Practice Problems: Earth Retaining Structures
Question 1
A geotechnical engineer is designing a cantilever retaining wall for a highway project. The wall retains 18 ft of granular backfill with a unit weight of 120 pcf and an angle of internal friction of 32°. The wall has a smooth vertical back. Using Rankine theory and assuming no surcharge loads, what is the total active lateral earth pressure force per unit length of wall?
(a) 5,832 lb/ft
(b) 6,480 lb/ft
(c) 7,128 lb/ft
(d) 7,776 lb/ft
Question 2
A structural engineer is analyzing a 5-m high concrete retaining wall. The wall retains saturated clay with cohesion of 25 kPa, unit weight of 18.5 kN/m³, and friction angle of 0° (undrained conditions). The wall-soil interface has adhesion equal to 0.6 times the soil cohesion. What is the total active earth pressure force per meter length of wall using Rankine theory?
(a) 106 kN/m
(b) 118 kN/m
(c) 125 kN/m
(d) 231 kN/m
Question 3
A civil engineer is designing a sheet pile wall for a waterfront facility. The wall is 25 ft high and retains sand with a unit weight of 115 pcf and φ = 35°. A uniform surcharge load of 500 psf acts on the backfill surface. Using Rankine theory, what is the lateral earth pressure at the base of the wall?
(a) 985 psf
(b) 1,135 psf
(c) 1,285 psf
(d) 1,435 psf
Question 4
A geotechnical engineer needs to design a gravity retaining wall 4 m high. The backfill is compacted sand with γ = 19 kN/m³ and φ = 34°. The friction angle between the concrete base and the soil foundation is 28°. If the total active force is 35 kN/m, what minimum width of the base is required to satisfy a factor of safety of 1.5 against sliding? Assume the wall weight is 110 kN/m.
(a) 1.2 m
(b) 1.5 m
(c) 1.8 m
(d) 2.1 m
Question 5
A retaining wall engineer is evaluating a 20-ft cantilever retaining wall with a heel extending 12 ft and toe extending 3 ft. The stem thickness is 1.5 ft. The backfill has γ = 120 pcf and φ = 30°. The concrete unit weight is 150 pcf. What is the total vertical force acting on the base per foot of wall length (including soil over heel)?
(a) 23,400 lb/ft
(b) 25,650 lb/ft
(c) 27,900 lb/ft
(d) 30,150 lb/ft
Question 6
A coastal engineer is designing an anchored sheet pile wall for a marina. The wall height is 8 m, and the anchor is located 1.5 m below the top. The backfill sand has γ = 18 kN/m³ and φ = 36°. Using the free earth support method and Rankine pressures, what is the anchor force per meter of wall if the depth of embedment provides zero moment at the toe?
(a) 142 kN/m
(b) 168 kN/m
(c) 194 kN/m
(d) 220 kN/m
Question 7
A civil engineer is checking the bearing capacity safety of a 6-m high retaining wall. The base is 3.5 m wide. The resultant vertical force is 185 kN/m at an eccentricity of 0.4 m from the centerline. The allowable bearing pressure of the foundation soil is 250 kPa. What is the maximum bearing pressure under the base?
(a) 143 kPa
(b) 163 kPa
(c) 183 kPa
(d) 203 kPa
Question 8
A geotechnical engineer is analyzing a basement wall 15 ft deep that retains sand with γ = 118 pcf and φ = 33°. The water table is at 8 ft below the surface. The saturated unit weight is 125 pcf. What is the total active earth pressure force per foot of wall using Rankine theory?
(a) 5,240 lb/ft
(b) 6,120 lb/ft
(c) 6,890 lb/ft
(d) 7,450 lb/ft
Question 9
A retaining wall designer is evaluating a reinforced concrete wall with a stem height of 22 ft. The wall uses Coulomb theory with wall friction angle δ = 20°, soil friction φ = 35°, and backslope angle β = 10°. The backfill unit weight is 120 pcf. What is the active earth pressure coefficient Ka for this condition?
(a) 0.248
(b) 0.267
(c) 0.286
(d) 0.305
Question 10
A transportation engineer is designing a mechanically stabilized earth (MSE) wall 7 m high for a highway embankment. Geogrid reinforcement layers are spaced at 0.5 m vertically. The backfill has γ = 19 kN/m³ and φ = 38°. For the reinforcement at 3.5 m depth, what is the maximum tensile force per meter width if Ka = 0.24?
(a) 15.96 kN/m
(b) 18.24 kN/m
(c) 20.52 kN/m
(d) 22.80 kN/m
Question 11
A civil engineer is designing a counterfort retaining wall 26 ft high with counterforts spaced at 12 ft on center. The backfill is granular soil with γ = 115 pcf and φ = 32°. Using Rankine theory, what is the total horizontal force on one panel between counterforts?
(a) 38,500 lb
(b) 42,800 lb
(c) 47,100 lb
(d) 51,400 lb
Question 12
A geotechnical engineer evaluates overturning stability of a 5-m retaining wall. The base width is 3 m. The resisting moment from wall weight and soil is 620 kN-m/m. The active earth force is 48 kN/m acting at H/3 = 1.67 m above the base. What is the factor of safety against overturning?
(a) 6.2
(b) 7.0
(c) 7.7
(d) 8.5
Question 13
A retaining wall engineer designs a wall for a site where seismic considerations are critical. The wall is 16 ft high, retaining sand with γ = 120 pcf and φ = 34°. The horizontal seismic coefficient kh = 0.25. Using the Mononobe-Okabe method, what is the dynamic active earth pressure coefficient?
(a) 0.38
(b) 0.42
(c) 0.46
(d) 0.50
Question 14
A structural engineer is checking a 4.5-m high concrete retaining wall for overturning. The wall has a base width of 2.8 m with toe of 0.6 m and heel of 1.6 m. The stem is 0.6 m thick at the base. The eccentricity of the resultant force is 0.35 m. Is the resultant within the middle third of the base?
(a) Yes, e < b/6="0.467">
(b) No, e > B/6 = 0.467 m
(c) Yes, e < b/6="0.350">
(d) No, e > B/6 = 0.350 m
Question 15
A civil engineer designs a 10-ft high cantilever retaining wall. The passive pressure coefficient Kp = 3.0 and the unit weight of soil in front of the wall is 125 pcf. A 2-ft depth of soil in front of the toe provides passive resistance. What is the passive resisting force per foot of wall?
(a) 375 lb/ft
(b) 750 lb/ft
(c) 1,125 lb/ft
(d) 1,500 lb/ft
Question 16
A geotechnical consultant analyzes a braced excavation 12 m deep in soft clay with undrained shear strength cu = 40 kPa and unit weight γ = 18 kN/m³. Using Peck's apparent pressure diagram for soft to medium clay, what is the maximum apparent earth pressure?
(a) 120 kPa
(b) 160 kPa
(c) 200 kPa
(d) 240 kPa
Question 17
A retaining wall designer evaluates drainage behind a 20-ft wall. The backfill permeability is 0.015 ft/min and the hydraulic gradient is 0.6. If the drainage system fails and the wall becomes fully saturated, what is the increase in lateral pressure at the base due to hydrostatic pressure? (γw = 62.4 pcf)
(a) 748 psf
(b) 936 psf
(c) 1,124 psf
(d) 1,248 psf
Question 18
A highway engineer is designing a gabion retaining wall 6 m high. The gabion unit weight is 18 kN/m³ and the backfill has γ = 19 kN/m³ with φ = 35°. The wall batter (inclination from vertical) is 6:1 (H:V). Using Ka = 0.27, what is the required base width for a factor of safety of 2.0 against overturning?
(a) 3.2 m
(b) 3.6 m
(c) 4.0 m
(d) 4.4 m
Question 19
A consulting engineer analyzes a tieback anchor system for a 30-ft deep excavation. The anchors are installed at 15° below horizontal, spaced 10 ft horizontally and 8 ft vertically. If the lateral earth pressure diagram yields a total force of 800 lb/ft² at mid-height, what is the anchor load per anchor?
(a) 52,000 lb
(b) 56,000 lb
(c) 60,000 lb
(d) 64,000 lb
Question 20
A geotechnical engineer is designing a soil nail wall for a 9-m high cut. The nails are 12 m long, spaced 1.5 m horizontally and 1.5 m vertically. The soil has γ = 19.5 kN/m³ and φ = 32°. The design lateral earth pressure coefficient is 0.30. What is the maximum tensile force in the critical nail located at mid-height?
(a) 59 kN
(b) 67 kN
(c) 75 kN
(d) 83 kN
