'=0 method Assumptions:- infinite, dry slope.
- 27. 2.0 COHESIVE SOIL 2.1 Circular Failure Surface 2.1.2 The Basic Idea Assumptions:- circular arc, radius R, centre O.
- 30. 2.1.2 Method of Slices Assumptions:- circular arc, radius R, centre O The soil mass above a trial failure surface is divided into slices by vertical planes. Each slice is taken as having a straight line base. The Factor of Safety of each slice is assumed to be the same, implying mutual support between the slices, ie. there must be forces acting between the slices.
- 32. 2.1.3 Bishop's Method Another method which follows from the basic "Method of Slices".
- 34. 2.2 NON-CIRCULAR FAILURE SURFACE 2.2.1 Janbu's Method The difficulty in analysing a non-circular failure surface is that it is difficult to find a single point through which many of the force components act. So, the moment equilibrium method used for circular surfaces is no longer the most appropriate. Janbu chose instead to use the force equilibrium method in the analysis which follows.
- 38. 2.2.3 Stability Charts 2.2.3.1 Taylor’s Chart 2.2.3.2 Spencer’s Chart It is not practical or a good use of an engineer's time to carry out long stability calculations on each modification of a slope. The following charts show a range of stability characteristics for slopes with various soil properties and shapes. 2.2.3.2 Taylor’s Chart
- 40. Example of Taylor’s Chart
- 41. 2.2.3.2 Spencer's Charts These include the effects of porewater pressure. The charts are broadly similar to Taylor's Charts, but introduce the parameter ru, the porewater pressure ratio. Each of the charts is calculated for a single ru value. In a slope, ru will vary at different points but we use a mean value for simplification. As the variance isn't large, this is not an over-simplification Spencer chose to use ru = 0, 0.25, 0.50. We estimate a FoS for the slope in question using each individual chart, and then interpolate for the actual ru value for the slope.
- 42. GROUND INVESTIGATION: Before any further examination of an existing slope, or the ground onto which a slope is to be built, essential borehole information must be obtained. This information will give details of the strata, moisture content and the standing water level. Also, the presence of any particular plastic layer along which shear could more easily take place, will be noted. Piezometer tubes are installed into the ground to measure changes in water level over a period of time. Ground investigations also include:- •in-situ and laboratory tests, •aerial photographs, •study of geological maps and memoirs to indicate probable soil conditions, •visiting and observing the slope.
- 43. In homogeneous soils relatively unaffected by faults or bedding, deep seated shear failure surfaces tend to form in a circular, rotational manner. We aim to find the most dangerous, ie.the most critical surface, and using the assumption above, we can find this surface using "trial circles". The method is as follows:- Consider a series of slip circles of different radii but the same centre of rotation. Plot for each of these circles against radius, and find the minimum FoS. the Factor of Safety (FoS) MOST CRITICAL FAILURE SURFACE:
- 45. This should be repeated for several circles, each investigated from an array of centres. The simplest way to do this is to form a rectangular grid from the centres:- Each centre will have a minimum FoS, and the overall lowest FoS from all the centres shows that FoS for the whole slope. This assumes that enough circles, with a large spread of radii , and a large grid of centres have been investigated.
- 46. We then have an overall failure, surface, with smaller individual ones which should not be ignored.
- 47. TENSION CRACKS: A tension crack at the head of a slide suggests strongly that instability is imminent. Tension cracks are sometimes used in slope stability calculations, and sometimes they are considered to be full of water. If this is the case, then hydrostatic forces develop as shown below:- Tension cracks are not usually important in stability analysis, but can become so in some special cases. We should therefore assume the cracks don't occur, but take account of them in analysing a slope which has
- 48. SUBMERGED SLOPES: When an external water load is applied to a slope, the pressure it exerts tends to have a stabilising effect on the slope. The vertical and horizontal forces due to the water must be taken into account in our analysis of the slope.
- 50. What is the common cause of slope failures shown above? • Failure is along discontinuities • Orientation of discontinuities controls failure
- 51. Kinematic Analysis • Potential for global failure or releasing rockfalls • Dependent on discontinuity orientations Types of Discontinuities Bedding Foliation Shear zones Fault planes
- 52. Kinematic Analysis Planar failure where the discontinuity intersects the slope face Two discontinuities intersect and also intersect the slope face Steeply dipping discontinuities cause slabs and columns to separate from face Circular failure in soil, waste or heavily fractured rock with no definable structural pattern Planar Wedge Topple Circular
- 53. Plane Failure • Discontinuity should be parallel to slope face • Discontinuity should dip at a gentler angle than slope face • Discontinuity dip should be greater than friction angle
- 54. Wedge Failure • Line of intersection should intersect the slope face • Line of intersection should plunge at a gentler angle than slope face • Line of intersection should be greater than friction angle
- 55. Toppling Failure Criteria The kinematic requirement for toppling failures according to Goodman (1989) is: “If layers have an angle of friction Φj, slip will occur only if the direction of the applied compression makes an angle greater than the friction angle with the normal to the layers. Thus, toppling failure with a slope inclined α degrees with the horizontal and discontinuities dipping at σ can occur if (90 - σ) + Φj < α”.
- 56. TOPPLING OF ROCK SLOPES FAILURE Toppling of columnar basalt recorded by Alexander von. Humboldt during his exploration of the Rio Magdelana in Columbia in 1797
- 57. • Whenever the resultant weight of a block, W, projects beyond the downslope outside corner of a rectangular shaped blocks, toppling can result, as sketched here. • Toppling usually occurs when low friction discontinuities dip between 50 and 70 degrees from horizontal. These can be joints, bedding, or foliation planes W
- 58. Flexural toppling • Flexural toppling occurs when the length-to-width ratio of adjacent blocks causes the center of gravity to fall beyond the lower hinge point, or corner of the block.
- 59. Slope creep is often confused with toppling and vice versa. This shows classic slope creep in the Ozarks of Missouri, along iron stained joints in a precambrian rhyolite, leading up into the bedrock creep zone and overlying residuum.
- 60. Toppling is often easy to recognize by the textural contrast with the country rock. This shows the Clear Creek Toppling Complex developed in the Vishnu Schist, in the Granite Gorge of the Grand Canyon, near River Mile 84.
- 61. Rock topple along a forest road near Coos Bay, Oregon which killed two and injured another. Rain had preceded the event.
- 62. Blocky, jointed rock masses can be modeled using programs like UDEC, shown here. This shows an example of a toppling failure
- 63. Topple Failure Previous failure – sliding of a rock or soil mass along an existing or induced sliding surface Toppling failure – Involves rotation of columns or blocks of rock about a fixed base Condition – the tension crack is wider at the top than at the base
- 64. Types of toppling failure Individual columns are formed by a set discontinuities dipping steeply into the face 2nd set, widely spaced orthogonal joints – column height Pseudo-continuous flexure along long columns, divided by numerous cross joints Accumulated displacements on the cross joints – toppling Continuous columns, well developed, steeply dipping discontinuities; bend forward Thinly bedded shale and slate, orthogonal jointing is not well developed Toe sliding, excavation and erosion – start the toppling process Lower part – disordered fallen blocks Block toppling Block-flexure toppling Flexure toppling
- 65. Limit Equilibrium analysis of toppling failure Involves limit equilibrium analysis Analysis = dimensions and forces acting on the blocks are calculated; starting the uppermost block Each block = quantified as stable, toppling and sliding Overall slope is unstable = the lowermost block is either sliding or toppling Basic requirement: Friction angle, at base of the slope > than the dip angle of the base – no sliding occur Rectangular block; width = ∆x; height = yn Dip of the base of the blocks = Ψp Dip of the orthogonal planes forming the faces of the blocks = Ψd (Ψd = 90 – Ψp) Slope height = H Angle of excavation = Ψf Upper slope above the crest = Ψs Step 1: Dimension calculation
- 66. Limit Equilibrium analysis of toppling failure Step 2: Stability calculation An intermediate set of toppling The center of gravity lies outside the base A set of blocks in the toe region Pushed by the toppling blocks above Stable, topple or slide, depends on slope and block geometric Stable blocks in the upper part Friction angle of the base > dip of the plane Height is limited, the center of gravity lies inside the base Define the dimensions of the blocks, position and direction of all the forces acting on the blocks
- 67. Probabilistic analysis • Design parameters – assumed to be the average and best estimate values • In reality – each parameter has range of values; natural variability, changes over time, the degree of uncertainty • FS = realistically expressed as a probability distribution, rather a single value • Method: • The margin of safety method • Monte Carlo method
- 69. Stereonet-Based Kinematic Analysis Discontinuity Orientation Measurements Strike and dip of the beds. 1-Strike 2-Dip vector 3- Dip direction 4-Angle of dip
- 70. Great Circles Stereonet-Based Kinematic Analysis Discontinuity Orientation Measurements
- 71. Pole Dip Vector Stereonet-Based Kinematic Analysis Plotting Discontinuity Orientation
- 72. Great Circles Poles Dip Vectors Stereonet-Based Kinematic Analysis Plotting Discontinuity Orientation
- 73. Poles Contoured Poles Stereonet-Based Kinematic Analysis Plotting Discontinuity Orientation
- 74. Stereonet-Based Kinematic Analysis Identifying representative great circles using Dips software
- 75. Stereonet-Based Kinematic Analysis Plane failure criteria Pole Dip Vector
- 76. Stereonet-Based Kinematic Analysis Wedge failure criteria
- 77. Stereonet-Based Kinematic Analysis Wedge failure criteria - based on lines of intersections
- 78. Stereonet-Based Kinematic Analysis Wedge failure criteria - based on lines of intersections
- 79. Outcrop No. Lith- ology Form- ation Type of disc. Disc. Set no. Dip Dip Dir. Aperture Continuity Water flow Spacing Discontinuity Data – Data collection format