Alasdair’s Engineering Pages © A. N. Beal 2016              www.anbeal.co.uk

Alasdair’s Engineering Pages

www.anbeal.co.uk

NOTES FOR EARTH RETAINING WALL DESIGN TO BS8002


EARTH PRESSURE ON WALLS

Soil Strength parameters

In BS8002, the design shear strength of the soil is based on the tangent of the friction angle reduced by a mobilisation factor M. For convenience, design values of Φ' for M =1.2 are tabulated below.





The design wall friction δ depends on the wall surface and the situation being considered but tanδ must not exceed 0.75 × design tanΦ'. Maximum values of δ based on this limit are tabulated below.





Active Earth Pressure

Coefficients for the horizontal component of active earth pressure based on Coulomb’s theory (as extended by Mayniel and Muller & Breslau) are tabulated below. This gives very similar answers to the charts in BS8002 but the tables have been extended to cover walls with sloping backs. Values are tabulated for δ = 0, δ = 20º (the maximum value for a smooth wall surface) and also for tanδ = 0.75tanΦ', which is the maximum permitted by BS8002 for a rough wall surface.




















































The values of Ka in the tables are for the horizontal component of the active pressure and are calculated from the formula

Ka =  cos²(Φ' - α)___________________________________

           cos²α [1 + √{sin(Φ'+δ)sin(Φ'-β)/(cos(δ+α)cos(β - α))}]²


Coefficients for Rankine active pressure are tabulated below

Ka  =  cos²β(cosβ - √(cos²β - cos²Φ))
(cosβ + √(cos²β - cos²Φ))














Passive earth pressure

The coefficient Kp for passive pressure based on Rankine theory (smooth wall face, level soil surface) is tabulated below.

Kp =  (1+sinΦ’)/(1-sinΦ’)













GROUND BEARING CAPACITY - SERVICEABILITY

The bearing pressure on the soil under the toe of the wall should not exceed the allowable bearing pressure recommended by BS8004, taking into account soil conditions, groundwater level and also foundation depth and breadth. Where earth pressures in a cohesive soil are estimated on the basis of undrained shear strength, BS8002 Cl. 4.2.2.2 requires them to be based on a mobilisation factor M of between 2 and 3. For convenience, presumed allowable bearing values from BS8004 Table 1 are reproduced below.
















    

 
   
   
   
    
    




Bearing Capacity - ultimate

The allowable maximum ground bearing pressure under a retaining wall should be checked in accordance with standard soil mechanics theory, taking into account the inclination and eccentricity of the applied loads (cf. BS8002 Cl. 4.2.2.1) and not exceeding the ultimate bearing capacity from BS8004 (cf. BS8002 Cl. 3.1.3.2). For this calculation the soil properties used to calculate the bearing capacity should be derived on the same basis as those used to calculate the earth pressures - i.e. the design value of Φ' should be used, incorporating a mobilisation factor M of 1.2 or based on the critical state soil strength. Where design is based on the undrained shear strength of clay (cu), M should be 1.5, or greater for a clay which requires large strains to mobilise its peak strength .

For calculating the allowable maximum ground bearing pressure, BS8002 states that engineers should refer to BS8004 and Terzaghi & Peck (1967) but unfortunately neither of these actually gives guidance on foundations subjected to eccentric and inclined loads. CIRIA Report 516 gives the following recommendations, based on research by Brinch Hansen as incorporated in Eurocode 7. They are based on the use of a rectangular stress block for the soil bearing pressure. The formulae presented below apply to foundations where the length is substantially greater than the breadth, as in most retaining walls. Where this is not the case, reference should be made to relevant soil mechanics textbooks.

Undrained conditions

Ultimate bearing resistance

Fv/B’ = 5.14cuic + q

where

cu is the soil cohesion,

q is the vertical pressure at the
level of the bearing stratum and

ic = 0.5(1 + √(1- (FH/ B’cu))

Drained conditions

Maximum average ground bearing pressure
F
v/B´ = q’Nqiq + ½γ’B’Nγiγ + cNcic

where

Nq = eΠtanΦ’tan²(45 + Φ’/2)

Nc = (Nq - 1)cotΦ’

Nγ = 2(Nq - 1)tanΦ’ (when δ ≥ Φ’/2)

iq = (1 - 0.7FH/FV

iγ = (1 - FH/Fv

ic = (iqNq - 1)/(Nq - 1)

where B’ is the effective breadth of equivalent concentric foundation with a uniform bearing pressure (i.e. using a rectangular stress block) and Fv is vertical load/metre, q’ is the effective (i.e. net of water pressure) vertical stress on the bearing stratum in front of the wall, γ’ is the effective soil density (i.e. buoyant density if water is present) and c is the soil cohesion.



EARTH PRESSURE: COMPACTION PRESSURES

BS 8002 Cl. 3.1.9 draws attention to situations where the earth pressure on a wall may exceed the calculated active pressure. Cl. 3.3.3.6 discusses the effects of compacting fill behind a retaining wall but it gives no detailed recommendations, referring the engineer to other publications for guidance. The following recommendations are based on BS8002 and guidance in CIRIA report C516.

Where some movement of a wall can be tolerated, this will release the locked-in pressures generated by compaction of backfill, so compaction pressures need not be considered when calculating the overall stability of the wall. However in situations where this does not apply, e.g. when designing of the stem of a reinforced concrete wall, compaction pressures should be taken into account.

Heavy compaction of soil behind a retaining wall should be avoided where possible. Within 2 metres of the wall, vibratory rollers should not exceed 1 tonne, or a mass per metre width of 1.3t/m; vibrating plate compactors should not exceed 1 tonne; vibro-tampers should not exceed 75kg in weight.

The recommended design procedure for walls retaining compacted fill is as follows:

1.  check the overall stability of the wall with active earth pressures on the ‘virtual back’ of the wall, in accordance with BS8002;

2.  calculate forces on the wall stem, which are the worst of either:

(a) active pressure from the retained material behind the wall (including surcharge) or

(b) compaction pressures as follows:









STABILITY OF THE GROUND MASS CONTAINING THE RETAINING WALL

In  addition to failure of the earth retaining structure by forward rotation or sliding, consideration should also be given to the possibility of failure by a deep slip involving the whole of the earth retaining structure and the earth mass in which it is placed. According to BS8002 Cl. 3.1.3.1, this may occur where:

(a)  the wall is built on sloping ground which is itself close to limiting equilibrium,

(b) the structure is underlain by a substantial depth of clay which has an undrained strength which does not increase appreciably with depth,

(c) the structure is built on a strong stratum underlain by weaker strata, or

(d) high pore water pressures may develop in the strata underlying the structure.

BS8002 does not include detailed recommendations for checking the stability of the earth mass and refers instead to the Code of Practice for Earthworks, BS6031. It should be noted that, unlike  BS8002, BS6031 uses the traditional approach to analysis and design, with soil properties taken at their representative values and a safety factor applied in calculations to achieve a safe design.

Slip surfaces

1. Rotational slides

For simplicity in analysis, a two-dimensional analysis of a slip on a circular arc is usually considered (see figure).

A series of trial circles is drawn and in each case the moment of the sum of the disturbing forces about the centre is compared with the moment of the sum of restoring forces generated by shear in the soil along the slip plane and the factor of safety is defined as the ratio between these moments. The critical circle (which gives the lowest factor of safety) is found by a process of trial and error.

Where there is anisotropy in the soil, or there is a relatively strong layer at a horizontal or shallow inclination where sliding can take place on this layer, a non-circular slip surface may need to be considered and a more advanced computer analysis may be necessary.

2. Planar Slides

When the wall is built on a slope, or the stability of sloping ground retained behind a wall needs to be checked, it may also be necessary to consider a planar slide (see figure) (ref. BS6031 Cl. 6.4.2.3). In this analysis, the factor of safety F is calculated from the formula

F = (c’ + (zcos² - u)tan’/(zsincos)

Soil Strength

According to BS6031 (Cl.6.4.2.1), the intermediate and long-term stability of slopes should be analysed by effective stress methods:

‘The values of c’ and used in slope stability calculations should be obtained from drained shear strength tests, or undrained tests with pore pressure measurement. The type of test, the test conditions, and the selection of parameters from a range of tests should take account of the factors listed in 6.2.2.1, with particular reference to the effects anisotropy, the rate of applying the deviator stress and the geological history of the site’.

Cl. 6.2.2 gives detailed advice on the sampling and testing of soils and rock. In any analysis it is important to consider the ground water level that is likely to give the highest pore water pressure at the slip surface.

Safety Factors

Where the consequences of failure on neighbouring structures, railways etc. are not particularly serious (Cl. 5.3.1, 2) and there has been a good standard of investigation, BS6031 recommends the following safety factors against soil slips (Cl. 6.5.1.2):

(i) for first-time slides: between 1.3 and 1.4;

(ii) for slides involving entirely pre-existing slip surfaces, about 1.2.

If the consequences of failure would be serious, or if the investigation has been limited, higher safety factors are recommended.

Φ’max

10°

15°

20°

25°

30°

35°

40°

45°

Design Φ (M=1.2)

8.4°

12.6°

16.9°

21.2°

25.7°

30.3°

35.0°

39.8°

design Φ'

10°

15°

20°

25°

30°

35°

40°

max. δ

3.8°

7.5°

11.4°

15.3°

19.3°

23.4°

27.7°

32.2°

β/Φ’ = 0














α =

+20°


α =

+10°


α =


α =

-10°


Φ’            δ

20°

δmax

20°

δmax

20°

δmax

20°

δmax

10

0.782

--

0.703

0.745

--

0.675

0.704

--

0.642

0.658

--

0.601

15

0.691

--

0.591

0.642

--

0.558

0.589

--

0.518

0.531

--

0.47

20

0.609

--

0.498

0.551

--

0.462

0.49

--

0.418

0.426

--

0.368

25

0.535

--

0.419

0.471

--

0.382

0.406

--

0.338

0.339

--

0.288

30

0.468

0.367

0.352

0.401

0.326

0.316

0.333

0.279

0.272

0.266

0.228

0.223

35

0.407

0.323

0.293

0.338

0.279

0.259

0.271

0.23

0.217

0.206

0.179

0.171

40

0.353

0.283

0.242

0.283

0.237

0.211

0.217

0.187

0.171

0.156

0.138

0.129

β/Φ’ = 0.4














α =

+20°


α =

+10°


α =


α =

-10°


Φ’            δ

20°

δmax

20°

δmax

20°

δmax

20°

δmax

10

0.843

--

0.773

0.799

--

0.738

0.753

--

0.699

0.703

--

0.654

15

0.767

--

0.676

0.707

--

0.631

0.646

--

0.581

0.582

--

0.526

20

0.693

--

0.588

0.621

--

0.537

0.549

--

0.481

0.475

--

0.42

25

0.622

--

0.508

0.541

--

0.454

0.462

--

0.396

0.383

--

0.333

30

0.554

0.452

0.436

0.467

0.393

0.381

0.384

0.33

0.322

0.304

0.266

0.26

35

0.49

0.402

0.37

0.399

0.338

0.317

0.315

0.273

0.259

0.236

0.209

0.2

40

0.428

0.355

0.31

0.336

0.288

0.26

0.253

0.222

0.205

0.179

0.16

0.151

β/Φ’ = 0.8














α =

+20°


α =

+10°


α =


α =

-10°


Φ’            δ

20°

δmax

20°

δmax

20°

δmax

20°

δmax

10

0.94

--

0.891

0.887

--

0.845

0.834

--

0.797

0.78

--

0.746

15

0.895

--

0.827

0.82

--

0.763

0.747

--

0.698

0.673

--

0.631

20

0.842

--

0.758

0.748

--

0.681

0.659

--

0.605

0.571

--

0.526

25

0.783

--

0.685

0.674

--

0.6

0.572

--

0.516

0.474

--

0.431

30

0.719

0.627

0.611

0.598

0.532

0.521

0.488

0.44

0.433

0.385

0.351

0.346

35

0.651

0.569

0.537

0.522

0.466

0.445

0.409

0.37

0.356

0.305

0.279

0.271

40

0.581

0.509

0.463

0.449

0.402

0.373

0.334

0.304

0.287

0.234

0.216

0.206

Φ’

β

0

10°

15°

20°

25°

30°

35°

40°

10


0.704

0.732

0.97

--

--

--

--

--

--

15


0.589

0.602

0.653

0.933

--

--

--

--

--

20


0.49

0.498

0.523

0.582

0.883

--

--

--

--

25


0.406

0.41

0.424

0.453

0.514

0.821

--

--

--

30


0.333

0.336

0.344

0.36

0.389

0.447

0.75

--

--

35


0.271

0.273

0.277

0.287

0.302

0.329

0.382

0.671

--

40


0.217

0.218

0.221

0.227

0.235

0.249

0.273

0.32

0.587

Φ’

Kp

10

1.42

15

1.7

20

2.04

25

2.46

30

3

35

3.69

40

4.6

Category

Types of rock or soil

Presumed allowable
bearing value (kN/m²)

Remarks

Rocks

Strong igneous and gneissic rocks in sound condition

Strong limestone or strong sandstone

Schists and slate

Strong shale, mudstone and siltstone

10000

4,000

3,000

2,000

These values are based on the assumption that the foundations are taken down to unweathered rock. For weak, weathered and broken rock, see BS8004

Non-cohesive

Dense gravel or sand & gravel

Medium dense gravel or sand & gravel

Loose gravel or sand & gravel

Compact sand

Medium dense sand

Loose sand

>600

<200-600

<200

>300

100-300

<100
(depends on looseness)

Width of foundation not less than 1m. Groundwater level assumed to be a depth not less than the base of the foundation. For effect of relative density and groundwater level see BS8004

Cohesive




Very stiff boulder clay and hard clay

Stiff clay

Firm clay

Soft clay or silt

300-600

150-300

75-150

<75

Susceptible to long-term consolidation settlement (see BS8004). Soil consistencies as defined in BS8004.

Effective line load of roller (kN/m)

5

8

10

20

Horizontal earth pressure (kN/m²)

8

10

11

16

Note: For vibratory rollers, if better information is not available the effective line load may be taken as twice the dead load of the roller.