Slopes Exam 1

Stress in Soil

sigma = sigma prime + pwp (terzagh’s)

Shear Strength in Soil applications

earth slopes, retaining walls, structural foundations, tunnel linings, highway pavement

Mohr-Coulomb Failure Criteria

tau f = sigma prime * tan phi +c prime

Solving Shear Strength on Horizontal and Vertical Planes 

sigma prime = sigma prime v, sigma prime h = sigma prime v * k, k = sigma prime h / sigma prime v 

Causes of Slope Failure 

rainfall, earthquake, external loading, erosion, rapid drawdown, geological features, construction activities 

Categories of Slope Failure

falls, topples, flows, slides, spread

Types of Slides

rotational, translational, compound, complex & composite

Quantitative Analysis

stability - to estimate whether the slope is stable for the given loading AND movement - to estimate how much the slope will move given loading condition

Stability Analysis (general approach) 

assume failure shape, select trial failure surface, write equilibrium equations, calculate normal and shear forces, calculate shear strength and shear stress, calculate Factor of Safety, repeat to find lowest factor of safety 

Mass Procedure - D

D = H2/H1

Seismic Nr

Wcosalpha - Pssinalpha

Seismic Tr

Wsinalpha + Pscosalpha

Fully Saturated Clay Soil 

c’ = 0, phi’ = 0, use Cu

Doward Seepage gamma prime

gamma sat - gamma water

Doward Seepage pwp

gamma w cos squared beta

Categories of Slopes

natural, cut, fill

Cut Slopes 

decrease in total stress, negative pore water pressure, decreases effective stress, leading to failure long after

Fill Slopes

increase in total stress, positive pore water pressure, decrease in effective stress and shear strength, leading to failure immediately after

FS slope vs. FS trial failure surface

For slope you run multiple iterations to find lowest FS and trial surface one iteration

Planar Failure Surface

common in steep slopes made of coarse-grained soil or along bedding planes

Curved Failure Surfaces 

Common in slopes made of fine-grained soils 

What is different from an infinite slope compared to finite?

shear strength and stress vary along failure plane

Degrees to Radians

degree * (pi/180)

Ordinary Method of Slices

neglect intershear forces, sliding soil mass is divided into several vertical slices, stability of each slice is considered separately

Bishop’s Simplified Method of Slices

considers interslice normal force but ignores shear force

Spencers Method 

considers both normal and shear interslice forces, but assume resultants of the normal and shear forces are inclined at the same angle from theta

Mass Procedure 

soil above the failure surface is considered as a single unit for calculating shear strength and stress 

Inertial Instabilities

failure caused by direct ground shaking (stability and displacement analysis)

Pseudostatic Method

(OMS) neglecting inter-slice forces, Ps = kw

Severity of Earthquake can be expressed in terms of

moment scale, richter magnitude scale, mercalli scale

PGA 

peak ground acceleration, largest value from the acceleration-time plot 

Seismic Coefficient selected from

dynamic material strengths and minimum factor of safety

Terzaghi k values

severe = 0.1, violent = 0.25, catastrophic = 0.5

Seed k values

k = 0.15 if Fs-slope > 1.15

Hynes-Griffin & Franklin k values 

k = 0.5 * PGA for Fs-slope>1 and 80% soil strength 

Surface Method Monitoring

crack monitors, surveying, photographic image analysis, gps

Subsurface monitoring methods

inclinometers, borehole probes, time-domian reflectometry, extensometers