{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture 25 - EP1 LATERAL EARTH PRESSURE Pressure on...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
EP1 LATERAL EARTH PRESSURE Pressure on Structures Geostatic Stresses, At Rest Pressure (at a point, overburden only) o Coefficient of Earth Pressure at Rest, K 0 , is the ratio of horizontal effective to vertical effective stress. The at rest horizontal pressure develops naturally due to weight of the overburden soils. v h 0 ' ' K σ σ = (K 0 = 1 for water, i.e. same pressure both directions) Cantilever Retaining Wall Gravity Retaining Wall Anchor Sheet Pile Wall Braced Excavation Culverts, Tunnels, Sewers, Pipes Dry (or unsaturated) γ m , z σ v = Σγ mi z i σ v = σ v σ h = K 0 σ v σ h = σ h Submerged σ v = Σγ i z i u = γ w z w σ v = σ v - u σ h = K 0 σ v σ h = σ h + u z γ m γ sat , z w
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
EP2 o In general the total stresses must be calculated including water pressure and v h 0 K σ σ o For NC soils the Jaky equation is commonly used: ) sin 1 ( K 0 φ - = o Overconsolidation may lock in some of the higher past horizontal stress (soils have a “memory”). For OC soils Mayne and Kulhawy (1982) developed the following equation: o The at rest Mohr’s circle plots beneath the failure envelope: o If we could insert a rigid wall into the soil without disturbance, the horizontal pressure distribution on the wall would be triangular, linearly increasing with depth as the vertical stress increases. o In a dry soil, cohesionless, the pressure distribution and resultant, P 0 , shown at right would act against the wall: (note: soils possessing cohesion can stand on a vertical cut without any wall – more on cohesion later) o If water is present (undesirable) we must also add a triangular water pressure distribution and the at rest effective stress is no longer triangular. H/3 (centroid of triangle) H σ h = K 0 γ H at z = H σ h = 0 at z = 0 P 0 = ½(K 0 γ H)(H) = ½K 0 γ H 2 H σ h = K 0 ( γ H 1 + γ ’H 2 ) at z = H σ h = 0 at z = 0 H 1 H 2 σ h = K 0 ( γ H 1 ) at z = H 1 u = 0 at z = H 1 u = γ w H 2 at z = H 2 σ h = K 0 ( γ H 1 ) at z = H 1 σ h = [K 0 ( γ H 1 + γ ’H 2 ) + γ w H 2 ] at z = H σ h = 0 at z = 0 Shear Stress, τ Normal Stress, σ c σ 3 = σ h = K 0 σ v σ 1 = σ v φ Mohr-Coulomb Failure Envelope τ f = c + σ tan φ OCR ) sin 1 ( K sin 0 φ φ - =
Image of page 2
EP3 o For braced excavations, basements and pipes we do design for at rest pressure. For walls, in general, we consider two limit states at the plastic equilibrium (where every point in the soil mass is on the verge of failure): o Active case (K a ): wall moves away from soil, vertical stress remains constant but horizontal stress decreases to the minimum allowable without failure.
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern