In Situ Stresses Geotechnical Engineering II

topics !   Stresses in Saturated Soil without Seepage

!   Stresses in Saturated Soil with Upward Seepage

!   Stresses in Saturated soil with Downward Seepage

!   Seepage Force

!   Effective Stress in Partially Saturated Soil

!   Capillary Rise in Soils

!   Effective Stress in the Zone of Capillary Rise

Stresses in Saturated Soil w/o Seepage

σ(total stress) can be divided into: 1.  A portion is carried by water in the

continuous void spaces. This portion acts with equal intensity in all directions.

2.  The rest of the total stress is carried by the soil solids at their points of contact.

Effective Stress (σ’): The sum of the vertical components of the forces developed at the points of contact of the solid particles per unit cross-sectional area of the soil mass.

The space occupied by water

σ(total stress) σ’ (effective stress) u (neural stress)

The effective stress at any point is independent of the depth of water above

the submerged soil.

The definition of effective stress is mostly true for granular soils; however, for fine-grained soils, intergranular contact may not physically be there, because the clay particles are surrounded by tightly held water film.

Important Notes on Effective Stress (σ’): 1.  It is approximately the force per unit area

carried by the soil skeleton. 2.  It controls the volume change and

strength of soil mass. 3.  Increasing the effective stress induces soil

to move into a denser state of packing. 4.  The compressibility and shearing

resistance of soil depend to a great extent on the effective stress.

Important Notes on Effective Stress (σ’): 5.  It is important in solving geotechnical

engineering problems, such as the lateral earth pressure on retaining structures, the load-bearing capacity and settlement of foundations, and the stability of earth slopes.

Example: Calculate the total stress, pore water pressure, and effective stress at points A, B, and C.

Stresses in Saturated Soil with Upward Seepage

If water is seeping, the effective stress at any point in a soil mass will differ from that in the static case. It will increase or decrease, depending on the direction of seepage.

If the rate of seepage and thereby the hydraulic gradient gradually are increased, a limiting condition will be reached. Under such situation, soil stability is lost. This situation is referred to as boiling, or a quick condition.

Example: A 20ft thick layer of still saturated clay is underlain by a layer of sand. The sand is under artesian pressure. Calculate the maximum depth of cut H that can be made in the clay.

Stresses in Saturated Soil with Downward Seepage

Exercise: Refer to the soil profile provided: a.  Calculate the variation of σ, u, and σ’ with

depth. b.  If the water table rises to the top of the

ground surface, what is the change in the effective stress at the bottom of the clay layer?

c.  How many meters must the groundwater table rise to decrease the effective stress by 15kN/m2 at the bottom of the clay layer.

Seepage Force

Soil Volume

#Heaving in Soil Due to Flow Around Sheet Piles

Seepage force per unit volume of soil can be used for checking possible failure of sheet pile structures where underground seepage may cause heaving of soil on the downstream side. Terzaghi concluded that heaving generally occurs within a distance D/2 from the sheet piles (when D equals the depth of embedment of sheet piles into the permeable layer).

for Flow around a sheet pile in a homogeneous soil:

#Use of Filters to Increase the Factor of Safety against Heave

v In practice, a minimum factor of safety of about 4 to 5 is required for the safety of the structure.

v One way to increase the factor of safety against heave is to use a filter in the downstream side of the sheet-pile structured.

A FILTER is a granular material with openings small enough to prevent the movement of the soil particles upon which it is placed and, at the same time, is pervious enough to offer little resistance to seepage through it.

#Filter Design

When seepage water flows from a soil with relatively fine grains into a coarser material, there is danger that the fine soil particles may wash away into the coarse material. This process may clog the void spaces into the coarser material.

Conditions

1.  The size of the voids in the filter should be small enough to hold the larger particles of the protected material in place.

2.  The filter should have a high hydraulic conductivity to prevent buildup of large seepage forces and hydrostatic pressures in the filters.

If three perfect spheres have diameters greater than 6.5 times the diameter of a smaller sphere, the small sphere can move through the void spaces of the larger ones.

If the pore spaces in a filter are small enough to hold D85 of the soil to be protected, then the finer soil particles also will be protected. The effective diameter of the pore spaces in the filter should be less than D85 of the soil to be protected. The effective pore diameter is about 1/5 (D15) of the filter.

US Navy conditions for the design of filters:

Assignment: Submit a 2 to 3-page written report on the research article:

“A Case Study on Seepage Failure of Bottom Soil within a Double-Sheet-Pile-Wall-Type Ditch.”

Effective Stress in Partially Saturated Soil

In partially saturated soil, water in the void spaces is not continuous, and it is a three-phase system: •  Solid •  Pore Water •  Pore Air

Χrepresents the fraction of a unit cross-sectional area of the soil occupied by water. χ= 0, for dry soil χ= 1, for saturated soil

Intermediate values of χ will depend primarily on the degree of saturation S. It is also influenced by factors such as soil structure.

Capillary Rise in Soils

The continuous void spaces in soil can behave as bundles of capillary tubes of variable cross section. Because of surface tension force, water may rise above the phreatic surface.

The smaller the capillary tube diameter, the larger the capillary rise.

Notes: 1.  Capillary tubes formed in soils because of the

continuity of voids and have variable cross sections.

2.  There is a variation of the capillary rise due to nonuniformity of void spaces.

3.  There is a variation in the degree of saturation with the height of the soil caused by capillary action.

Hazen, 1930

With the decrease of D10, the pore size in soil decreases, which causes higher capillary rise.

Effective Stress in the Zone of Capillary Rise

The pore water pressure at a point in a layer of soil fully saturated by capillary rise is: u = -γwh h = height of the point under consideration measured from the groundwater table.

For Partial Saturation caused by capillary action, the pore water pressure is:

Exercise by pair: The soil profile as shown, plot the variation of σ, u, and σ’ with depth. H1 = 5m, H2 = 3m, H3 = 3.5m, S = 65% in the capillary rise zone.

Example: Find the factor of safety against heave on the downstream side of the single-row sheet pile structure. Thickness of permeable layer = 10m and depth of penetration of sheet pile = 6m. Assume γsat = 19kN/m3.

Exercise by pair: Calculate σ, u, and σ’ at A, B, C, and D for the following cases and plot the variation with depth.