Flexible Retaining Structures and Coffer Dams

A cofferdam is a temporary watertight enclosure built in water-bearing ground (river, lake, sea or wet soil) from which the water is pumped out so that foundations, piers or other structures can be built in dry conditions.

Types, sketches and uses

1. Earthen (and rockfill) embankment cofferdam

   ~~~ water ~~~\
                 \___________
                  /  clay core \
   ______________/______________\____

Used in shallow, slow rivers and low water depth (up to 3 m) for dams and bridge piers.

2. Single-wall (braced) sheet pile cofferdam

   ~~~ water   |sheet|====strut====|sheet|  water ~~~
               |pile |             |pile |
               |_____|  dry area   |_____|

A ring of interlocking sheet piles braced by wales and struts; used for piers and small foundations in water up to about 6-10 m deep.

3. Double-wall cofferdam

   | sheet pile |  sand/gravel fill  | sheet pile |
   |            |  (tied by rods)    |            |

Two parallel sheet-pile walls tied together with a gravel or sand fill between; used for deeper water (up to about 12 m).

4. Cellular cofferdam (circular, diaphragm or cloverleaf cells of steel sheet pile filled with sand/gravel)

    ()  ()  ()   (a row of circular cells joined by arcs,
   (  )(  )(  )   filled with granular soil)

Used for large works, dams, locks and deep water (up to about 25 m); self-supporting without internal bracing.

5. Crib (timber or concrete) and other special types: boxes or cribs filled with stones; used in rocky riverbeds.

Relative merits and demerits

A cofferdam is a temporary enclosure built in water or water-bearing ground, pumped dry to allow construction below water level.

A cellular cofferdam consists of a row of connected cells made of interlocking flat-web steel sheet piles, filled with sand, gravel or rock fill. Cells may be circular, diaphragm (arcs with cross walls) or cloverleaf.

   Plan:  ( )( )( )( )    Section:  | fill |
           circular cells            |      |  ~~~ water
        joined by connecting arcs    |______|    (dry on right)

• The sheet piles act in tension (ring tension) and hold the fill; the filled cell behaves as a gravity wall resisting water pressure by its own weight.
• It is self-supporting, so no internal bracing blocks the working area.
• Stability is checked for sliding, overturning, interlock tension (hoop tension $T = p\,r$), shear along the centre line of the cell, and bearing.
• Uses: piers, locks, dams, deep water work; reusable and quick.

A sheet pile wall is thin and long (slender), with low flexural rigidity $EI$ compared to a gravity or cantilever wall. Under the earth pressure it bends and deflects, mostly in the cantilever or between supports, and it does not move as a rigid body. Its stability depends on bending and the passive resistance of the embedded part and anchors, rather than on its own weight. Therefore it is called a flexible retaining structure.

A sheet pile is a slender, interlocking section of steel, timber or concrete driven into the ground to form a continuous wall that retains soil or water (e.g. in excavations, cofferdams and waterfronts).

Deflected shapes

 (i) Cantilever       (ii) Anchored,       (iii) Anchored,
                          shallow depth        deeper depth
  |  soil side         T o-->|                T o-->|
  |                          |                      |
  |\                         |\                     |  | \                        | \                    |  -|--\- dredge line        --|--\- dredge        --|--\- dredge
  |   )                      |   )                  |    )
  |  /  toe moves back       |  /  tip free         |   (  contra-
  | /   (pivot point)        | /   (rotates)        |    ) flexure
  |/                         |/                     |   / fixed toe

• (i) Cantilever: the wall deflects toward the excavation and pivots about a point near the lower third of the embedded length; the toe moves backward.
• (ii) Anchored bulkhead, shallow depth (free earth support): the pile is held at the anchor and rotates freely about the tip; single curvature, no fixity at the bottom.
• (iii) Anchored bulkhead, deeper depth (fixed earth support): the toe is fixed in the soil, so the deflected curve has a point of contraflexure, with reverse curvature near the bottom.

Assumed condition: sheet pile wall retaining $H = 5$ m of dry sand ($\phi = 30^\circ$, same on both sides), $\gamma$ the same on both sides, passive resistance with $FS = 1$ for the comparison, anchor at 1 m below the top (free earth support).

(a) Cantilever wall: the moment about the toe must balance:

(b) Anchored wall (free earth support): take moments about the anchor point (the anchor force $T$ drops out):

Solving, $D_{anch} = 1.90$ m, and the anchor force from $\sum H = 0$ is

(with $\gamma = 18$ kN/m$^3$, $T \approx 45$ kN/m).

Comparison: $D_{anchored} = 1.90$ m $\ll D_{cantilever} = 4.63$ m, about 59% less. The anchor supplies the horizontal reaction that the cantilever wall must get from the passive resistance of a deep embedment, so the embedment, and also the pile length and bending moment, are reduced.

Uses of sheet piles

• Retaining walls for waterfront structures (quay walls, bulkheads, jetties).
• Temporary support of excavations (braced cuts and trenches).
• Cofferdams for bridge piers and underwater foundations.
• Cut-off walls under dams, seepage control, flood protection.
• Protection against scour and for river training, and landfill containment.

Free earth support method (granular soil)

Assumption: the pile tip is free to rotate (no fixity); the active pressure acts on the full height $(H+D)$ on the back, passive pressure acts only in front; the wall is simply supported by the anchor and the passive resistance.

1. Compute $K_a = \tan^2(45^\circ-\phi/2)$ and $K_p = \tan^2(45^\circ+\phi/2)$; use $\gamma'$ below water table and include surcharge and water pressure.
2. Draw the active pressure diagram on the back from top to depth $H+D$ and the passive pressure diagram in front from the dredge line to depth $D$ (using $K_p/FS$ if a factor of safety is applied to passive resistance).
3. Find the active resultant $P_a$ and its lever arm from the anchor level.
4. Find the passive resultant $P_p$ (in terms of $D$) and its lever arm from the anchor.
5. Take moments about the anchor point: $P_a\, l_a = P_p\, l_p$ and solve for the embedment $D$ (trial and error).
6. Find the anchor force per metre $T$ from horizontal equilibrium: $T = P_a - P_p$.
7. Increase $D$ by 20-30% for the design depth, then find the maximum bending moment (at zero shear) and select the sheet pile section from $Z = M_{max}/\sigma_{allow}$.

Data and assumptions: excavation depth $H = 8$ m (dredge level); $\gamma = \gamma_{sat} = 20$ kN/m$^3$, $\phi = 33^\circ$; water table at 6.5 m below ground, taken at the same level on both sides (the excavation is flooded to the water table, no seepage and no net water pressure), so effective stresses with $\gamma' = 20 - 9.81 = 10.19$ kN/m$^3$ are used below the water table. Moments are taken about the pile tip (simplified cantilever method).

Coefficients

Pressures

• Active (back), depth $z$: $p_a = K_a\sigma_v'$; at 6.5 m $= 38.32$ kN/m$^2$; below 6.5 m the effective stress increases with $\gamma'$.
• Passive (front), depth $y$ below the dredge line: $p_p = K_p\gamma' y = 34.57\,y$ kN/m$^2$.

Moment equilibrium about the tip: for a trial embedment $D$,

Setting $M_{active} = M_{passive}$ and solving by trial and error:

(Active force 699 kN/m, passive force 1430 kN/m at this depth.)

Design depth: increase by 20% for safety (practice 20-40%):

Answer: theoretical embedment $D \approx 9.1$ m (below the 8 m dredge level); provide $\approx 11$ m, i.e. a total pile length of about 19 m. For comparison, without the water table, $D = 6.4$ m.

Data: $H = 5$ m, $\gamma = 22$ kN/m$^3$, $\phi = 33^\circ$, no water above the pile tip. Cantilever sheet pile, simplified moment method (moments about the toe).

Forces (with $D$ = embedment below the dredge line, $\gamma$ same on both sides):

• Active force on the back: $P_a = \tfrac12K_a\gamma(H+D)^2$, acting at $(H+D)/3$ above the tip.
• Passive force in front: $P_p = \tfrac12K_p\gamma D^2$, acting at $D/3$ above the tip.

Moment about the tip

Design depth: since the method assumes full passive resistance and ignores the extra tip reaction, increase by 20%:

Answer: theoretical embedment $D = 3.98$ m; adopt $D \approx 4.8$ m (total pile length about 9.8 m).

Data: deposit (in which the pile is driven): $\phi_2 = 35^\circ$, $\gamma_2 = 22$ kN/m$^3$. Backfill 3 m high on one side: $\phi_1 = 32^\circ$, $\gamma_1 = 18$ kN/m$^3$. $FS = 2$ on passive resistance. Water table below the pile tip. Simplified method: moments about the pile tip.

Coefficients

Active pressures (back, depth $z$ from the top of the backfill; the dredge line is at $z=3$)

• Backfill ($0 \le z \le 3$): $p = K_{a1}\gamma_1 z$, giving 16.59 kN/m$^2$ at 3 m.
• Below 3 m (in the deposit): $p = K_{a2}\,[18\times3 + 22(z-3)] = 14.63 + 5.962(z-3)$ kN/m$^2$.

Passive pressure (front, depth $y$ below the dredge line)

Moments about the tip (embedment $D$): the active moment is

and the passive moment is $M_p = \tfrac16\,(K_p\gamma_2/FS)\,D^3 = 6.765\,D^3$. Solving $M_a = M_p$ by trial and error gives

(active force 99.0 kN/m, passive force 195.6 kN/m).

Answer: required depth of penetration $D \approx 3.10$ m below the 3 m backfill (dredge) level. Since $FS = 2$ is already applied to the passive resistance, no further increase is needed; the total pile length is about 6.1 m.

Data and assumptions (figure values as read): height above dredge level $H = 8.0$ m; anchor (tie rod) at 2.5 m below the top; soil above the water table: $\gamma = 16$ kN/m$^3$, $\phi = 35^\circ$ for the top 3.0 m; below: $\gamma_{sat} = 19$ kN/m$^3$, $\phi = 35^\circ$. Water level is taken the same on both sides (no net water pressure), so $\gamma' = 19 - 9.81 = 9.19$ kN/m$^3$ is used below the water table. Free earth support method, passive resistance with $FS = 1$ for the theoretical depth.

Active pressure (back, depth $z$): $p_a = K_a\sigma_v'$

• $z = 3$ m: $\sigma_v' = 48$, $p_a = 13.01$ kN/m$^2$.
• $z = 8$ m (dredge): $\sigma_v' = 48 + 9.19\times5 = 93.95$, $p_a = 25.46$ kN/m$^2$.
• Below the dredge line: the effective stress increases by $\gamma'$ per metre.

Passive pressure (front): $p_p = K_p\gamma' y = 33.91\,y$ kN/m$^2$, $y$ measured below the dredge line.

Moment about the anchor (level 2.5 m): for a trial embedment $D$,

Equating and solving by trial and error:

At this depth: active force $P_a = 189.3$ kN/m, passive force $P_p = 112.0$ kN/m.

Design embedment: increase by 30% (free earth support): $D_{design} = 1.3\times2.57 = 3.3$ m.

Tension in the anchor from horizontal equilibrium:

Answer: depth of embedment $D \approx 2.57$ m (adopt about 3.3 m); anchor force $T \approx 77$ kN per metre run.