This document discusses the use of hand calculations versus computer programs for sheet pile wall design. It analyzes 8 design examples comparing hand solutions to computer solutions. Key lessons learned include the importance of cantilever wall design, different methods for selecting factors of safety, challenges with determining earth pressures for sloped backfills, issues with cohesive soil designs producing large embedment depths, and limitations of using Terzaghi-Peck pressure diagrams to determine braced wall member forces. While computer programs make design faster, hand calculations provide better understanding of design details that programs often omit.

1. ARE HAND CALCULATIONS STILL USED?
StanVitton, P.E., Ph.D.
Professor
Department of Civil & Environmental Engineering

2. Are Hand Calculations Still Used?
■ Motivation
■ Sheet PileWall Designs
■ Lessons Learned?? – “The devil is in the detail”
■ Conclusions

3. Motivation
■ Civil Engineering Senior Class Design Projects
■ Minimal background in sheet pile wall design
■ DOT developing a sheet pile wall design manual & training course
 Eight problems – comparing hand solutions to computer solutions
 SupportIT© (GTSoft Ltd - United Kingdom of Great Britain)
 SPW511© (Pile Buck International, Inc. – Florida,USA)
■ Should be a good learning experience, i.e., I’m not an expert in sheet pile design!

4. Sheet PileWall Designs:
Using Limit Equilibrium Methods
8 - Design Examples:
■ Cantilever – Level Backfill - Granular
■ Cantilever – Sloped Backfill – Granular
■ Cantilever – Level Backfill - Cohesive
■ Anchored – Level Backfill – Granular
■ Anchored – Level Backfill – Cohesive
■ BracedWall – Level Backfill – Granular
■ BracedWall – Level Backfill – Cohesive
■ Cantilever SoldierWall - Granular
Soils:
■ Granular  = 32°
■ Cohesive: c = 1,500 psf

5. Reference Sources:
■ Started With:
 USS Steel Sheet Piling Manual – 1984 edition
 California DOTTrenching & Shoring Manual – 1990 revised 1996
 I wish I had used the 2011 Edition
 Foundation Engineering Design Books:
 Terzaghi (1948),Teng (1962),Tschebotarioff (1973 rev), Jumikis (1971), Peck et al. (1953, 1973),
Coduto, 2nd & 3rd Editions (2015)
■ Ended with the following references in attempting to match hand calculation to computer solutions:
– Deep Excavation:Theory and Practice - Chang-Yu Ou (2006)
– Embedded retaining walls: guidance for economic design – CIRIA C580 London (2003)
– Piling Handbook 8th Edition Arcelor RPS Group (This follows the 7th British Piling Handbook)

6. Lessons Learned?
1. Importance of cantilever sheet pile wall design!
2. Conventional cantilever design versus Simplified cantilever design??
3. Selection of Factor of Safety (FOS)??
4. Earth pressure determination for sloped backfill??
5. Cohesive Soils – these soils can stand on their own - so how high can they stand??
6. Braced wall design – correct use of theTerzaghi-Peck Pressure Diagrams??

7. 1. Importance of cantilever wall design!
Cantilever wall design: Anchor wall design:
Braced wall design: Soldier pile wall design:

8. 2. Conventional cantilever method vs
Simplified cantilever method??
USS Steel Sheet Piling Manual (1984 edition) Figure 15 (afterTeng, 1962)
Convention Method (net
pressure)
Simplified Method (gross
pressure)

9. “The simplified method is useful in the initial design of
cantilever sheet piling in homogeneous granular soils, but
the conventional method must be used for finial analysis.”
California DOTTrenching & Shoring Manual – 1990 revised 1996
Note: Not from the 2011 edition
OK BUT!!!
1. What about solving for multiple soil layers, e.g., clay and sand layers?
2. Adding addition loads – surcharge, line loads, foundation loads, etc.?
3. What about ending up with two complex equilibrium equations that
gives Matlab a hard time solving?

10. BracedWall : Staged Construction – Final Stage Example:

11. Development of the simplified method:
■ According to Oy (2006), the simplified method has been commonly adopted in
engineering design; referencing - Padfield and Mair (1984)
■ SupportIT© and SWP511© use the simplified method for analysis.
■ Who developed the simplified method?
– USS Sheet Pile Manual referencesTeng (1962)??
– Teng (1962) doesn’t provide a reference (not listed in the author index)
– Terzaghi (1943) references Blum 1931, 1936
– Tschebotarioff (1951, 1973) references Blum 1931, 1936
– Jumikis (1973) references Blum 1931, 1936
■ Who is Blum (1931, 1936)?

12. 1.20  = 40°
 = 20°
What about  = 0°
German
1931 Doctoral Dissertation

13. 3. Selection of Factor of Safety (FOS)??
1. Increase the embedment length, Do, by 20 to 40%
2. Decrease the passive resistance by a factor of safety or Kp = Kp/FOS.
3. Gross pressure: Mpassive/Mactive = FOS
4. Net Pressure: Mpassive/Mactive = FOS
5. Burland-Potts: Applies the FOS to the net available passive resistance
6. Adjust soil strength:  𝑟𝑒𝑑𝑢𝑐𝑒𝑑 =
′
𝐹𝑂𝑆
; 𝑐′ 𝑟𝑒𝑑𝑢𝑐𝑒𝑑=
𝑐′
𝐹𝑂𝑆
There are at least six difference methods to apply a FOS to a sheet
pile design problem.
According to Burland & Potts (1981),These methods can lead to widely differing levels of safety with
respect to shear strength for a variety of conditions and sometimes gives illogical results.The present
position is clearly thoroughly unsatisfactory. Note: this statement is referring mostly to the analysis of
low strength soils, e.g.,   20°to 0.

14. 4. Earth pressure determination for
sloped backfill with wall friction??
■ Use Rankine and Coulomb for level backfill – smooth wall (no wall friction) – and assuming
plane failure surfaces - OK!
■ For sloped backfill with wall friction – use: Log-Spiral method or Caquot-Kersiel method
USS Sheet Pile Manual:
Example #1
Note:
Includes wall friction:
/ = -0.5

15. USS Sheet Pile Manual:
Figure 5a (Caquot-Kersiel chart)
 = 35° & / = -0.5
Kp’ = about 10
Kp = Kp’ x Rd
Kp = ~10 x 0.674  6.7
Close to Kp = 6.56 OK!
Coulomb (no friction):
Kp = tan2(45 – (35/2)°) = 3.70 !
A significant difference!
SupportIT© uses European Code 7 (1995):
𝐾ℎ = 𝑐𝑜𝑠2
𝛽.
1 + sin ∅′
sin (2𝑚 𝑤 + ∅′
1 − sin ∅′ sin(2𝑚𝑡 + ∅′ )
. exp 2𝜈 𝑡𝑎𝑛∅′
𝑚𝑡 =
𝑐𝑜𝑠−1
−
sin 𝛽
sin ∅′ − ∅′
− 𝛽
2
𝑚 𝑤 =
𝑐𝑜𝑠−1 sin 𝛿
sin ∅′ − ∅′
− 𝛿
2
𝜐 = 𝑚𝑡 + 𝛽 − 𝑚 𝑤
 = 35°

16. 5. Cohesive Soils: For soft soils why do I get such
large embedment depths?And for stiff soils how
high can the soil stand unsupported??
■ The problem Su (undrained shear strength, c) is “assumed” constant with depth,
while ground pressures increase along with Ka = Kp. For soft clay limit equilibrium
methods produce excessive embedment depths.
■ Critical Height?Assuming  = 0°
Hc
𝐻𝑐 = 𝟒
𝑺 𝒖
𝜸
Terzaghi (1943)
𝐻𝑐 = 𝟑. 𝟖𝟓
𝑺 𝒖
𝜸
Fellenius (1927)
Hc
𝑧 = 𝟐
𝑺 𝒖
𝜸
Tension Crack
intersecting a
potential failure
surface
Tension Crack
𝐻𝑐 = 𝟐. 𝟔𝟕
𝑺 𝒖
𝜸
Terzaghi (1943)

17. Typical Design procedure for cohesive soils
(not considering wall adhesion, Sw,max):
■ Earth pressures: Ka = Kp
■ Utilize a “Minimum Fluid Pressure” acting on the wall”
■ Where ground water is unlikely to be present, an alternative substitution for zero net
pressure in cohesive soils is to assume a pressure due to an equivalent fluid of density
5kN/m³ (Ref: “BSPH (7th Edition)”; “CIRIA Report 104”). 5 kN/m3  31.8 pcf

18. 6. Braced wall design:
■ Calculation of maximum strut loads:
 Terzaghi-Peck Apparent Pressure Diagrams: Peck et al., (1953, rev. 1974):
Peck’s Figure 27.6
Peck’s Figure 27.7

19. Determination of shear and moments in
braced excavation sheeting?
■ Peck et al. (1973 edition) Page 460-461
 “Thus, an apparent pressure envelope represents a fictitious pressure distribution for
estimating maximum strut loads in a system of bracing”
 “It does not, however, indicate the magnitude or distribution of loading on the sheeting or
wales.”
 “No consideration is given in the procedure to the actual continuity of the sheet piles or
soldier piles, because no continuity was assumed when the apparent pressure envelopes
were developed from the measured loads.”
■ While the maximum strut loads can be determined using theTerzaghi-Peck apparent pressure
diagrams, it “appears” that they were NOT meant to be used to determine the maximum
shear and moments in braced excavation sheeting.
 Then why do we use the pressure diagrams to determine shear and moments?
 Most current sheet pile literature recommends against usingT-P apparent pressure to
determine shear and moments in sheeting.

20. Conclusions
■ There are a number of methods for designing sheet pile walls, e.g, FOS, earth
pressure assumption, etc.
■ The “devil’, however, IS in the details. Many design issues are NOT
adequately explained in current sheet pile manuals, making it difficult for
beginning engineers to “understand” how computer programs are conducting
the analysis.
■ And why is sheet pile design always at the end in foundation engineering
books or not included at all?
■ On a positive note – (walking the plank on this one) I realized working on these
problems that the design of sheet pile walls is an excellent topic for teaching
the combination of soil mechanics and structural mechanics. In fact, I would
recommend that sheet pile design be taught “before” bearing capacity of
settlement – splash! Both bearing capacity and settlement analysis utilize
complex theories in understanding the mechanics of the problem. Sheet pile
design is relatively straightforward in its basic mechanics, e.g., effective stress,
summation of forces and moments, although earth pressure theories can be
problematic.