Foundation engineering

P-wave

"primary" compression wave longitudinal wave

S-wave

"secondary" shear wave transversal wave

Temporary or permanent excavations

- Free slope - Cantilever sheet pile wall - Anchored sheet pile wall - Braced sheet pile wall - Diaphragm walls - Secant pile walls

Earth pressure according to Rankine, assumptions

- Frictionless vertical wall - Horizontal pressure - Evenly distributed load on the surface

Explain the reason why in design, the pore water pressure is the lowest assumed value of the active earth pressure

Active earth pressure can't be negative (then it's passive) so we assume that the water pressure is the lowest value because of rain (???) In cohesive soils the active lateral earth pressure is at least equal to the water pressure on top of the soil layer. (part 1 bls 8)

Difference between active and passive earth pressure

Active: pressure exerted by the soil that overturns or slides the retaining wall Passive: pressure that the soil exerts on retaining walls, caused by the interaction between the soil and the structure, "passar" að hann detti ekki

What does it mean that soil is nonlinear?

At high strains, soil behavior is very plastic and the relative motion between particles is significant. If the soil is loose, compaction and densification occur. For cyclic loading at large strain, the soil material changes its properties in each loading cycle. At very low strains, soil behaves almost elastic (linear), denoted the small-strain behavior. As strain becomes higher, the degree of non-linearity increases. (sjá graf bls 38) (bls 37 lecture notes

Material damping

Caused by relative movement between soil particles, which consumes energy due to friction between particles. Larger strain -> More relative movement between particles -> Higher damping Material damping / Inner damping Mostly influenced by: - soil type - shear strain magnitude Caused by internal friction between soil particles. (bls 39 lecture notes)

Dynamic load vs static load

Dynamic load is time-dependent, static load is time-independent

List the driving forces and resisting forces for a back-anchored sheet pile wall

Earth pressure, water pressure, external loads, anchor forces (part 1 bls 4)

Difference between the excitation frequency and the natural frequency of a system

Excitation frequency: frequency of the applied force/external force (bls 23 lecture notes) Natural frequency: the frequency in which a system will oscillate in the absence of a driving force (bls 14 lecture notes)

Difference between force amplitude and displacement amplitude of a SDOF

Force: maximum magnitude or strength of the force applied to a vibrating or oscillating system [kN] Displacement: maximum magnitude or extent of the back and forth movement of a particle or object within a vibrating system [m]

Vertical displacement amplitude

Higher vertical displacement amplitude => Better soil compaction

The equivalent-linear method is applied to only one type of damping, which one? Why is it not applied to the other type of damping?

It is applied to material damping, because it is strain dependent. Geometric damping is strain-independent.

Shear strength (G)

Lower G => Lower resonant frequency => Excitation frequency closer to resonance => Increased response Lower G => Increased static response (F/k) => Larger displacement

What happens when the damping ratio (D, e) = 0

M = 1/(1-beta^2), phi=atan(0/(1-beta^2) beta < 1: force and displacement are in phase, phi = 0 beta -> 1: resonance beta > 1: force and displacement move out of phase, phi=pi

Amplitude

Maximum displacement in every cycle (A)

Compaction

Most common ground improvement method, static or dynamic Main purposes: - Increase soil shear strength - Reduce compressibility, permeability, soil liquefaction potential - Control swelling/shrinking - Reduce material deterioration

Single degree of freedom system

Moves only in a single direction u(t) Composed of a mass, spring stiffness, viscous dashpot coefficient Subjected to external force

Frequency

Number of cycles per second [Hz]

What characterizes a dynamic load generated by a rotating eccentric mass?

P0 = m_e * e * w^2 m_e: eccentric mass, e: eccentric distance, w: circular frequency The eccentric mass produces a centrifugal force in its direction rotating.

Rayleigh wave

R-wave surface wave travel along the free surface

Dimensionless frequency, beta

Ratio of the applied frequency to the natural frequency of the system

Which parameters does the equivalent-linear method apply to?

Shear strain, damping ratio and shear modulus

Displacement amplitude

Static deformation (deformation of a spring with the stiffness k as a result of a load F_0), multiplied by the dynamic magnification factor (the response in relation to the static response) Vertical displacement of a system that is oscillating

Geometric damping

Strain independent Radiation damping Arises because mechanical waves propagate away from the foundation into the surrounding soil High emission of waves means high damping of the foundation (bls 44 lecture notes)

Natural frequency

The frequency at which a system naturally oscillates

Resonant frequency

The frequency where maximum amplitude occurs

Explain why the max of the two expressions shall be used for the moment in the sheet pile wall below the lowest anchor level

The sheet pile wall under the lowest anchor level can be interpreted as either a cantilever beam or a continuous beam with evenly distributed pressure. To be conservative, the larger moment of the two models is taken as the design value. (svör við Workshop)

Difference between Rankine and Swedish practice

The swedish method uses sigma_p,net (net pressure) to calculate the pressure under the excavation level. sigma_p,net = sigma_p-sigma_a Stille (maður??) showed that the stability of the wall is highly influenced by the vertical bearing capacity of the sheet piles -> the use of sigma_p,net instead of Rankine's earth pressures (part 1, bls 9)

Period

Time it takes to complete one cycle (T)

What is the purpose of the equivalent-linear method?

To analyze non-linear behavior of soil at moderate to high strains

Why is pore pressure (u) not multiplied by the earth pressure coefficients (Ka, Kp)?

U is the same in all directions Hydrostatic

Harmonic vibration

Vibration is a dynamic movement around an equilibrium point, characterized by their: - amplitude - cyclic frequency, circular frequency or period - phase angle

When does the Swedish practice give the same expression as Rankine theory?

When Ncb=4

When is the equivalent-linear method used?

When the strain is moderate to high and the soil stops behaving elastically

Ultimate limit state 2. Structural failure

a. Failure in the sheet pile, anchor or wale beam M_Rd > M_Sd (moment) V_Rd > V_Sd (shear force) The moment or shear force exceeds the bearing capacity -> failure. b. Vertical instability. The vertical component of the anchor force exceeds the vertical bearing capacity. The bearing capacity depends on the friction and cohesion between the soil and the wall. c. Failure in the dowel The moment or shear force in the dowel exceeds its bearing capacity. (part 1 bls 13)

Ultimate limit state 1. Soil failure

a. Overall stability: A slip surface behind the anchor and under the sheet pile wall due to insufficient length of the sheet piles under the excavation level as well as insufficient anchor length. The sheet pile wall and the anchors rotate together. b. Excessive base heave: In soft soils (clay), bearing capacity failure due to unloading. c. Hydraulic base heave (hydraulic uplift): The water pressure in a permeable layer (fx. sand) becomes so high that an overlaying impermeable layer (fx. clay) heaves. d. Hydraulic base failure (flæðirit): Water flows through a permeable soil and causes internal erosion. e. Rotational instability: The sheet pile wall rotates around the anchor level due to insufficient pile length under the excavation level. (part 1 bls 10)

What are piles?

deep foundations transfer the structural loads to deep competent strata in the ground limit the settlements of heavy superstructures

Circular frequency

w=sqrt(k/m) A SDOF system will always oscillate with circular frequency regardless of its initial conditions, as long as they are non-zero [rad/s]