Scope This sheet calculates maximum design actions (M*, V*) and the associated capacities of concrete sleepers and steel posts in a retaining wall structure. It also calculates the lateral capacity of the short pile (bored pier) foundation and its adequacy in withstanding the forces exerted by the retained soil. General Notes The sheet has 3 main output outcomes:
  • Sleeper Design: Structural adequacy of the sleeper member based on deflection and moment criteria from forces caused by retained soil. The sheet does calculations for both single and double sleeper layers
  • Post Design: Structural adequacy of the steel post based on moment and deflection criteria caused by retained soil
  • Post Foundation Design: Adequacy of footing depth to resist lateral and overturning action of retained soil on the retaining wall, provided the foundation is still considered a rigid pile according to Brom’s Method.
Information/inputs required from the user:
  • Retaining Wall Geometry
    • Selected member for timber sleeper member
    • Selected member for steel post
    • Spacing of steel posts, cts
    • Retaining wall height from ground level of the retained soil, H. Total height of the wall is expected to be a multiple of the depth of the sleeper, which is checked by the total layer of sleepers. If sleepers need to be cut, the number of sleeper layers will display an error check.
    • Risk Classification (A,B,C) according to AS4678, relevant to the impact of failure of the retaining structure
    • Total layers of double sleepers, ndouble. If double sleepers are not considered in the design, a number of 0 is used. Otherwise, an integer value is input, and is assumed to be stacked at the bottom of the retaining wall to resist the critical forces of the retained soil.
  • Backfill (retained soil) properties
    • Condition of soil (controlled/uncontrolled fill or in-situ material as per AS1289) in order to account for on-site uncertainties
    • Effective friction angle, Ï• of the retained soil. Derived from the Mohr-Coulomb failure criterion and describes the shear strength of soil
    • Soil incline, β of the retained soil.
    • Soil unit weight, γ
    • Cohesion of backfill soil, c’. Based on the Mohr-Coulomb failure criterion, cohesion of the backfill is the drained shear strength determines the ability of the soil to stand upright without lateral compressive support
    • Poisson’s ratio of backfill soil, ν. Based on Terzaghi theory for cohesive soils, if the soil is at rest, the at rest pressure of a cohesive soil is a function of its Poisson’s ratio. See below for typical values for Poisson’s ratio.
  • Footing and footing soil properties
    • Condition of soil (controlled/uncontrolled fill or in-situ material as per AS1289) in order to account for on-site uncertainties
    • Footing depth, df. User is to input a footing depth for trial and error calculation to determine the resistance to lateral forces
    • Footing diameter, ⊘. Each post is founded on a concrete bored pier, user is to specify the diameter of footing to resist lateral forces
    • Footing soil effective friction angle, Ï•f. Derived from the Mohr-Coulomb failure criterion and describes the shear strength of soil
    • Soil unit weight, γf
    • Undrained shear strength of soil at footing, Suf. Soil is assumed to be undrained at footing, therefore the value can be determined from a CU test as (σ1-σ3)/2
    • Cohesion of soil at footing, c’f. Based on the Mohr-Coulomb failure criterion, cohesion of the footing is the drained shear strength and determines the ability of the soil to stand upright without lateral compressive support
    • Modulus of horizontal subgrade reacton, k
  • Surcharge load (live loads). A minimum design surcharge load is assumed from AS4678 depending on the classification of the structure and the incline of the retained soil.
Assumptions and Limitations
  • The retaining wall is assumed to be vertical, further calculations in future will incorporate wall slope toward the soil
  • Conventional retaining wall analysis for sliding and overturning is condensed into a single computation due to the non-trivial analysis of the bored pier foundations idealised as short, rigid piles by Brom’s Method. This can be inspected through the equation for lateral capacity that incorporates the eccentricity of the loads applied to the wall
  • This sheet idealises the sleepers as simply supported members, where the soil acts as a line load across the beam on its weak axis. Deflections and moments are calculated under that assumption. Sleepers (wales) are not to be cantilevered beyond the post locations
  • This sheet idealises the steel post as a fixed cantilever, fixed at the ground level and cantilevered upwards. The lateral load due to soil is idealised as a dead load linearly decreasing line load acting from the fixed end and a live load as a UDL along the cantilever for deflection calculations
  • Lateral earth pressures are assumed to follow Rankine theory for lateral earth pressures. Friction due to contact surface between soil and wall is disregarded. Additionally, user may specify to use at-rest earth pressures for a more conservative calculation if required.
  • The bored pier foundations are assumed to be idealised as short, rigid, free-head piles under Broms theory of laterally loaded pile foundations (1964). As such, the following assumptions and limitations are necessary
    • Failure mechanism is solely due to failure due to soil lateral capacities versus the applied load due to the retained soil. Therefore, plastic hinge due to pile deformation does not form, and failure of the pier material is not considered
    • Soil is assumed at worst case and is at maximum deflection/rotation of the pile as a rigid body
    • Broms theory applies differently in cohesive versus non-cohesive soils. Cohesion of soil at footing determines which formulas are used. (0 cohesion implies granular, cohesionless soils, and > 0 cohesion implies cohesive soils).
    • Broms theory makes use of undrained shear strength of soils, which is not always equal to the cohesion of soil. Judgement is required on the part of the engineer to determine the adequate input values
    • Since the bored pier is idealised as short, rigid piles in Brom’s method, only effectively short piles can be used in this analysis. Therefore, footing depth and footing diameter combinations are checked in accordance with this criteria. Longer piles that fail in flexure require a different analysis
    • Ground surface deflection relies on the digitisation of Brom’s ground surface deflection charts, therefore there are some conditions where the deflection criteria is not specified (i.e. if the eccentricity of load is too high compared to the depth of the footing in a cohesive soil).
  • Typical values of soil strength can be found below for undrained shear strength of clays, or cohesion and angle of friction for sands Table 1: Soil strength properties (source: Typical Shear Strength Values, GEOTip)
    Undrained Shear StrengthSu(kPa)
    Solid silty clays / oily silts (oc)Su> 150 kPa
    Stiff silty clays (oc)Su = 75 ~ 150 kPa
    Soft-stiff silty clays (oc)Su = 40 ~ 75 kPa
    Soft silty clays / tonic silts (nc)Su = 20 ~ 40 kPa
    Pulpy silty clays / tonic silt (nc)Su <20 kPa
    Drained shear strengthC ‘[kPa]Φ ’[°] (φ’ cv - φ ’ max)
    Dense quartz sand035 ° - 45 + °
    Loose quartz sand033 ° - 35 °
    Mica in sand fraction025 ° - 31 °
    Feldspar in sand fraction037 ° - 45 °
  • The dead loads due to retained soil is assumed to be linearly increasing toward the ground level, therefore is applied at an eccentricity of a third of the height of the retaining wall from the bottom
  • The live loads due to surcharge is assumed to be a UDL, therefore applied at an eccentricity of half the height of the retaining wall when resolved
  • Typical soil elastic properties may be found from below at the user’s discretion Table 2: Soil elastic properties (source: Bowles 1996)
    Poisson’s ratiov
    Mostly Clay Soils0.4 to 0.5
    Saturated Clay Soils0.45 to 0.5
    Cohesionless, medium and dense0.3 to 0.4
    Cohesionless, loose to medium0.2 to 0.35
  • Typical approximated values for modulus of subgrade reaction kh can be found below in MN/m−3\text{MN/m}^{-3}
Table 3: Approximate values of the increase of kh lateral subgrade reaction with depth (source: Adapted from Sulzberger (1927) taken from Bowling (2011)
Type of soilUSCRange of k in MN m^(-3)
Light peat and boggy soilPt3 - 5
Heavy peat, find loose sandPt & SP5 - 8
Rubble, poorly compactedGP5-10
Wet ClayCL to CH10 - 15
Damp Clay20 - 25
Dry Clay30 - 50
Sand Clay with some GravelSC to GC40 - 50
Sand Silt Gravel MixSW to GM50 - 60
  • Typical values from Terzaghi (1955) for cohesionless soil for nh horizontal subgrade reaction in MN/m−3\text{MN/m}^{-3}
Table 4: Typical values of Coefficient of Horizontal Subgrade Reaction Terzaghi (1955)
ConsistencyLoose (N between 4 - 10)Medium to Dense (N between 11 - 30)Dense (N between 31 - 50)
Dry to Moist Sand2.26.617.6
Submerged Sand1.34.410.7
References AS1720.1-2010 – Timber Structures AS4100-1998 – Steel Structures AS4678-2002 – Earth Retaining Structures Bell (1915). The Lateral Pressure and Resistance of Clay and the Supporting Power of Clay Foundations Bond A. J., Schuppener B., Scarpelli G., Orr T. L. L. (2013). Eurocode 7 – Geotechnical Design Bowles J. E. (1996) Foundation Analysis and Design (5th Edition). McGraw Hill Broms (1964). Lateral Resistance of Piles in Cohesionless Soils Geotechnical Engineering Office of Civil Engineering and Development Department of The Government of the Hong Kong Special Administrative Region (2006). Foundation Design and Construction GEOTip (2017) Typical Shear Strength Values. Retrieved from http://geotip.igt.ethz.ch/index.php?&gfield=knowledge&gmenuleft=blocs&gopennodes=4\_43\_46&gblocid=223&PHPSESSID=01n86ctd7qnbo419v4k9i2dsk3s Hubbell Inc. (2003). Helical Screw Foundation System Design Manual for New Construction Ivey D. L. (1966). Signboard Footings to Resist Wind Loads Ohi S. J. & Abedin M. Z. (2012). Use of Brom’s Charts for Evaluating Lateral Load Capacity of Vertical Piles in Two Layer Soil System. OneSteel (2014). Seventh Edition Hot Rolled and Structural Steel Products Poulos H. G. & Davis E. H. (1980). Pile Foundation Analysis and Design Teymur B. (2016). Lateral Earth Pressures and Retaining Walls Wood Products Victoria (2009). Structural Timber: Products Guide