This article aims to compare different methods for calculating the embedment depth of piles subjected to horizontal loads from sleeper retaining walls. In the first section, semi-empirical methods will be compared. In Section 2, the results obtained through the ClearCalcs sleeper retaining wall calculator will be compared with design guides from the manufacturers Tuff Ozy and Nuway.

1 - COMPARISON OF SEMIEMPIRICAL METHODS

1.1 Methods Analysed

The following semi-empirical methods are compared against ClearCalcs approach:

• HOSKING, A. K. Applied Structural Design, 1993
• Australian Standards AS/NZS 4676:2000 Appendix I - Structural design requirements for utility service poles (deprecated)
• 2021 International Building Code (IBC), Section 1807.3.2.1. (United States)

ClearCalcs uses the BROMs method for the calculation of strength and soil deflection calculations

See BROMS, B. The lateral resistance of piles in cohesive soils, Journal of the Soil Mechanics Division, American Society of Civil Engineers, Vol. 90, No. SM2, March 1964, pp. 27–63

1.2 - Scope of Review

Within Scope:

• Embedment Depth Checks based on Soil Plastic Bearing Capacity
• Static Loading (Wind & Earth Pressure) is converted to equivalent shear & moments applied at the top of pile.

Out of Scope:

• Magnitude of soil movement and any serviceability concerns (e.g. ratcheting effect causing non-elastic behaviour with repeated loads, deflection)
• Loading (Wind & Earth Pressure) and Beam Statics above the top-of-pile are not available on the alternate methods.
• Moment & Shear Capacity of Post, Pile or Sleeper.

1.3 Parameters and Assumptions

• The horizontal loads (H*) and bending moments (M*) on the top of the piles are calculated for a retained height of 1000 mm, 1400 mm and 2000 mm, and pile spacing of 1500 mm.

• The pile diameter is 450 mm in all cases and the pile is assumed rigid for the distribution of loads on the soil, with a free head (top of pile is allowed to rotate).
• Rankine equation is used to calculate the forces due to earth pressure and surcharge. See AS 4678:2002 Figure E2 for details. The retained soil is assumed to have no cohesion (worst case).
• To determine the loading applied to the top of pile for each method, the H and M forces have been calculated using ClearCalcs calculators, and used consistently with all other methodologies for the pile design. The assumptions used for ClearCalcs loading is available in our calculator e.g. AS 4678:2002 is used for the uncertainty factors, the applied surcharge for height ≤ 1500 mm = 2.5 kPa and for greater heights = 5 kPa.
• No groundwater table is present for comparison, although ClearCalcs does allow for considering ground water effects.
• Controlled backfill (Class I) is flat, although ClearCalcs does allow sloped backfill.

H and M forces have been calculated by using ClearCalcs calculators, and used consistently with all other methodologies for the pile design.

The parameters adopted for the foundation soil are shown in the following table.

• ClearCalcs requires the foundation soil (adjacent to pile) to have an Undrained Shear Strength (soil cohesion) = Su or Cu, whereas some comparison methods take the Effective Cohesion c'.
• To provide an accurate comparison of drained and undrained strengths, estimates per AS 4678:2002 (Table D1 and D4) and AS 1726:2017 (Table 11) respectively are used.
• The method proposed by the IBC (2021) uses the allowable vertical bearing capacity, which is estimated according to Table 1806.2 of this standard. Please note this comparison is difficult to precisely correlate, therefore the comparison with IBC should be taken as for information only.
• In-situ soil has been chosen for the comparison. This affects the Uncertainty Factors for strength & serviceability Φuc and Φuϕ per Table 5.1(B) AS 4678:2002.

1.4 Results

The graphs below show the results of pile embedment length for 1 to 2 m height sleeper retaining walls, in soft, firm and stiff clay.

2 - COMPARISON WITH DESIGN GUIDES

2.1 Reference Manuals

The ClearCalcs Sleeper Retaining Wall Calculator is compared with Tuff Ozy and Nuway technical design guides. Tuff Ozy and Nuway have different parameters and assumptions for designing a typical sleeper retaining wall, hence the comparison will be carried out in different sections.

2.2 Tuff Ozy

2.2.1 Parameters and Assumptions

IMPORTANT: According to Cl. 1.2.2 (AS4678:2002) when the retaining height is >1500 mm, the structure is considered Class B and the minimum surcharge should be 5 kPa (Table 4.1 AS 4678:2002). However, Tuff Ozy & Nuway always consider 2.5 kPa. A surcharge of 2.5 kPa will be assumed in this comparison, although ClearCalcs will follow the minimum surcharge by default.

• SECTION 2.2: 100UC15 posts are to be cast into bored piers of 400mm minimum diameter and 150UC23 posts are to be cast into bored piers of 450mm minimum diameter.

• SECTION 2.3: Footings are to be cast in a minimum of N25 concrete, with 100mm minimum cover to post :
• SECTION 2.4:
  • Wind Region = B
  • Terrain Category = 2
  • Importance Level = 1
  • Design Life = 50 years - Equivalent to N3
  • It is assumed general zone

• SECTION 2.5: Backfill behind the retaining wall is to be placed as Controlled Fill – Class 1 as specified in AS4678 ‐2002. Both retained and foundation soil is assumed to be the same material.

• It is unknown if a reduction due to effective cohesion of retained soil is considered in Tuff Ozy analysis, the comparison will be carried out adopting no cohesion and also allowing c' = 2.5 and 7.5 kPa for soft and stiff clay, respectively, based on AS 4678:2002 Table D1 values.
• SECTION 2.6: designed to structure classification ‘A’ in accordance with AS4678 ‐2002. As such, a surcharge load of 2.5kPa acting at the top of the wall has been allowed for.

• SECTION 2.7: The design graphs in section 5.0 of this brochure have made no allowance for hydrostatic loads (e.g. water pressure). As such, it is imperative that the wall builder implements an appropriate and effective drainage system behind the wall.
• A post spacing of 1.5 m will be considered.

Limitations

• SECTION 2.2: Sleeper retaining walls within this brochure are not permitted to be installed within 1km of the coastline, or a large body of salt water.
• SECTION 2.4: General Zone: A maximum 1800 high fence that is further than 3.6m away from a free end may be installed on top of the wall. Fence posts located within this ‘general zone’ are subjected to only half the wind pressure of those within the ‘end zone’.
• SECTION 2.4: Please note that this design guide does not cover fences within cyclonic areas.
• SECTION 2.8.3: The design graphs in section 5.0 of this brochure have made no allowance for a battered backfill (refer Figure 4 in section 5.0).

2.2.2 Results

The graphs below show the comparison of pile embedment length for 0.5 to 2 m height sleeper retaining walls, in soft and stiff clay. The post spacing is 1.5 m.

We also compared the results of embedment lengths when the retained height is above 2 m, not usual for sleeper retaining walls.

2.3 Nuway

2.3.1 Parameters and Assumptions

• SECTION 4.4.1: Same soil type is used for both backfill and subgrade embedment.
• SECTION 5: Soil parameters: Soft clay - density = 18 kPa, cohesion = 18 kPa; Stiff clay - density = 20 kPa, cohesion = 75 kPa.
  • Nuway doesn't specify the angle of internal friction for clay. Similarly to Tuff Ozy, it will be assumed 25 kPa for soft and stiff clay, respectively.
  • It is unknown if a reduction due to effective cohesion of retained soil is considered in Nuway analysis, the comparison will be carried out adopting no cohesion and also allowing c' = 2.5 and 7.5 kPa for soft and stiff clay, respectively, based on AS 4678:2002 Table D1 values.
• SECTION 5: Backfill behind the retaining wall is placed in a manner that is consistent with Controlled Fill - Class 1
• SECTION 6: _ The post holes shall be of a minimum diameter of 400mm or 450mm with a minimum 100mm concrete cover. _This comparison will consider 450mm. _
• SECTION 7: The retaining walls specified in this document have been designed based on a 2.5kPa surcharge load in accordance with AS4678-2002.
• SECTION 12:
  • Maximum Fence Height: 1.8m
  • Wind Region B to AS/NZS1170.2-2011
  • Terrain Category 2
  • N2 Wind Rating
  • It is assumed general zone
• SECTION 13: The subgrade into which the posts are to be placed is in an undisturbed natural state during the construction of the retaining wall.
• For a retained height up to 2m, Nuway limits the post spacing to 1.2m, in soft clay, with a fence. This spacing will be adopted for this analysis, for all cases.

2.3.2 Results

The graphs below show the comparison of pile embedment length for 0.5 to 2 m height sleeper retaining walls, in soft and stiff clay. The post spacing is 1.2 m.

3 - CONCLUSIONS

Section 1: Comparison of Semi-Empirical Methods

In the first section of this article, semi-empirical methods were compared by calculating the pile embedment based on equivalent input parameters and assumptions. Broms method, which is used by ClearCalcs, generally resulted in shallower piles, except when compared with the procedure in the deprecated AS/NZS 4676:2000.

IBC 2021 typically used in Table 1806.2 considers different soil parameters to Australian methods. An assumption has been made for bearing strength based on clay stiffness. This comparison should be taken for information only, as it is difficult to correlate the differing methods:

• Soft Clay: 2000 psf (equivalent to 96 kPa)
• Firm Clay: 3000 psf (equivalent to 144 kPa)
• Stiff Clay: 4000 psf (equivalent to 192 kPa)

AS/NZS 4676:2000 uses Table I1 to estimate the bearing strength of soil; this table allows a big range of soil types (clay, silt, sand and gravel), not specifically for clay. Therefore, the following assumptions are made:

• Soft Clay: 60 kPa
• Firm Clay: 100 kPa
• Stiff Clay: 150 kPa

Section 2: Comparison with Design Guides

The minimum pile embedment typically showed a good correlation between Tuff Ozy and Nuway and ClearCalcs. The values are similar when cohesion of backfill (retained soil) is allowed. The design guides offer simplicity in determining the pile embedment, however, they do not allow flexibility in design. It is important to mention that both design guides consider 2.5 kPa as a surcharge when the retained height is above 1.5m, which does not comply with the AS4678:2002: 5 kPa should be allowed for a Class B retaining wall if the backfill is flat.

When compared with Tuff Ozy, ClearClacs method resulted in longer piles in soft clay and very results in stiff clay with a 1.8 m fence. In a stiff clay when no fence is present, ClearCalcs resulted in shorter piles.

Nuway recommends deeper piles in soft clay when the retaining height is less than 1.5 m and shallower values when above this value. In stiff clay, ClearCalcs calculates less pile embedment when no fence is present, and similar results when a 1.8 m fence exists.

For further questions or feedback on the methods & assumptions in this article, contact hello@clearcalcs.com.