CE 4780 Hurricane Engineering II. Section on Flooding Protection: Earth Retaining Structures and Slope Stability. Table of Content

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1 CE 4780 Hurricane Engineering II Section on Flooding Protection: Earth Retaining Structures and Slope Stability Dante Fratta Fall 00 Table of Content Introduction Shear Strength of Soils Seepage nalysis Methods of Slope Stability nalysis Design of Earth Retaining Structures Example Problems Three weeks of classes 1

2 Introduction There are two types of earth retaining structures Embankments (slope stability analysis) Retaining walls (rigid - gravity - and flexible walls) Basic Concepts of Lateral Earth t Rest or K o Condition The horizontal strain is zero σ u σ σ K σ V ' V ' H o H = = γ w = σ w + γsat ( z zw ) ( z z ) V o ' H = K σ = 1 sin = σ u ' V ( φ) + u w (for NC soils) Z w Z σ H σ V γ γ sat WT

3 Basic Concepts of Lateral Earth ctive K and Passive K P Conditions There is horizontal deformation wall K a K p K o B Initial condition (at rest) Basic Concepts of Lateral Earth ctive K and Passive K P Conditions Limit equilibrium analysis Coulomb (1776): upper bound theorem Rankine (1857): lower bound theorem ssumptions: The earth retaining wall is vertical The wall earth interface is frictionless (no shear stresses) The soil surface is horizontal (no shear stresses) The wall is rigid and the soil is dry, homogeneous and isotropic The soil is loose and initially at rest 3

4 Basic Concepts of Lateral Earth ctive K and Passive K P Conditions Coulomb (1776): upper bound theorem F ai Rankine zone φ R W 45+φ/ F a W F p φr 45-φ/ F pi Rankine zone Basic Concepts of Lateral Earth ctive K and Passive K P Conditions Rankine (1857): lower bound theorem φ τ 45+φ/ Failure surface 45-φ/ K a σ v K o σ v σ v K p σ v σ 1 sin( φ) 1+ sin( φ) = 1+ sin( φ) p = 1 sin( φ) K a K 4

5 Basic Concepts of Lateral Earth ctive K and Passive K P Conditions Rankine zone K (lateral earth pressure coefficient) F a K p F p Rankine zone H F = γk a 45+φ/ 1 a H K o K a 45-φ/ F = γk p 1 p H Wall rotation x/h Example Problem ctive Case Determine the resultant earth force (magnitude and position) and the factors of safety against sliding and overturning m 5 m WT 5 m γ = 15 kn/m3 φ = 30 deg γ sat = 0 kn/m 3 γ w = 10 kn/m 3 φ = 35 deg γ concrete = 5 kn/m 3 φ rock-concrete = 45 deg Impervious rock 3 m 5

6 The Effect of Pore Water ctive Case No Drains Determine the resultant earth force (magnitude and position) and the factors of safety against sliding and overturning WT γ sat = 0 kn/m 3 γ w = 10 kn/m 3 φ = 35 deg m γ concrete = 5 kn/m 3 φ rcok-concrete = 45 deg 5 m Impervious rock 3 m The Effect of Pore Water ctive Case Drains Determine the resultant earth force (magnitude and position) and the factors of safety against sliding and overturning WT 5 m γ sat = 0 kn/m 3 γ w = 10 kn/m 3 φ = 35 deg m γ concrete = 5 kn/m 3 φ rcok-concrete = 45 deg drain Impervious rock 3 m 6

7 Cantilever Sheet Pile Walls nalysis H o d d o O R H o = depth of excavation d = depth of embedment d o = depth of rotation Pressure distribution pproximated pressure distribution Cantilever Sheet Pile Walls nalysis (cont.) Select a point O (arbitrary) Calculate the and earth pressures (reduce the strength parameters: φ/f φ, where F φ = 1. to 1.5) Calculate the net pore water pressure and the seepage force. Determine the depth d o by summing moments about O. Determine d = 1. to 1.3 d o. Calculate R by summing forces horizontally over the depth (H o +d). 7

8 Cantilever Sheet Pile Walls nalysis (cont.) Determine net resistance between d o and d. Check that R is greater than net resistance. If not extent the depth of embedment and determine new R. Calculate the maximum bending moment M max over H o -d o. Determine the section modulus: S = M max /σ allow References and Bibliography bramson, L. W., Lee, T. S., Sharma, S., and Boyce, G. M. (00). Slope Stability and Stabilization Methods. Second Edition. John Wiley & Sons. New York. 71 pages. tkinson, J. (1993). The Mechanics of Soils and Foundations. MacGraw-Hill. Budhu, M. (000). Soil Mechanics and Foundations. Wiley & Sons. Duncan, J. M. (1996). Soil Slope Stability nalysis in Landslides: Investigation and Mitigation, Ed.. K. Turner and R. L. Schuster. Special Report 47. Transportation Research Board. Washington, DC. pp McCarthy, D. F. (00). Essentials of Soil Mechanics and Foundations. Sixth Edition. Prentice-Hall. Upper Saddle River, NJ. 8

Foundation Analysis LATERAL EARTH PRESSURE

Foundation Analysis LATERAL EARTH PRESSURE INTRODUCTION Vertical or near-vertical slopes of soil are supported by retaining walls, cantilever sheet-pile walls, sheet-pile bulkheads, braced cuts, and other