A N Beal EARTH RETAINING STRUCTURES - …

1 A N Beal EARTH RETAINING STRUCTURES - worked examples1 worked examples of RETAINING wall design to BS8002 The following worked examples have been prepared to illustrate the application of BS8002 to RETAINING wall design . They are not full detailed calculations such as might be prepared for a real wall design but are limited to the calculation of EARTH pressure and bearing capacity, showing how the recommendations of BS8002 are applied in practice. BS8002 introduces radical changes in the design of RETAINING walls. Traditionally, the forces applied to a wall have been calculated using representative values of key parameters such as soil strength and then safety and satisfactory service performance are ensured by applying suitable safety factors to the results of the calculations.

2 BS8002 takes a completely different approach: there are no formal safety factors and instead safety and satisfactory performance in service are ensured by using applied forces and soil strengths which are conservative estimates, in order to produce what is effectively a 'worst case analysis. To assist understanding of the changes introduced by BS8002 and how they affect design , in the examples each wall is first designed in accordance with the traditional method (CP2) and it is then designed again in accordance with BS8002 and the results are compared.

3 It is hoped that this will assist engineers changing over to the new Code, by letting them see how the new design method works and also giving them some feel for how it compares with past practice. A N Beal EARTH RETAINING STRUCTURES - worked Concrete = 4m, RETAINING compact medium sand, no water DesignNo 2,Table 3 Soil properties (Table 2) compact sand: = 35 -40 , loose sand = 30 -35 ;assume = 35 Density = 19kN/m3Cl friction = 20 Table 1 Active EARTH pressure coefficientKa = overturning stability, the load resultant in a gravity wall must be kept within middle third of wall; a safety factor of 2 against sliding is required1500mm thick wallConsider base moments about wall centre line (all forces kN/m)PWlaMActive pressure Pan 19 4 weight -wall friction 35 tan20 eccentricity = = , middle 1/3 limit = = < OKPeak ground bearing pressure = )(1+( ))= 199 Minus overburden- - 11 Peak net ground bearing pressure188kN/m Table 8 Allowable net bearing pressure = 2-4t/ft = 215-430kN/m 188 < 215kN/m OKCl.

4 : base friction = tan35 . Sliding force = 35kN/m, resistance = = Safety Factor = = (Note: passive resistance also from soil in front of wall.)F of S = > 2 OK1500mm thick wall OKCP2 DesignConsider with 10kN/m surcharge with WlaM1750mmActive pressure Pan 19 4 weight -wall friction (35+ ) tan20 eccentricity = = 1/3 limit = < OK1750mm thick wall OKA N Beal EARTH RETAINING STRUCTURES - worked examples3BS8002BS8002 DesignTable 1 Dense medium sand, moderate grading: density = Assume sub-angular soil particles, SPT N = 20 at 3m depthCl A = 2 , B = 2 , Fig. 2 Overburden pressure = = : N /N = Table 3so N = 20=34, so C = max = 30+2+2+ max tan max crit = 30+2+2 crit 34 tan crit friction = 20 Cl.

5 design tan = tan max/M or tan crit. = or tan = (M = ) design = Cl. tan = tan 20 or tan = or tan = tabledesign = , design = 20 Ka = A10kN/m surcharge on retained soil behind 1400mm thick pressure= self weight = friction= eccentricity e = e = bearing pressure at toe = + - = 263kN/m . Dense sand, allowable pressure = 600kN/m 263 < 600 kN/m OKUltimateCheck ultimate allowable bearing pressure to CIRIA C516 Base effective breadth B = - 2 = Average bearing pressure = = Bearing capacity = q Nqiq + B N i Horizontal/Vertical FH/Fv = design = iq = (1 - FH/Fv) = , i = (1 - FH/Fv) = design = Nq = , N = , q = = Bearing cap.

6 = + > OKCl. ,Sliding: base coefficient of friction = tan crit or ( design tan ) or Vert. load x friction = = force = , < OKCase BUnplanned excavation in front of wall but no surcharge behind. Depth of excavation = 10% of clear height of wall = pressure= weight = friction= pressure at toe = + = 220 < 600 kN/m OKA N Beal EARTH RETAINING STRUCTURES - worked examples4 UltimateLoad eccentricity = = breadth B = - 2 = Bearing pressure = = Bearing capacity = q Nqiq + B N i FH/Fv = design = iq = , i = , q = = Bearing capacity = + = < kN/m OKCl.

7 , Sliding force = = = < OKCase A (surcharge) is critical, 1400mm thick wall If there is a 10kN/m2 surcharge behind the wall, BS8002 requires a thinner wall than CP2 (1400mm thick compared with 1750mm). However if there is no surcharge, the two codes give similar results (BS8002: 1400mm, CP2: 1500mm), because BS8002 requires a surcharge to be considered in all cases. (If the wall designed for surcharge to BS8002 is checked to CP2, the calculated load eccentricity on the foundation is , approximately on the edge of the middle half of the section, rather than the middle third.)

8 A N Beal EARTH RETAINING STRUCTURES - worked Mass concrete wall as but with water behind wall (Assume soil below base of wall has low permeability; assume water table at front of wall is at ground level. Assume head of water at front of wall varieslinearly between 0 and andat back between 0 and )CP2CP2 DesignTable 3 Buoyant density of soil = 11kN/m No surchargeTry 3000mm thick MthickActive pressure 19 19 11 pressure weight -Wall friction ( + + )tan20 uplift (1) (2) Load eccentricity = = middle 1/3 limit = 3000/6 = e= < OKPeak bearing pressure = ( )x(1+6 ) = Table 8 Allowable pressure (submerged) = 1-2t/ft = 107-215kN/m say OK Sliding.

9 Force = base friction resistance = = passive resistance + water pressure in front of wallKp = Pp = 11 + = + = total resistance = + = Cl. S against sliding = = > 2 OKA N Beal EARTH RETAINING STRUCTURES - worked examples6 SurchargeConsider with 10kN/m2 surcharge behind wallCP2CP2 DesignTable 3 Buoyant density of soil = 11kN/m 3300mmTry 3300mm thick Mactive + water pressure friction( + + + )tan20 uplift (1) (2) Load eccentricity = = middle 1/3 limit = 3300/6 = < OKPeak bearing pressure = ( )x(1+6 ) = Table 8 Allowable pressure (submerged) = 1-2t/ft = 107-215kN/m say OK Sliding.

10 Force = base friction resistance = = passive resistance + water pressure in front of wallKp = Pp = 11 + = + = total resistance = + = Cl. S against sliding = = > 2 OKWith surcharge, 3300mm thick wall requiredA N Beal EARTH RETAINING STRUCTURES - worked examples7BS8002BS8002 DesignTable 1 Soil saturated density = kN/m ; buoyant density = = Assume variation of water pressure below wall same as CP2 example . Case A surcharge 10kN/m 2900mmthick wallServiceabilityPressure under toe = + = UltimateLoad eccentricity = = B = - 2 = effective bearing pressure = = Bearing capacity = q Nqiq + B N i FH/Fv = = (1 - FH/Fv) = = (1 - FH/Fv) = = Nq = , N = , q = = Bearing capacity = + 37 = kN/m > OKSliding.