7 - Embedded Retaining Walls

Question 1

What is the primary purpose of an embedded retaining wall?

Answer 1

To resist lateral earth pressures by mobilizing active and passive soil forces through deep embedment.

Question 2

Name four common types of embedded retaining walls.

Answer 2

Sheet pile, diaphragm, contiguous pile, and secant pile walls.

Question 3

How are embedded retaining walls treated for design purposes?

Answer 3

As vertical cantilevers strong enough to resist bending, assuming a plastic hinge forms.

Question 4

What must engineers check for after completing the initial design of an embedded wall?

Answer 4

Possibility of various failure modes, including bending failure.

Question 5

What causes failure of anchorage in an embedded retaining wall?

Answer 5

Excessive surcharge loading and inadequate fixings or tie-rods.

Question 6

What are common causes of propping failure in retaining walls?

Answer 6

Undersized props, inadequate penetration, and unintentional surcharge loading.

Question 7

What leads to outward toe movement failure in retaining walls?

Answer 7

Inadequate penetration or unintentional reduction in toe resistance.

Question 8

What are additional failure modes of embedded retaining walls not shown in the main figure?

Answer 8

Overall slip of the system and heave into the excavation.

Question 9

Which soil type is associated with failures like overall slip and excavation heave?

Answer 9

Clay soils.

Question 10

What is the significance of Figure 7.1 in relation to embedded retaining walls?

Answer 10

It shows schematic plan views of different types of embedded retaining walls.

Question 11

What is the formula for horizontal effective stress in an infinitely large soil mass?

Answer 11

σ′h = K0σ′v

Question 12

What does K0 represent in lateral earth pressure equations?

Answer 12

The ‘at rest’ earth pressure coefficient.

Question 13

What is the approximate value of K0 for normally consolidated soils?

Answer 13

K0 ≈ 1 – sinφ′

Question 14

How does K0 typically behave in overconsolidated soils?

Answer 14

K0 is usually greater than 1.

Question 15

What is the Eurocode 7 formula for K0 in overconsolidated soils?

Answer 15

K0 = (1 – sinφ′)√OCR

Question 16

What happens to the stress state in soil upon construction of an embedded wall?

Answer 16

It is altered, and K0 is no longer applicable.

Question 17

What are σ1 and σ3 in the context of principal stresses?

Answer 17

σ1 is the major principal stress; σ3 is the minor principal stress.

Question 18

What does pa(z) represent?

Answer 18

Active lateral earth pressure at depth z.

Question 19

What does pp(z) represent?

Answer 19

Passive lateral earth pressure at depth z.

Question 20

What is the condition for active failure of a retaining wall?

Answer 20

The wall moves away from the soil, reducing horizontal stress.

Question 21

What is the condition for passive failure of a retaining wall?

Answer 21

The wall moves into the soil, increasing horizontal stress.

Question 22

What is the expression for Ka (active earth pressure coefficient)?

Answer 22

Ka = (1 – sinφ′)/(1 + sinφ′) = tan²(45° – φ′/2)

Question 23

What is the expression for Kp (passive earth pressure coefficient)?

Answer 23

Kp = (1 + sinφ′)/(1 – sinφ′) = tan²(45° + φ′/2)

Question 24

Under what condition are Ka and Kp valid?

Answer 24

Drained soil conditions.

Question 25

In drained active conditions, what are σ′1 and σ′3?

Answer 25

σ′1 = σ′v, σ′3 = σ′h

Question 26

In drained passive conditions, what are σ′1 and σ′3?

Answer 26

σ′1 = σ′h, σ′3 = σ′v

Question 27

What is the maximum shear stress in drained conditions?

Answer 27

τmax = σ′ tanφ′

Question 28

What is the active pressure formula in undrained conditions?

Answer 28

pa(z) = σv(z) – 2cu

Question 29

What is the passive pressure formula in undrained conditions?

Answer 29

pp(z) = σv(z) + 2cu

Question 30

What are σ1 and σ3 in undrained active conditions?

Answer 30

σ1 = σv, σ3 = σh = pa

Question 31

What are σ1 and σ3 in undrained passive conditions?

Answer 31

σ1 = σh = pp, σ3 = σv

Question 32

What is required for a retaining wall to mobilise limiting earth pressures?

Answer 32

The wall must move horizontally to induce sufficient strain in the soil.

Question 33

How much strain is required to mobilise full passive resistance in dense sands?

Answer 33

3% to 6% strain.

Question 34

How much strain is required to mobilise full passive resistance in loose sands?

Answer 34

5% to 15% strain.

Question 35

How much strain is required to mobilise active resistance compared to passive?

Answer 35

About 10 times less strain is required for active resistance.

Question 36

Why is less strain needed to mobilise active resistance?

Answer 36

Soils resist extension more easily than compression.

Question 37

What does Figure 7.4 illustrate?

Answer 37

The relationship between lateral strain and the lateral earth pressure coefficient.

Question 38

What is essential in long-term effective stress analysis of a retaining wall?

Answer 38

Estimating steady-state pore water pressures around the wall.

Question 39

What can cause disturbed pore pressures around a retaining wall?

Answer 39

Excavation near the wall altering the water table.

Question 40

What basic assumption is made in simplified seepage analysis?

Answer 40

The difference in water table levels creates a linearly distributed hydrostatic head.

Question 41

In Figure 7.5, what is the pore pressure at the water table?

Answer 41

Zero (uA = 0 and uB = 0 at the water table).

Question 42

What does the term β represent in seepage calculations?

Answer 42

Distance from Point A along the wall depth.

Question 43

How is total head at a point around the wall calculated?

Answer 43

hβ = hA – ((hA – hB) / (h1 + h2)) × β

Question 44

How is pore pressure at any point (β) calculated?

Answer 44

uβ = γw × (hA – ((hA – hB)/(h1 + h2)) × β – hz)

Question 45

Why are pore pressures equal at the base of the wall?

Answer 45

Seepage ensures equilibrium, even with differing water table levels.

Question 46

What does the pore pressure example calculation in Section 7.1.3 demonstrate?

Answer 46

That seepage must be considered for accurate pore pressure distribution, not just depth from the water table.

Question 47

What are the three ULS checks covered for embedded retaining walls?

Answer 47

ULS-1: Horizontal translation, ULS-2: Rotation, ULS-3: Bearing failure.

Question 48

What is the critical failure mode for unpropped cantilever walls?

Answer 48

Rotational failure near the toe of the wall.

Question 49

Why can’t simple moment and horizontal equilibrium solve unpropped wall rotation?

Answer 49

There are two unknowns, so an iterative solution is required.

Question 50

What does a tie-back or prop do in a propped cantilever wall?

Answer 50

Provides a restoring moment to counteract wall rotation.

Question 51

What are tie-backs typically made of?

Answer 51

High-tensile steel cables or rods anchored behind the wall.

Question 52

What is assumed about the wall in free earth support conditions?

Answer 52

The wall is stiff and does not bend.

Question 53

How is the depth of embedment determined for a propped wall?

Answer 53

By solving moment equilibrium about the level of the prop or tie-back.

Question 54

What is done after determining embedment depth in propped wall design?

Answer 54

Use horizontal equilibrium to solve for the prop or tie-back force.

Question 55

What is the first step in EC7 Design Approach 1b?

Answer 55

Apply partial factors to characteristic material properties.

Question 56

What surcharge should be allowed in EC7 wall design?

Answer 56

A minimum surcharge of 10 kPa on the retained side.

Question 57

How should over-excavation be accounted for in design?

Answer 57

Consider the greater of 0.5 m or 10% of retained height.

Question 58

How is vertical stress calculated at key depths?

Answer 58

σv = q + γz

Question 59

How is effective vertical stress calculated?

Answer 59

σ′v = σv – u

Question 60

How is horizontal stress behind the wall calculated?

Answer 60

σh = Kaσ′v + u

Question 61

How is horizontal stress in front of the wall calculated?

Answer 61

σh = Kpσ′v + u

Question 62

Why must total stress be used in equilibrium calculations?

Answer 62

Because both soil and pore water exert pressure on the wall.

Question 63

What assumption is made about passive resistance in wall design?

Answer 63

Full passive resistance is assumed to be mobilised.

Question 64

Why might full passive resistance not be mobilised in reality?

Answer 64

Because it requires much greater strain than active failure.

Question 65

What is the wall friction angle (δ)?

Answer 65

A proportion of the soil friction angle φ′, depending on wall material.

Question 66

What is the effect of a higher wall friction angle?

Answer 66

Reduces required depth of embedment by lowering Ka and Kp.

Question 67

What is the purpose of ground anchorages in retaining wall design?

Answer 67

To provide lateral support as an alternative to propping.

Question 68

What are common types of deadman anchors?

Answer 68

Sheet pile deadman anchors.

Question 69

What are common types of deadman anchors?

Answer 69

Sheet pile deadman, mass concrete deadman, and grouted ground anchors

Question 70

What is the function of a ground anchor?

Answer 70

To resist tie-back forces using shaft or passive resistance, similar to piles

Question 71

Where must a plate anchor be placed relative to the wall?

Answer 71

Behind the YZ plane, outside the active failure zone (between wall and XY plane).

Question 72

What must be true about anchor width b for full passive resistance to develop?

Answer 72

b must be greater than da/2 (half the anchor embedment depth).

Question 73

When b > da/2, what resistance assumption can be made?

Answer 73

Passive pressure acts over the entire anchor depth da.

Question 74

What pressure acts on the front and back of the plate anchor?

Answer 74

Passive pressure (Pp) on the front, active pressure (Pa) on the back

Question 75

What is the general formula for anchor resistance Pu?

Answer 75

Pu = ½(Kp – Ka)γ′da²l – Kaσqdal

Question 76

What does each variable in the anchor resistance equation represent?

Answer 76

Pu = resistance; l = length per tie; γ′ = unit weight; da = anchor embedment depth; σq = surface surcharge.

Question 77

How are spaced anchors typically modeled in design?

Answer 77

As a continuous beam with force per meter of wall length (kN/m).

Question 78

What minimum factor of safety is recommended for anchor resistance?

Answer 78

At least 2× the calculated tie-back force from the wall design.

Question 79

Why is a 2× resistance factor used for anchors?

Answer 79

To ensure load redistribution if a tie-rod fails, improving redundancy.

Question 80

What happens if an anchor lies within the active failure wedge?

Answer 80

It may not provide sufficient resistance, as active soil movement reduces effectiveness.

Question 81

What ensures that passive pressure is fully mobilized on the anchor?

Answer 81

Sufficient distance from the wall and appropriate embedment depth.

Question 82

What is a grouted ground anchor typically composed of?

Answer 82

A steel tendon grouted into a borehole to transfer load via shaft friction.

Question 83

What’s the benefit of using a grouted anchor over a deadman?

Answer 83

Higher capacity in tighter spaces and better performance in various soil types.

Question 84

How is the effective length of a ground anchor determined?

Answer 84

Based on the bond length between the grout and soil, beyond the active zone.

Question 85

How are deadman anchors generally installed?

Answer 85

Buried steel plates or concrete blocks, placed behind retaining walls at sufficient depths.

Question 86

Why is spacing between anchors important in design?

Answer 86

To avoid overlap of pressure bulbs and ensure individual anchor performance.

Question 87

What load transfer mechanism is used by ground anchors?

Answer 87

Shaft friction between the grout and surrounding soil or rock.