For a sheet pile with embedment D=10 ft, the average hydraulic gradient in the heave zone is iav=0.36. The soil has a saturated unit weight of 112 lb/ft3. What is the factor of safety against heaving? Use a unit weight of water of 62.4 lb/ft3.

Correct answer: 2.30

Explanation

To solve this problem, you first calculate the submerged unit weight of the soil. Then, you use the provided average hydraulic gradient and the unit weight of water to find the uplift pressure gradient. The factor of safety is the ratio of the submerged unit weight to this uplift pressure gradient, as per Equation (9.15).

Other questions

Question 1

What is the relationship between total stress (σ), effective stress (σ'), and pore water pressure (u) in a soil mass according to the principle of effective stress?

Question 2

A soil profile consists of a 6 m layer of dry sand above a layer of saturated clay. The dry unit weight of the sand is 16.5 kN/m3, and the saturated unit weight of the clay is 19.25 kN/m3. The groundwater table is at the boundary between the sand and clay. What is the effective stress at a depth of 19 m from the ground surface?

Question 3

What is the effect of upward seepage on the effective stress at a point within a soil layer?

Question 4

The condition where upward seepage reduces the effective stress in a soil mass to zero, causing a loss of soil stability, is generally referred to as what?

Question 5

A soil has a submerged unit weight (γ') of 10.5 kN/m3. Given the unit weight of water (γw) is 9.81 kN/m3, what is the critical hydraulic gradient (icr) for this soil?

Question 6

What is the direction of the seepage force per unit volume in an isotropic soil?

Question 7

For a sheet pile structure, the submerged weight of soil in the potential heave zone (W') is calculated to be 300 kN/m, and the uplifting force from seepage (U) is 200 kN/m. What is the factor of safety against heaving?

Question 8

What is the value of the parameter χ in Bishop's equation for effective stress when a soil is fully saturated?

Question 9

What is the nature of pore water pressure in the zone of capillary rise, with atmospheric pressure taken as the datum?

Question 10

A point in a soil profile is 3 ft above the groundwater table within a zone of capillary rise. The degree of saturation at this point is 50 percent. What is the pore water pressure (u) at this point, if the unit weight of water is 62.4 lb/ft3?

Question 11

What is the effect of downward seepage on the effective stress at a point within a soil layer?

Question 12

In the analysis of heaving around a sheet pile with embedment depth D into a permeable layer, what are the dimensions of the soil zone typically investigated for stability?

Question 13

For a submerged soil, the saturated unit weight is 19.81 kN/m3 and the unit weight of water is 9.81 kN/m3. Downward seepage is occurring with a hydraulic gradient (i) of 0.4. What is the effective stress (σ') at a depth (z) of 5 m?

Question 14

According to Bishop's equation for effective stress in partially saturated soil, σ' = σ - ua + χ(ua - uw), the term (ua - uw) is referred to as what?

Question 15

What is the primary mechanism that causes capillary rise in soils?

Question 16

A soil profile has a groundwater table at a depth of 5 m. Below this is a 10 m thick layer of saturated sand. What is the pore water pressure at the bottom of the sand layer (15 m from the surface)?

Question 17

In the factor of safety calculation against heaving, FS = W' / U, what does the term W' represent?

Question 18

What is the primary function of a filter placed on the downstream side of a sheet pile wall, as described in Section 9.6?

Question 19

For a fine sand, what is the approximate range of capillary rise in feet according to Table 9.2?

Question 20

An exploratory drill hole is made in a 20 ft thick layer of stiff saturated clay underlain by a sand layer under artesian pressure. Water in the drill hole rises to a height of 12 ft above the top of the sand layer. How deep can an open excavation proceed into the clay before the bottom heaves?

Question 21

The effective stress principle, σ = σ' + u, was first developed by whom?

Question 22

In a soil with upward seepage, the total stress at a point C at depth z is σC = H1γw + zγsat. The pore water pressure is uC = (H1 + z + (h/H2)z)γw. What is the correct expression for the effective stress σ'C?

Question 23

What is the seepage force per unit volume of soil when water is flowing with a hydraulic gradient 'i' and the unit weight of water is 'γw'?

Question 24

The factor of safety against heaving can be expressed as FS = γ' / (iavγw). What does 'iav' represent in this formula?

Question 25

A sheet pile is driven into a permeable soil layer with a total thickness T = 60 ft. The embedment depth D is 20 ft. What is the value of the coefficient Co used for heaving analysis, based on Table 9.1?

Question 26

In a partially saturated soil, how does the parameter χ in Bishop's equation typically vary with an increasing degree of saturation (S)?

Question 27

What is the approximate range of capillary rise for silt, in meters, according to Table 9.2?

Question 28

A soil profile consists of a top layer of dry sand (H1=6 ft), a middle layer of sand in a capillary zone (H2=3 ft), and a bottom layer of saturated clay (H3=6 ft). The groundwater table is between the capillary zone and the saturated clay. For the sand, Gs=2.65 and e=0.5. For the clay, w=42 percent and Gs=2.71. What is the effective stress at the bottom of the clay layer (depth of 15 ft)?

Question 29

For fine-grained soils, the definition of effective stress as the sum of vertical components of intergranular contact forces may not be physically accurate because...

Question 30

What is the factor of safety against heave for a sheet pile with embedment D=6 m in a permeable layer of thickness T=10 m, a total head difference H=3.4 m, and a soil submerged unit weight of 9.19 kN/m3? The unit weight of water is 9.81 kN/m3.

Question 31

A soil has a void ratio (e) of 0.52 and a specific gravity of solids (Gs) of 2.67. What is its saturated unit weight (γsat) if the unit weight of water (γw) is 9.81 kN/m3?

Question 32

What is the primary factor that determines the height of capillary rise in a clean glass tube?

Question 33

What is the general relationship between effective stress (σ'), intergranular stress (σig), electrical attractive force (A'), and electrical repulsive force (R') in fine-grained soils?

Question 34

In a layer of soil under upward seepage, the critical hydraulic gradient (icr) is 1.05. If the actual hydraulic gradient (i) is 0.8, what is the factor of safety against boiling?

Question 35

According to Figure 9.16, which shows the capillary effect in a sandy soil column, what happens to the degree of saturation with increasing height above the free water surface?

Question 36

If a filter with an effective unit weight (γ'F) of 11 kN/m3 and thickness (D1) of 1.5 m is added to a heave zone of depth (D) 6 m, what is the additional submerged weight (W'F) per unit length provided by the filter?

Question 37

A soil profile consists of two layers. Layer I has H1 = 5 ft and dry unit weight γd = 112 lb/ft3. Layer II has H2 = 6 ft and saturated unit weight γsat = 120 lb/ft3. The groundwater table is at the interface of the two layers. What is the effective stress at the bottom of Layer II?

Question 38

What does the term 'neutral stress' refer to?

Question 39

In a soil with a void ratio of 0.81 and a specific gravity of solids of 2.73, what is the critical hydraulic gradient?

Question 40

A cut is made in a stiff saturated clay that has a saturated unit weight of 1900 kg/m3. The clay is underlain by a sand layer. What should be the height of water, h, in the cut so that the stability of the 7 m thick clay layer is not lost, given the artesian pressure from the sand corresponds to a head of 5 m above the clay-sand interface?

Question 41

What is the primary reason that the effective stress principle is considered the most important concept in geotechnical engineering?

Question 42

For a soil with an average hydraulic gradient of iav = 0.25 at the bottom of the heave zone and a factor of safety against heaving of FS = 4.0, what is the ratio of the soil's submerged unit weight to the unit weight of water (γ' / γw)?

Question 43

In a soil profile where the groundwater table must be raised, how many meters must it rise to decrease the effective stress at the bottom of a clay layer by 15 kN/m2?

Question 44

Which of the following soil types would be expected to have the highest capillary rise?

Question 45

If upward seepage is occurring in a sand layer with a hydraulic conductivity (k) of 0.12 cm/sec, a thickness (H2) of 2.5 m, a head loss (h) of 1.5 m, and a cross-sectional area of 0.45 m2, what is the rate of upward seepage of water in m3/min?

Question 46

If a soil is boiling, what is the value of its effective stress?

Question 47

A soil has a void ratio of 0.55 and a specific gravity of solids of 2.68. The head causing upward flow is 1.2 m through a soil layer of 2 m thickness. Will boiling occur?

Question 48

A soil has a void ratio of 0.6 and Gs of 2.65. A capillary zone with 100 percent saturation exists above the water table. What is the effective stress at a point 1.5 m above the water table?

Question 49

For the purposes of analyzing in situ stresses, how are the magnitudes of electrical attractive (A') and repulsive (R') forces generally treated for granular soils, silts, and clays of low plasticity?