R. Sundaravadivelu 1 Chennai
India
6.1 INTRODUCTION
The berthing structures are constructed for berthing and mooring of vessels to enable loading and unloading of cargo and for embarking and disembarking of passengers, vehicles. The design of berthing structures depends on various factors. However, the vessel characteristics govern the design of berthing structures.
The various structures constructed along the coast can be classified as Port and Harbour Structures, Coastal Protection Structures, Sea water Intake Structures and Effluent discharge structures. Port and harbor structures are constructed along the coast to provide berthing facilities to ships for loading and unloading of cargo or for embarking and disembarking passengers. The different types of berthing structures are given in this section.
6.2 TYPES OF BERTHING STRUCTURES
Berthing structure is a facility where the vessel may be safely moored. The berthing arrangements can be classified as along side type, open dolphin type or ferry type as shown in Figure 6.1 (Gaythwaite (1990)).
The berthing structure can also be classified as vertical face type or open type structure. Typical examples are shown in Figure 6.2 (Agerschou et al (1985). In vertical face
structures, sheet pile wall, block wall, caissons are used, while open type structures are represented by open piled construction.
Fig 6.1 Types of Berthing Structures FERRY (SLIP) TYPE
OPEN DOLPHIN TYPE
FINGER PIER OR DOLPHINS
TRANSFER BRIDGE GUIDE DOLPHINS TRESTLE TO SHORE LOADING PLATFORM MOORING DOLPHIN BREASTING DOLPHIN ALONGSIDE TYPE
R. Sundaravadivelu 1 Fig 6.2 Types of Vertical Face Berthing Structures
(a) CAISSON
(c) OPEN PILED STRUCTURES (b) SHEET PILE WALL
The berthing structures can also be classified depending on the type of cargo handled. The Madras Port outer harbour basin has oil berth, ore berth and container berth where oil, ore and containers are handled respectively. The berthing structures can also be classified as follows:
(A) GRAVITY STRUCTURES (i) Masonry wall (ii) Concrete block walls (iii) Concrete caissons (B) FLEXIBLE STRUCTURES
(i) Steel sheet piles - Tie back
- Cantilever
(ii) Diaphragm walls - Cantilever
- Tieback
- Relieving platform
(iii) Jetties - consist Berthing & Mooring Dolphin, Jetty Head & Approach Jetty.
The minimum length of a berthing structure should be sufficient for mooring the longest ship expected to arrive. The minimum depth includes a bottom clearance equivalent to 10 % of the draught of the largest vessel using the terminal. The top surface of the berthing structure should be built above the highest high water level.
The dimension of the berth as recommended by IS 4651 (Part V) - 1980 is given in Appendix 6.1 for various size of Passenger ships, Freighter, Tankers, Ore Carriers and Large Fishing Vessels.
6.2.1 Quay or Wharf
Quays are defined as one or more berths, continuously bordering on and it contact with a land or dock area. The inner harbour basin of Madras Port has North, South, East and West Quays where berthing facilities are provided for number of ships.
R. Sundaravadivelu 1
A jetty consists of a number of structures such as berthing dolphin, mooring dolphin, loading platform, trestle to shore each of which has special type of functions.
The mooring dolphins pick up the pull from the hawsers. Mooring dolphins for breast lines shall be located at bow and stern at a distance (about the beam of the ship) from the berth line, which will not make the moorings too steep.
The berthing dolphins support fenders which absorb berthing impacts. The berthing dolphins should be placed as wide apart as possible. The distance should neither exceed the length of the straight side of the smallest vessel nor be less than approximately one-third of the maximum length of the largest vessel.
The loading platforms support special loading or unloading equipment but normally no horizontal forces apart from wind loads will act on the loading Platforms.
6.2.3 Offshore Berthing Structures
Offshore berthing structures are used for liquid cargo (oil or gas) or for dry cargo, for iron ore, coal, sugar, phosphates or grains. The design for offshore berthing structures should consider the following :
a) Single type of cargo
b) Rapid loading and unloading (10,000 T of Iron ore per hour or 60,000 bbl (barrel) of oil per hour)
c) Sufficient storage on shore
e) Construction practicability
f) DWT of the vessel in the range of 0.1 million T to 0.3 million T
The type of ship loader generally governs the design of offshore berth. The three main types of ship loader are (1) Fixed type (2) travelling Gantry type and (3) Slewing telescopic boom loaders. The fixed loader is used in small ships. The travelling gantry loader is expensive, since the loader is to be supported by a berth which is continuous. The above three types of loaders are to be critically evaluated for dry bulk cargo terminals, whereas for liquid cargo, the loading system does not influence the offshore berthing structure. The approach jetty to the offshore berthing structure is the critical component and governs the total cost of the facility. The offshore terminal at CAPE Santa Clara in the Atlantic ocean consists of a principal berth to load 2,80,000 DWT ship, moored 7400 m from shore. The mooring and berthing force in the offshore berth is to be critically evaluated for the safe design of the offshore berthing structure.
6.3 LOADS ON BERTHING STRUCTURES
The berthing structures are designed for the following forces : (i) Berthing force
(ii) Mooring force (iii) Dead load
(iv) Live load - Rail
- Road
- Bulk unloaders
- Cranes etc.
- UDL due to cargo
(v) Active earth pressure if the berth retains the earth (vii) Environmental forces - Wind
- Wave
- Current
- Differential water pressure
(viii) Seismic force
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caused by berthing and vessel’s pull from bollard. The forces caused by berthing of vessels are determined from the velocity and angle of approach of the vessels. For the vessels lying at the berth, the forces are determined due to wind, waves and currents on the vessel. The vertical forces from sea side are due to vessels hanging upon the fendering system, vertical component of the forces from bollards etc.
6.3.1.2 Loads from Deck
The important loads from the deck are the vertical loads caused by self weight of the deck, superimposed loads from buildings and handling equipments. Horizontal loads are mostly due to wind forces on buildings and structures and also due to the breaking force of cranes. 6.3.1.3 Loads from Landside
Horizontal loads are caused from landside due to the earth pressures and differential water pressure. Vertical loads are caused by the weight of filling and superimposed load on filling.
6.3.2 Live Loads
6.3.2.1 Vertical Live Loads
Surcharges due to stored and stacked material such as general cargo, bulk cargo, containers and loads from vehicular traffic of all kinds including trucks, trailers, railway cranes, containers handling equipment and construction plant, constitute vertical live loads.
6.3.2.2. Truck loading and Uniform loading
The berths shall be generally designed for the truck loading and uniform loading as given in Table 6.1 (IS 4651 (Part III) - 1974).
Table 6.1 Truck Loading and Uniform Loading
Function of Berth Truck Loading
(IRC class)
Uniform Vertical Live Loading (T/m2)
Passenger berth B 1.0
Bulk unloading and loading berth
A 1 to 1.5
Container berth A or AA or 70 R 3 to 5
Cargo berth A or AA or 70 R 2.5 to 3.5
Heavy cargo berth A or AA or 70 R 5 or more
Small boat berth B 0.5
Fishing berth B 1.0
6.3.2.3 Crane Loads
Concentrated loads from crane wheels and other specialised mechanical handling equipment should be considered. An impact of 25 percent shall be added to wheel loads in the normal design of deck and stringers, 15 percent where two or more cranes act together and 15 percent in the design of pile caps and secondary framing members.
6.3.2.4 Railway Loads
Concentrated wheel loads due to locomotive wheels and wagon wheels in accordance with the specification of the Indian Railways for the type of gauge and service at the locality in question. For impact due to trucks and railways one third of the impact factors specified in the relevant codes may be adopted.
6.3.2.5 Special Loads
Special loads like pipeline loads or conveyor loads or exceptional loads such as surcharges due to ore stacks, transfer towers, heavy machinery or any other type of heavy lifts should be individually considered.
R. Sundaravadivelu 1
where
E = Berthing energy in T- m WD = Displacement tonnage in T
V = Berthing velocity in m/sec Cm = Mass coefficient
Ce = Eccentricity coefficient CS = Softness coefficient
g = Acceleration due to gravity in m/sec2
6.3.3.1 Mass Coefficient
When a vessel approaches a berth and as its motion is suddenly checked, the force of impact which the vessel imparts comprises of the weight of the vessel and the effect of water moving along with the moving vessel. Such an effect, expressed in terms of weight of water moving with the vessel, is called the additional weight (WA) of the vessel or the
hydrodynamic weight of the vessel. Thus the effective weight in berthing is the sum of displacement tonnage of a vessel and its additional weight, which is known as virtual weight (WV) of a vessel.
a. The mass coefficient (Cm) is calculated using the following equation
B D 2 1
where
D = Draught of the vessel in m, B = Beam of the vessel in m.
b. Alternative to (a) in case of a vessel which has a length much greater than its beam or draught or generally for vessels with displacement tonnage greater than 20,000 the additional weight may be approximated to the weight of a cylindrical column of water of height equal to the length of vessel and diameter equal to the draught of vessel, then
D 2 4 m W Lw D 1 C π + = (6.3) where
D = Draught of the vessel in m, L = Length of the vessel in m
w = Unit weight of water (1.03 T/m2 for sea water) WD = Displacement tonnage of the vessel in tonnes.
Wv = WD x Cm
6.3.3.2 Eccentricity Coefficient
A vessel generally approaches a berth at an angle, denoted byθ and touches it at a point either near the bow or stern of the vessel. In such eccentric cases the vessel imparts a rotational force at the moment of contact, and the kinetic energy of the vessel is partially expended in its rotational motion.
a) The eccentricity coefficient (Ce) may then be derived as follows:
2 2 2 e ) r / l ( 1 Sin ) r / l ( 1 C + θ + = (6.4) where
l = Distance from the centre of gravity of the vessel to the point of contact projected along the water line of the berth in m, and
R. Sundaravadivelu 1 Fig 6.3 Approaching Angle of Vessel with a Berth
BERTHING POINT OF THE VESSEL (l)
ECC ENTRI CI TY CO EFF ICI ENT (Ce) 0.6 0.1L 0.0 0.2 0.4 0.8 1.0 0.2L 1/4L 0.3L 0.4L 0.5L G θ Forθ = 0
c) The rotational radius of a vessel may be approximated to L/4 and in normal case the point of contact of the berthing vessel with the structure is at a point about L/4 from the bow or stern of the vessel which is known as a quarter point contact. If the approach angleθ is nearly 0° and r = 0.25 L, then Ce = 0.5.
6.3.3.3 Softness Coefficient
This coefficient (Cs) indicates the relation between the rigidity of the vessel and that of the
fender, and also the relation between the energy absorbed by the vessel and the fender. Since the ship is relatively rigid compared with the usually yielding fendering systems, a value of 0.9 is generally applied for this factor, or 0.95 if higher safety margin is thought desirable.
Quinn (1961) has suggested a suitable formula for calculating the berthing energy assuming 50% of the total energy of the berthing vessel to be absorbed by fenders.
= mv2 2 1 2 1 E (6.5)
where m is the (mass + added mass) of the vessel and v is the berthing velocity.
6.3.4 Mooring Loads
The mooring loads are the lateral loads caused by the mooring lines when they pull the ship into or along the dock or hold it against the forces of winds or current.
6.3.4.1. Forces due to Wind
The maximum mooring loads are due to the wind forces on exposed area on the broad side of the ship in light condition
F = Cw Aw P (6.6)
Where
F = Force due to wind in kg Cw = Safe factor = 1.3 to 1.6
Aw = Windage area in m2 and
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should be increased by 50 percent to allow for wind against the second ship.
Gaythwaite (1990) has suggested the following formulas to calculate windforce in the longitudinal (Fwx) and lateral (Fwy) force components and a yawing moment (Myw).
Fwx = 0.0034 CDx V2w Ax (6.8)
Fwy = 0.0034 CDy V2w Ay (6.9)
Myw = Fwy LOA Cym (6.10)
Where
Fwxand Fwy = Wind Force along x and y directions in pounds
Myw = Yawing Moment in pounds-ft
CDxand CDy = Drag Coefficients along x and y directions
Vw = Wind speed in Knots
Ax and Ay = End-on and Side projected areas of vessel (including the areas
of masts, stacks, rigging, deck cargoes, etc.) LOA = Overall Length of Ship in ft
The hydrodunamic coefficients are the functions of angle of wind approach(θ). The yaw moment is given in terms of the lateral force times the vessel’s length overall (LOA) and Cym. The total resultant force for wind from any direction (Fw(θ)) is found from this
equation:
6.3.4.2 Forces due to Current
Pressure due to current will be applied to the area of the vessel below the water line when fully loaded. It is approximately equal to w v2/2g per square metre of area, where v is the velocity in m/s and w is the unit weight of water in T/m3. The ship is generally berthed parallel to the current. With strong currents and where berth alignment materially deviates from the direction of the current, the likely force should be calculated by any recognised method and taken into account.
Ship is aligned predominantly in head sea condition with current direction.
Example problem 1:
Calculate the berthing force, and Mooring force due to 30,000 DWT bulk carrier approaching the berth at Kandla Port with a berthing angle of 10°. The site condition is moderate wind and swells and the berthing condition is moderate. Use the following informations. (Design data)
Length of the berth = 240 m
Width of the berth = 55 m
Top level = + 9.74 m
Dredge level = - 11.10 m
Length of the vessel = 205 m Width of the vessel = 26.5 m
Draught = 10.70 m
Berthing force
Site conditions : Moderate wind and swells
Berthing condition : Moderate
As per IS 4651 (Part III)-1974 for the above site condition and berthing condition Berthing velocity (v) = 0.2 m/s S e m D C C C g 2 V W E 2 =
R. Sundaravadivelu 1 600 , 39 Cm = 1.48 Ce =
( )
( )
2 r 2 2 r 1 sin 1 1 l + θ + l = L/4 = 205/4 = 51.25 m r = 0.2 L = 0.2 x 205 = 41 m θ = 10° Ce =( )
( )
2 4 25 . 51 2 2 41 25 . 51 1 10 sin 1 + + Ce = 0.41CS = 0.95 (As per code)
95 . 0 * 41 . 0 * 48 . 1 * 81 . 9 * 2 ) 2 . 0 ( * 600 , 39 E 2 = E = 46.54 T – m Ultimate energy = 1.4 x 46.54 = 65.2 T-m
Fender details : fender type - cell (from fender manufacture catalogue)
Size of fender – 1600H x 2005D x 1800 P Berthing force = 100 T
Mooring force
Length between perpendicular (Lp ) = 0.9 L = 0.9 x 205 = 184.5 m
Moulded depth of the ship (Dm ) = 14.3 m
Average light weight draft (DL ) = 10.3 m
Due to Wind
Aw = 1.175 x 184.5 (14.3 - 10.3)
Aw = 867.15 m2
P = 0.06 Vz2 (As per IS 875-1987) Vz = Vb k1 k2 k3
Vz = Design wind speed at any height
k1 = Probability factor (risk coefficient)
k2 = Terrain, height and structure size factor
k3 = Topography factor
Basic wind speed - 39 m/sec (at Kandla) Vb = 1.15 x 39 (for offshore area)
= 44.85 m/sec
K1 = 1.08, K2 = 1.05, K3 = 1
Vz = 44.85 x 1.08 x 1.05 x 1 = 50.86 m/s
P = 0.06 x (50.86)2 = 155 Kg/m2
Fw = 1.4 x 867.15 x 155 (as per Equation (6.6))
R. Sundaravadivelu 1 g = 9.81 m/s2 T 91 . 94 7 . 10 * 5 . 26 * 81 . 9 * 2 525 . 2 * 025 . 1 F 2 c = = Total force = sqrt(1882 + 952) = 210 T
The total force can be assumed to be equally distributed to four bollards, if the ship is mored to eight bollards. Force on each bollard = 210/4 = 52.5 T
The line pull as per Table 6.2 is 60 T for the 20000 DWT vessels and T for the 50000 DWT vessels.
Table 6.2 : Bollard Pulls
Displacement (Tonnes) Line Pull (Tonnes)
2,000 10 10,000 30 20,000 60 50,000 80 100,000 100 200,000 150 >200,000 200
Hence the mooring pull for 30,000 DWT vessel is 67. However the mooring pull is assumed as 75 T.
Fig. 6.4 Differential Water Pressure 6.3.5 Differential Water Pressure
In the case of waterfront structures with backfill, the pressure caused by difference in water levels at the fillside and the waterside has to be taken into account in design. The magnitude of this hydrostatic pressure is influenced by the tidal range, free water fluctuations, the ground water influx, the permeability of the foundation soil and the structure as well as the efficiency of available backfill drainage.
In the case of good and poor drainage conditions of the backfill the differential water pressure may be calculated on the guidelines given in Figure 6.4. The average of MLWS and LLW is assumed water level on the sea side for both poor and good drainage conditions. The average of MHW and MLW is assumed as ground water (GW) on the land side for poor drainage condition, while 0.3 m above MLW is assumed a ground water (GW) on the land side for good drainage condition
MHW - MEAN HIGH WATER MLW - MEAN LOW WATER MLWS - MEAN LOW WATER SPRINGS
GW - GROUND WATER LLW - LOWEST LOW WATER b
LLW
(a) POOR DRAINAGE CONDITION MHW
MLW MLWS
b
ASSUMED GW
(b) GOOD DRAINAGE CONDITION ASSUMED GW MLW MLWS LLW FLAP VALVE a a b b
MHW ELEVATION OF FLAP VALVE BOTTOM
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and is equal to the total dead load plus one-half of the live load as per IS 1893 (Part III)-1984.
The design values of horizontal seismic coefficient, in the Seismic Coefficient method shall be computed as given by the following expression:
αh = βIαo (6.13)
where
β = A coefficient depending upon the soil-foundation system I = A factor depending upon the importance of the structure αo = Basic horizontal seismic coefficient based on the zone
β, I and αo can be obtained from IS 1893-1984, depending on type of soil foundation, importance of the structure and the zone in which the structure is located.
6.3.7 Wave Forces
As far as analysis and computation of forces exerted by waves on structures are concerned, there are three distinct types of waves, namely,
1. Non-breaking waves 2. Breaking waves and 3. Broken waves
6.3.7.1 Non-breaking Waves
Generally, when the depth of water against the structure is greater than about 11/2 times the
maximum expected wave height, non-breaking wave conditions occur.
Forces due to non-breaking waves are essentially hydrostatic. ‘Sainflou Method’ may be used for the determination of pressure due to non-breaking waves.
6.3.7.2 Breaking Waves
Breaking waves cause both static and dynamic pressures. Determination of the design wave for breaking wave conditions may be based on depth of water about seven breaker heights (Hb) seaward of the structure, instead of the water depth at which the structure is
located. The actual pressures caused by a breaking wave is obtained by following the method suggested by Minikin.
6.3.7.3 Broken Waves
Locations of certain structures like protective structure will be such that waves will break before striking them. In such cases, no exact formulae have been developed so far to evaluate the forces due to broken waves, but only approximate methods based on certain simplifying assumptions are available.
6.3.7.4 Wave Force on Piles
Wave forces on vertical cylindrical structures, such as piles exerted by non-breaking waves can be divided into two components;
a. Force due to drag b. Force due to inertia
A set of generalised graphs which are available in shore protection manual together with the following formulae may be used to compute these;
FDM = 1/2 CDρg D H2 KDM (6.14) FIM = CMρg 4 D2 π H KIM (6.15) FM = φmρg H2D (6.16)
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g = Acceleration due to gravity
ρ = Mass density of sea water = (w/g) = 1025.2 kg/m3 D = Diameter of pile in m
H = Wave height in m
KDM = Drag force factor (Figure 6.5)
FIM = Total inertial force on a vertical pile from the seabed to the free surface
elevation in N
KIM = Inertial force factor (Figure 6.6)
SDM = Drag force moment arm (Figure 6.7)
SIM = Inertia force moment arm (Figure 6.8) αm,φm = Coefficients read from the Figures 6.9 to 6.16 CD,CM = Drag, Intertia coefficient (Figures 6.17 to 6.18)
FM = Maximum value of the combined drag and inertial force in N
MDM = Moment on pile about bottom associated with maximum drag force in N-m
SD = Effective lever arm for FDM from the bottom of pile in m
MIM = Moment on pile about bottom associated with maximum inertial force in N-m
SD = Effective lever arm for FIM from the bottom of pile in m
Fi g. 6 .5 K Dm versus Re lati ve Dep th (d / gT 2 )
R. Sundaravadivelu 1 Fi g. 6 .6 K IM versus Relativ e D epth (d / g T 2 )
Fig 6.7 S DM versus R el ative Dept h (d /gT 2 )
R. Sundaravadivelu 1 F ig 6 .8 SDM versus Relativ e D ept h (d/g T 2 )
Fi g 6 .9 Isol ines of φm versus H/ gT 2 and d/gT 2 (w = 0. 05 )
R. Sundaravadivelu 1 Fi g 6.10 Is olin es of φm versus H/gT 2 and d/gT 2 (W = 0.1 )
Fig. 6.1 1 Isol ines of φm vs H/ g T 2 an d d/g T 2 (W = 0. 5)
R. Sundaravadivelu 1 Fig 6 .1 2 Iso lin es o f φm versus H/ g T 2 and d/gT 2 (W = 1. 0)
Fi g 6.13 Isolines of αm versus H/gT 2 and d/g T 2 (W = 0 .05)
R. Sundaravadivelu 1 Fig 6 .14 Isolines of αm versu s H/gT 2 and d /gT 2 (W = 0.
Fig 6 .15 Isolines of αm ve rsus H/gT 2 and d /gT 2 (W = 0. 5)
R. Sundaravadivelu 1 Fi g. 6.16 Isolin es of αm versu s H/g T 2 a n d d/gT 2 (W = 1. 0)
R. Sundaravadivelu 1 Fig 6.18 Drag Coefficient for a Smooth Oscillating Cylinder
Example Problem 2 :
A design wave height of (H) 5.0 m and period (T) 10 secs acts on a vertical circular pile with a diameter (D) of 1 m and depth (d) 8 m. Assume Cm = 2.0 and P = 1025.2 kg/m3.
Find the maximum total horizontal force and the maximum total moment on the pile.
Solution Calculate 2 gT d = 2 ) 10 ( ) 8 . 9 ( 8 = 8.16 x 10-3
From Figure 3.26 the breaking limit curve
2 b gT H = 0.006 Hb = 0.006 x 9.8 x 102 = 5.88 m and b H H = 88 . 5 5 = 0.85
From Figures 6.5 and 6.6 using 2 gT
d
= 8.16 x 10-3 and
H = 0.85 Hb, Interpolating between curves H = Hb and H = 3/4 Hb; find
KDm = 0.620 Kim = 0.39 Fim = Cmρ 4 π D2HKim Fim = 3 10 ) 8 . 9 )( 2 . 1025 )( 2 ( 4 π (1)2 x 5.0 x 0.39 = 30.77 kN FDm = CD 2 1ρ g DH2 x KDm
R. Sundaravadivelu 1 2 gT H = 2 ) 10 ( ) 8 . 9 ( 5 = 0.005 2 gT d = 0.0082
using the Figures 6.11 and 6.12 find φm
W = 0.5 φm = 0.34 (from Figure 6.11)
W = 1.0 φm = 0.44 (from Figure 6.12)
W = 0.57
Interpolating the values of 0.5 and 1.0 we can get the values for W = 0.57.
W = 0.57 φm = 0.354
Fm = φmρg CDH2D
= 0.3554 (10,047) (0.7) (5)2 (1) = 62241.2 N
Fm = 62.24 kN
From the Figure 6.8 Sim = 0.8
Mim = Fim d Sim = (30774) x 8 x 0.8 = 196953.6 N m = 196.9 kN m MDM = FDM d SDM = (545040.76) x (8) x (0.996) = 434287.8 N m 4343 kN m
To findαm,using the Figure 6.15 and 6.16 are used.
W = 0.5 αm = 0.34 (from Figure 6.15)
W = 1.0 αm = 0.40 (from Figure 6.16)
Interpolating the values of 0.5 and 0.1, We can get the values of 0.57
W = 0.57 αm = 0.3484 Mm = αmρg CDH2 Dd = 0.3484 (10,047) (0.7) (5)2 (1) (8) = 490052.47 N m Mm = 490 kN m. 6.3.8 Combination of Loads
The combination of loadings for design is dead load, vertical live loads, plus either berthing load, or line pull or earthquake or wave pressure, for open type berthing structure. The worst combination should be taken for design. In addition to the above load earth pressure & differential water pressure shall be consider for vertical force typing structures.
R. Sundaravadivelu 1 Table 6.3 Partial Safety Factors for Loads in Limit State Design
Loading
Partial Safety Factor Limit State
Serviceability Limit State of Collapse
Dead load 1.0 1.0 1.5 1.2 (or 0.9) 1.2 (or 0.9) 1.2 (or 0.9) Vertical Live
Load
1.0 1.0 1.5 1.2 (or 0.9) 1.2 (or 0.9) 1.2 (or 0.9)
Earth Pressure 1.0 1.0 1.0 1.0 1.0 1.0 Hydrostatic and Hydrodynamic Forces 1.0 1.0 1.0 1.2 1.0 1.0 Berthing and Mooring Forces - 1.0 1.5 - - -Secondary Stresses 1.0 - - - - -Wind Forces - - - - 1.5 -Seismic Forces - - - - - 1.5
Table 6.4 Increase in Permissible Stresses
Sl.
No. Combination of Loads
Increase in Permissible
Stress Increase inAllowable Bearing Pressure Reinforced Concrete Other Materials such as steel and Timber 1 DL + LL + impact of breaking or
traction or vehicles + centrifugal forces of vehicles
Nil Nil Nil
2 DL + LL with impact, breaking or tractive and centrifugal forces + earth pressure, percent
15 15 15
3 DL with/without LL including impact, breaking or tractive and centrifugal forces + earth pressure + hydrodynamic and hydrostatic forces + berthing and mooring forces, percent
25 33 1/3 25
4 Wind forces on structures + load combination of (1) + (2) or (3) 5 Seismic forces + load combination of
(1), (2) or (3)percent
6 Secondary stress + load combination
of (1), percent 15 15 15
7 Erection stage stresses with DL and appropriate LL + earth pressure + hydrodynamic forces + wind forces, percent
15 33 1/3 25
6.4 ANALYSIS OF BERTHING STRUCTURES 6.4.1 Analysis of a Bulk Berth
The layout of a berth to receive 30,000 DWT bulk carrier is given in Figure 6.19. The dimension of 30,000 DWT bulk carrier as per IS 4651 (Part III)-1974 are as follows:
Overall length = 205 m
Width = 26.5 m
R. Sundaravadivelu 1 Fig. 6.19 Layout of Berth With 30000 Dwt Tanker
expansion joints are also constructed. However for these structures the loads due to variation of temperature shall be considered in addition to other loads. The typical cross section of a berth is shown in Figure 6.20. It consists of a diaphragm wall tied back by a cross beam to four rows of vertical pile.
The fully loaded draft is 10.7 m. Hence the dredge level is assumed as 10.7 + 10% of draft + 0.5 m for over dredge allowance. Hence dredge level should be greater than 12.27 m. The dredge level is assumed as 12.5 m. The tidal levels are
HHWL = + 3.25 m LLWL = + 0.40 m 25000 50000 50000 M1 = STERN LINE M2 = AFT BREAST LINE M4 = FORD SPRING LINE M5 = FORD BREAST LINE M6 = BOW LINE F1 & F2 = FENDERS B1 & B2 = BOLLARDS M3 = AFT SPRING LINE
50000 M1 B1 M2 B2 B33 M4 F1 50000 50000 B4 F2 M3 B5 M5 B6 16
Fig.6.20Typical Cross Section of Fertilizer Berth
Hence the top level of the jetty is assumed as (3.25 + H/2 + 1) m where, H is the expected wave height. The wave height inside the harbour during extreme weather condition is 1.2 m. Hence the top level is assumed as + 4.85 m. The third and fourth row of piles are provided below the conveyor columns, the second row of pile is provided below one of the rails of crane track.
It is preferable to carry out three dimensional analysis for each block considering all the rows of piles especially for berthing and mooring force. However it is a common practice to carry out a two dimensional analysis for a typical pile bent for 1/3 of berthing force and 1/3 or mooring force assuming that the berthing force and mooring force will be distributed to 3 pile bents.
6.4.1.1 Preliminary Analysis of System
A typical 4 m panel of 1100 mm thick diaphragm wall having 3.65 m deep beam supported by piles at 6 m, 12 m, 15.65 m and 22.45 m (Figure 6.21) is considered for the analysis. This depth of the beam is found to be very conservative. The economical depth is about
2515 -23.00 DREDGE LEVEL -12.50 +3.25 HWL +5.00 1100 THK DIAPHRAGM WALL (B) FINAL DESIGN -22.50 1000Ø PILE 1300Ø PILE -20.00 1300Ø PILE MAIN BEAM
R. Sundaravadivelu 1 Fig. 6.21 Idealization for Preliminary Analysis
-7.0m 500 3650 SECTION -YY SECTION - XX 7067 -17.0m 5940 11575 9800 7100 6942 6942 -23.0m -21.0m -19.0m K(T/M) 8319 7787 1197 920 -15.0m -13.0m -11.0m -9.0m 4000 1100 V1 -5.0m R3 V3 V2 R4 V4
1.65m. The preliminary analysis of the following three different systems (Raju et al. (1995)) has been carried out using the general purpose, Structural Analysis Program SAP IV developed by Bathe, K.J. (1973).
(A) Diaphragm wall with anchor rod and deadman diaphragm wall (Figure 6.22a). (B) Diaphragm wall with vertical and raker piles (Figure 6.22b1 & 6.22b2).
(C) Diaphragm wall with vertical piles (Figure 6.22c1, 6.22c2 & 6.22c3).
For the purpose of analysis the deck, diaphragm wall and pile systems are replaced by two-dimensional beams. The passive pressure on the diaphragm wall is idealised by spring elements. The piles are assumed to be rigid at top and bottom. The fixity depth for piles as per IS 2911 (Part 1/ Se. 2) -1979 for an nh of 0.5 kg/cm3 is 5 times d, where d is the dia
of the piles. Since the first row of piles is partly in the active zone of diaphragm wall, its fixity depth is increased to 6 m + 5 d and fixity depth for 2nd, 3rd and 4th rows of piles are assumed as 5d.
Since the lateral load governs the design of these structures, the analysis is carried out for lateral loads only. The active earth pressure on the diaphragm wall and 100 T pull are considered as two typical load cases for the analysis.
The shear force in diaphragm wall and piles at the top, the wind force in the raker piles, anchor force in the tie rod and the horizontal deflections at the top of diagram wall are summarized in Table 6.5.
R. Sundaravadivelu 1 Fig.6.22 Alternate Schemes
(b2) VERTICAL PILES WITH RAKER 100
110 130 100 75 75 110 75
(c3) VERTICAL PILES 75
100 130
(b1) VERTICAL PILES WITH RAKER
110 100 130 100 75 110
(a) VERTICAL PILES WITH ANCHOR
75 (c2) VERTICAL PILES 100 130 100 (C1) VERTICAL PILES
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the 3rd and 4th row of piles to take care of the lateral load. The 3rd and 4th row of piles can be strengthened either by increasing the diameter or by introducing additional raker piles. Results of both the alternatives are discussed below.
System ‘b’ - Diaphragm wall with Raker & Vertical Piles
Two different combination of raker and vertical piles are analysed. In b1 the 750mm dia
raker pile is in the 3rd row and in b2, the raker pile is in the fourth row. It can be
concluded from the results that one 750 mm dia raker pile takes almost the same amount of lateral force as that of 3 numbers of 80 mm dia HTS anchor rods. Compared to system b2,
system b1 performs better by taking more lateral load as axial force. The horizontal
displacement at top of diaphragm wall for system b1 is also less than that of system b2 (Ref.
Table 5).
Compared to the cost of installing 3 tie rods, the cost of installation of one 750mm dia raker piles is found to be cheaper.
System ‘c’ - Diaphragm wall with vertical piles
Three different combination of vertical piles are analysed. System c1 is similar to that of system ‘a’ without anchor rod. In system ‘a’ pile 2,3 and 4 takes 32, 21 and 12% respectively of the total load while anchor takes about 28%. In system c1, the piles 2,3 and
4 take 44, 28 and 17% respectively of the total load. In other words, the 28% load taken by the anchor rod is distributed to the 2nd, 3rd and 4th row piles as 12, 7 and 5% and the remaining 4% is transmitted to the diaphragm wall and pile 1.
The system c1 is found to be inadequate since the lateral load on pile 2 is more than 85 T for the combination of different loads. Hence, the 3rd and 4th row of pile diameter is increased to 1300 & 1000 mm for system c2 and all the 3rd and 4th row of piles are
increased to 1300 mm diameter for system c3. The system c3 is finally chosen since it
distributes lateral load equally to the 2nd, 3rd and 4th row of piles. The typical cross section of the final system as adopted is shown in Figure 6.23.
6.4.1.3 Detailed Analysis
A rigorous analysis of the final system (Figure 6.23) has been carried out using SAP IV program, by idealising the soil support using springs for both the diaphragm wall and piles. The nodes are at 1 m intervals along the depth of the diaphragm wall and piles. The springs are also placed at 1 m intervals. The spring spacing shall be nearly equal to the thickness of diaphragm wall or the pile diameter for effective modeling of soil support in finite element analysis. The spring constants at each node is calculated as the reaction offered by the soil in region 0.5 m above the node and 0.5 m below the node. The soil profile is given in Figure 6.24. The active earth pressure is also calculated at 1 m intervals and is applied as nodal load on the diaphragm wall. The nodal loads are given in Figure 6.25. The bending moment diagram for active earth pressure and a bollard pull of 30 T are given in Figure 6.26 & 6.27 respectively.
R. Sundaravadivelu 1
Ø Ø Ø
Fig 6.23 Idealization for Rigorous Analysis 1100 mm THICK DIAPHRAGM WALL -23.0m -13.0m 395 600 600 1000 mm PILE-I 1300 mmPILE-II 1300 mm PILE-III 680 1300 mm PILE -IV
Fig. 6.24 Soil Profile LEVEL IN M DESCRIPTION Y (T/M ) (T/M ) C Ø (M) H (SPT) N 3 2 -0.78 YELLOW SAND 1.95 0.0 30° 1.63 10 -3.78 YELLOW SAND 1.95 0.0 33° 3.00 20 -4.98 BLACK CLAY 1.70 2.0 0° 1.20 03 -7.78 CRAY SAND 1.95 0.0 33° 2.80 20 -11.76 GREY SAND 1.95 0.0 31° 4.00 15 -13.78 BLACK CLAY 1.80 4.0 0° 2.00 10 -15.78 GREY SAND 1.95 0.0 36° 2.00 30 -19.78 YELLOW SAND 1.95 0.0 34° 4.00 25 -20.78 BROWNISH 1.95 0.0 38° 1.00 40 -24.00 1.95 0.0 45° 3.20 60 BROWNISH SAND SAND BROWNISH
R. Sundaravadivelu 1 0.0 11.1 5.1 4.8 4.6 0 4.0 0 3.6 0 3.3 4.5 4.08 2.5 2.2 -13.0 -11.0 -9.0 -7.0 -5.0 -3.0 LEVEL IN M
NOTE: NODAL LOADS ARE FOR 1 metre WIDE PANEL
Fig.6.26. B.M Due to Active Earth Pressure
Fig.6.27 B.M Due to Bollard Pull of 30 Tons PILE II
PILE I DIAPHRAGM
WALL PILE III PILE IV
-23.0m -21.0m -15.0m -13.0m -9.0m 2 2 1 2 1 B A C DIAPHRAGM
WALL PILE I PILE II
-5.0m -1.0m +3.0m 1 3 E D -15.0m -13.0m -21.0m -23.0m PILE IV PILE III 187 200 42 42 B A 2 +3.0m -1.0m -9.0m -5.0m 16 16 E
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head and an approach jetty.
Fig 6.28 Layout of Jetty 20m ETHYLENE TANKER 75m 10m 25m 75m 8m 8m 8m 15m 1.2m WIDE WALK WAY 8m JETTY HEAD 25m 1.2 m WIDE WALK WAY 10m 8m 8m 20m STERN LINE 8m 8m LIQUID ETHYLENE PIPELINE TO STORAGE TANK
PILE APPROACH CUM PIPE BRIDGE MOORING DOLPHIN MOORING DOLPHIN SHORE LINE BOW LINE
The increase in vessel size has necessitated construction of offshore jetty in deep water in open sea and exposed to winds, waves and currents. Hence offshore jetty is a kind of structure totally different from those in a harbour. The length of approach jetty varies from 1000 to 2500 m and an economical design of approach jetty can be made only after analysing different types of pile configuration for varying water depths. The approach jetty for a length of about 2500 m may have five to seven typical pile bents and each pile bent have to be analysed for different environment forces and soil strata. Anchor bents with rakar piles to take of the longitudinal seismic / pipe line surge forces shall also have to be provided and a three dimensional analysis is necessary for such situations. In addition the berthing and mooring dolphins have to be designed not only for operating wave condition but also for extreme wave condition, during cyclones. Hence a computer aided analysis and design is required for the offshore jetty.
The layout of a mooring dolphin is given in Figure 6.29. The mooring dolphin consists of 16 piles of 760 mm dia. The four corner piles are kept vertical, whereas, the three piles in each face is kept inclined, 3 vertical to 1 horizontal. This configuration has been chosen based on the analysis of various configurations of piles (Ranga Rao & Sundaravadivelu (1994 A)). The mooring dolphin has 2440 mm thick deck slab. The dredge level is -14.00 m and founding level is -24.6 m. The piles are assumed to be fixed at 5D below dredge level i.e., fixity level = 14 + (5 x 0.76) = -17.8 m.
The analysis is carried out using SAP IV idealising the piles by beam elements and the deck using master slave option. The deck can also be idealised using brick element. In this case master-slave option is used since it is simple and gives comparable results with the brick element idealisation of the deck.
The analysis is carried out for the following load cases: (i) Dead load
(ii) Live load of 1 T/m2
(iii) 200 T bollard pull atθ equal to
(a) 45°
(b) 30°
(c) 15°
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Based on the results of the individual load cases (Table 6.6), the critical combination of the tensile and compressive forces on each pile is worked out.
Fig.6.29 Mooring Dolphin 3 1 3 1 DREDGE LEVEL -16.00m B SECTION 1-1 FOUNDING LEVEL -21.60m +1.00m
Table 6.6 Analysis of Mooring Dolphin Pile No Dead load Live load (T/m2)
Axial forces in piles (T) due to 200 T bollard pull at Max forces
45° 30° 15° 0° Tension Compression 1 -50 -7 0 -96 -58 -31 +99 -31 -58 -96 0 96 58 31 -99 31 58 96 26 50 71 21 -57 2 -45 -6 -101 -99 -91 - -152 3 -45 -6 -72 -80 -83 - -134 4 -45 -6 -56 -76 -91 - -142 5 -50 -7 97 87 71 49 -57 6 -45 -6 -6 20 46 - -97 7 -45 -6 -42 -22 0 - -109 8 -45 -6 -85 -68 -46 - -147 9 -50 -7 -26 -50 -71 - -128 10 -45 -6 102 99 91 57 -51 11 -45 -6 72 80 83 38 -51 12 -45 -6 56 76 92 47 -51 13 -50 -7 -87 -87 -71 - -156 14 -45 -6 6 -20 -46 - -97 15 -45 -6 42 22 0 13 -51 16 -45 -6 85 68 46 41 -51
6.4.3 Analysis of Container Berth
The typical layout of the extension of a container berth is given in Figure 6.30. The proposed extension of 220m of the container berth is divided into 4 blocks, each of 55 m. The width of the container berth is 20 m. The span of the container crane is 30 m. It will be uneconomical to provide 30 m width for the container berth and hence one row of piles are provided behind the berth to support the near rail of the container crane. Two container cranes are considered for the analysis. Each container has four legs and each legs has 8 wheels. The center to center distance between two legs is 16.5 m and center to center distance between two wheel is 0.8 m. The deck system consists of 0.4 m thick RCC slab, 0.05 m thick wearing coat, eight main beams of size 0.8 x 2.45 m, twelve secondary beams, three facia beams of size 1.0 x 2.45 m (Figure 6.31). The depth of the webs of all the beams are inclusive of the slab thickness except for the secondary beam which is not integral with the slab.
R. Sundaravadivelu 1 Fig. 6. 30 . La yo u t of Co ntain er B erth LAND S IDE MOORING 13 00Ø PILE CRANE RAI L PIL E MUFF FENDER 29 30 31 32 21 17 9 1 22 23 18 10 19 11 24 20 12 3 CL OF CRANE 1 4 33 34 30000 21 13 26 22 14 5 CL OF CRANE 2 6 6 000 5 50 00 1 8500 6380 8380 6 4 00 19000 4 0 00 9 000 5550 4 5 00 1000 10380 1 65 00 4900 4 5 00 4 0 00 1 650 1000 8380 1 8500 638 0 10380 5 50 00 2 0000 1 65 00 8380 8380
Three berthing points are provided for each panel, one at the middle and others at 10.74 m from each end of the panel. The mooring points are provided at 18.5 m c/c with the extreme one at 9 m from the respective panel edge. The various levels are given below.
Top level of deck : + 4.00 m
Lowest mean water level : 0.00 m The actual dredge level : - 13.75 m The design dredge level : - 14.00 m Cut-off level of piles : +1.50 m The following loads are considered for the analysis. a) Dead load
b) Live load = 5.5T/m2on deck slab
838 500 11 x 1480 152 200 200 MB2 MB1 490 165 CB FB SB12 SB11 SB10 SB9 SB8 SB7 SB6 SB5 SB4 SB3 SB2 SB1
Only CL of the beams are shown
FB - Fender beam - 1000x2450 CB - Crane beam - 700x1200
(Depth of the beam Exclusive SB - Secondary Beam -400x1000
MB3
All Dimensions are in mm of slab thickness) MB - Main Beam -800x2450
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ii) a + d
iii) a + e
iv) b + c + 250 T berthing force across the berth and 82 T along the berth at any one berthing point
v) a + f
vi) a + c
vii) a + b
viii) a + b + c
The increase in the permissible stresses for load combinations (i) to (v) as per IS-4651 (Part IV) is 25 % and the same is assumed in design.
6.4.3.2 Structural Analysis
The berth is analysed as a three dimensional structure using SAP IV Program (Structural Analysis Program - IV an inbuilt computer program). The pile is assumed to be fixed at 5 ‘D’ below the dredge level. Based on the results of the analysis, the piles are divided into four major groups and the axial forces and bending moments for two critical combinations are given in Table 6.7. Since 25% overstress is allowed for these combinations, the forces are reduced by 25% and the piles are designed.
6.4.3.3 Structural Design of Piles
Piles in Group I (23-26) are provided with 2.25% steel, Piles in Group 2 (11-14, 31-34) are provided with 0.8 % steel, Piles in Group 3 (2-7, 10, 15, 18, 19, 22, 29, 30, 35, 36) are provided with 3.0% steel and Piles in Group 4 (1,8, 9, 16, 17, 20, 21, 28) are provided with 2 % steel. Figure 6.32 and Table 6.8 gives the reinforcement details. Structural design of piles is done using the design charts for the circular piles given by Manohar, S.N. (1964).
Fig 6.32 Pile
reinforce
m
ent d
R. Sundaravadivelu 1 31, 32, 33, 34 III 2 to 7, 10, 14, 10, 15, 18, 19 22, 27, 29 30, 35, 36 375 158 59 156 IV 1, 8, 9, 16, 17 20, 21, 28 197 155 112 143
Table 6.8 Reinforcement Details
Pile Group No.
Percentage of Steel (p)
Area of Steel
(m2) No. Of 32 mmφbars in Lateral ties Zone ‘m’ Zone ‘n’ I 2.25 0.0299 38 26 Provide Y10-300 throughout the length of pile II 0.80 0.0107 14 14 -Do-III 3.00 0.0399 51 34 -Do-IV 2.00 0.0266 34 24
-Do-6.4.3.4 Foundation Design of Piles
The piles are designed based on the soil profile. The soil profile indicates silty sand from – 14.0 m to – 22.0 m ( SPT ‘N’ =30), cemented sand from -22.0m to -25.0m (SPT ‘N’ = 50) and rock (SPT ‘N’ >100) for depth below –25.0m. However rock level varies at certain locations. Though 1300mm dia piles founded at -23 m level are found adequate as a good engineering practice, founding depth is adopted with penetration ½ times diameter of pile in hard rock or 3 times diameter of pile in cemented sand strata whichever is earlier. The pile capacities are worked out based on SPT ‘N’ values and using Meyerhof’s correlations as given below.
Ultimate end bearing resistance in sand = 12 [ SPT ‘N’] T/m2 Ultimate skin friction in sand = [ SPT ‘N’] /10 T/m2
The capacity in rock is worked out as per Cole & Stroud as given below. qa = Nc Cb/F
fa = αCs
where
qa = allowable end bearing pressure Nc = bearing capacity factor taken as 9.0 Cb = shear strength of the rock at pile base F = factor of safety taken as 3.0
fa = allowable frictional resistance
Cs = average shear strength of rock along rock socket and α = shaft adhesion factor taken as 0.3.
For silty sand [ SPT ‘N’ = 30]
Ultimate end bearing = 12 x 30 = 360 T/m2
Allowable end bearing = 144 T/m2(ultimate end bearing /2.5) Ultimate skin friction = 30/10 = 3 T/m2
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Allowable friction resistance = 0.3 x 90 = 27 T/m2 Allowable end bearing = 9 x 90/3 = 270 T/m2
Pile Group I
Total load = 427 T
End bearing in rock = 270
4 3 . 1 2× × π = 358.37 = 358 T
Total skin friction from silty sand and cemented sand layers
1.3 (1.2 x 8 + 2 x 3) = 63.71 = 64 T
Required skin friction capacity from rock 427 - (358 + 64) = 5 T
A penetration of 1 m into the rock is recommended.
Hence, the founding depth of piles in Group I shall be -27.0 or 1 m penetration into hard rock which ever is earlier.
Pile Group II
Total load = 383 T
End bearing from cemented sand layer = 1.3 240 318.55T 4
2× =
× π
Total load = 318.55 + 63.71 = 382.26 T = 383 T
Give a penetration of 1 m into the rock. Hence, the founding level of piles in Group II shall be - 26.0 m or 1 m penetration into rock, whichever is earlier.
Pile Group III
Total load = 300 T
Hence, the total load required is less than the end bearing capacity of cemented sand layer. But from the minimum embedment depth criterion, an embedment depth of 5 times the diameter of the pile should be provided. 5 x 1.3 = 6.5 m. But, this falls in the silty sand layer.
Hence, give a penetration of 1 m in the cemented sand layer.
Hence the founding depth for the piles in Group III shall be - 23.0. Similarly the founding depth of piles in Group IV shall also be -23.0 m.
As the spacing between the groups of piles (23,24,25,26) & (31,32,33,34) is only 4.9 m, the foundling level for both these groups is kept as 1 m penetration to the rock or -27.0 m whichever is earlier.
For the same reason as stated above for the two groups of piles (11,12,13,14) & (3,4,5,6) the founding level is kept as 1 m penetration into the rock or -26 m, whichever is earlier. For the rest of the piles the founding level is -23.0 m.
6.5 DESIGN OF BERTHING STRUCTURES
Once the analysis of any structural system is completed, the next step would be the design of various elements in the structural system. Generally, the design process is iterative as the design variables chosen may not satisfy the allowable stress/strain parameters. This process should be repeated until a satisfactory solution is obtained. The design shall be carried out as per the guidelines specified in IS 456-1978. As per IS 4651 (Part IV) - 1989 the minimum grade of concrete to be used in berthing structures is specified as M 30. The minimum cement content of 0.4 T/m3 and maximum water cement ratio of 0.45 shall be maintained for all grades of concrete. The minimum thickness of cover for structures
R. Sundaravadivelu 1
There are two methods of design namely, Working Stress method and the Limit State method. In the working stress method the design is based on the linear stress strain relationship within the elastic limit. The structure shall be designed for the working loads and checked for the permissible stresses. The permissible stresses are the stresses obtained after applying a factor of safety to the yield strength of the materials.
In the limit state method the design is based on Limit State concept. The structure shall be designed to withstand safely all the loads liable to act on it throughout its life. It shall also satisfy the serviceability requirements such as limitations on deflection and cracking. The acceptable limit for the safety and serviceability requirements before failure occurs is called a “Limit State”. The diaphragm wall and pile are the two important structural elements of a berthing structure and the detailed design method for the diaphragm wall and pile is given in this section.
6.5.1 Design of Diaphragm Wall
The diaphragm wall is to be designed using the design philosophy given in the following section. Requirements of reinforcement are given in Section 6.5.1.2.
6.5.1.1 Design Philosophy
The basic assumption is that the maximum strain in concrete at the outermost compression is 0.0035, when the neutral axis lies within the section. The strain varies from 0.0035 at highly compressed edge to zero at the opposite edge when the neutral axis lies along one edge of the section. For purely axial compression, the strain is assumed to be uniformly equal to 0.002 across the section. The strain distribution lines for these two cases intersect each other at a depth of (3/7) D from the highly compressed edge. This point is assumed to
act as a fulcrum for the strain distribution line when the neutral axis lies outside the section as shown in Figure 6.33.
Fig 6.33 Strain Diagrams
Neutral Axis Lying Outside Section:
When the neutral axis lies outside the section, the shape of the stress block will be as indicated in Figure 6.34. The stress is uniform for a distance of (3/7)D from highly compressed edge because the strain is more than 0.002 and thereafter the stress diagram is parabolic. Let xu = kD and let ‘g’ be the difference between the stress at the highly
compressed edge and the stress at the least compressed edge. Considering the geometrical properties of a parabola,
0.0035
NEUTRAL AXIS WITHIN THE SECTION
0.0035 0.002 a X x b d' CENTRODAL AXIS d' yi HIGHLY COMPRESSED EDGE
R. Sundaravadivelu 1 Fig. 6.34 Stress Block when the Neutral Axis lies Outside Section
2 ck 3 k 7 4 f 446 . 0 g − = (6.21)
Area of the stress block = − − 2 ck 3 k 7 4 21 4 1 D f 446 . 0 (6.22)
The centroid of the stress block will be found by taking moments about the highly compressed edge.
STRAIN DIAGRAM
Moment about the highly compressed edge = 2 2 ck gD 49 8 2 D f 446 . 0 − (6.23)
The position of the centroid is obtained by dividing the moment by area.
While designing the diaphragm wall, the neutral axis at regular intervals is assumed. For each position of neutral axis, the strain distribution across the section and the stress block parameters are determined as explained earlier. The stresses in the reinforcement are also calculated from the strains. Thereafter the resultant axial force and the moment about the centroid of the section are calculated as follows:
) f f ( 100 pibD D b f C P si ci n 1 i ck 1 u = +
∑
− = (6.24) whereC1 = Coefficient for the area of stress block
Pi = (Asi/bD) where Asi is the area of reinforcement in the ith row
fsi = Stress in the ith row of reinforcement, compression being positive and tension being negative
fci = Stress in concrete at the level of ith row of reinforcement n = Number of rows of reinforcement
Taking moment of forces about the centroid of the section,
yi ) f f ( 100 pibD D C 2 D D b f C M si ci n 1 i 2 ck 1 u + − − =
∑
= (6.25) whereC2D = the distance of the centroid of the concrete stress block, measured from the
highly compressed edge
yi = the distance from the centroid of the section to the i th
row of the reinforcement, positive towards the highly compressed edge and negative towards the least compressed edge.
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6.5.1.2 Requirements of Reinforcement
The minimum reinforcement of 0.4% and the maximum reinforcement of 4% are incorporated for the design of diaphragm wall.
The shear reinforcement shall be provided to carry a shear equal to Vs = V-τc.bd. The spacing of the vertical stirrups, sv is given by
S sv y v V d A f 87 . 0 S = (6.28) where
V = Shear force due to design loads Vs = Strength of shear reinforcement
Asv = Total cross sectional area of stirrup legs
sv = Spacing of the stirrups along the length of the member τc = Design shear strength of the concrete
fy = Characteristic strength of the stirrup, which shall not be greater than 415 N/mm2
6.5.2 Design of Pile
Circular piles are widely used as foundations for coastal and offshore structures like berths, jetties, dolphins etc. Circular piles are preferred in these structures because they can be easily installed with a liner. As these sections have uniform c/s about any diametrical axis,
these sections are best suited to resist multi-directional wave loads (Srinivas & Sundaravadivelu (1987)). Piles are designed by working stress method to limit crack width.
6.5.2.1 Design Philosophy
The design of compression members can be carried out in two distinct stages.
1. Design based on uncracked section, i.e. there is no tension anywhere in the section or the resultant tensile stress is less than the permissible tensile stress of concrete. 2. Design based on cracked section, i.e. the resultant tensile stress is more than the
permissible tensile stress in concrete. Design of Uncracked Sections:
In general, for an assumed percentage of reinforcement and neutral axis depth the stresses under given loading are checked against permissible stresses. The various steps involved in the design are as follows:
1. Check by interaction formula : The interaction formula as given below has to be
satisfied. 1 f f cbc cbc cc cc ≤ σ + σ (6.29)
fcc = Calculated direct compressive stress in concrete σcc = Permissible axial compressible stress in concrete fcbc = Calculated bending compressive stress in concrete σcbc = Permissible bending compressive stress in concrete
For more exact calculations, the maximum permissible stress in a reinforced column or part there of having a ratio of effective column length to least radius of gyration above 40 shall not exceed those which result from multiplication of the appropriate maximum permissible stresses by the reduction coefficient, Cr given by the following formula
Cr = 1.25 - (lef)/(160 )imin (6.30)
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In case of cracked section design, the tensile stress of concrete is ignored. The design of cracked section is carried out using two equilibrium equations.
P = Cc + Cs- T (Force equilibrium) (6.31)
M = Cc Xc + Cs Xsc + TXst (Moment equilibrium) (6.32)
Where
Cc = Compression in concrete segment.
= β β + β β − β β − 4 2 sin cos 2 cos 3 sin ) cos 1 ( R f 2 cbc 2 3 (6.33)
Cs = Compression in steel reinforcement.
= ) cos 1 ( 100 p R fcbc 2 β − (1.5 m - 1) (1-d/R) (sinα -α α) (6.34)
T = Tension in steel reinforcement.
= ) cos 1 ( 100 mp R fcbc 2 β − (1-d/R) (sinα + (π -α) cosα) (6.35)
= β − β β − β β − 32 4 sin 3 sin cos 8 ) cos 1 ( R f 2 cbc 3 3 (6.36)
Cs Xsc = Moment of compression of steel about the center line.
= α− α − − β − 4 2 sin 2 ) R / ' d 1 ( ) 1 m 5 . 1 ( ) cos 1 ( 100 p R f 2 3 cbc (6.37)
TXst = Moment of tension in steel about the center line.
= π−α+ α − β − 4 2 sin 2 ) R / ' d 1 ( ) cos 1 ( 100 mp R f 2 3 cbc (6.38)
Equations (6.11) and (6.12) have to be solved for fcbc and eitherα orβ. Usually trial and
error method is used to solve these equations. Once these two equations are solved the stress in steel can be determined by using the following equations.
n ) ' d n R 2 ( mf fst cbc − − = (6.39) where
n = depth of neutral axis
= R (1 - cosα) (6.40)
= (R - r cosβ) (6.41)
Knowing the stress in steel, cover to the reinforcement and modulus of elasticity of concrete, crack width can be calculated using appropriate crack width formula.
6.5.2.2 Requirements of Reinforcement
The reinforcement shall not be less than 0.4% as per IS 2911 (part I)-1979. In general maximum reinforcement of 4% is considered in the design due to the difficulty in placing more than 4% reinforcement. The diameter of the reinforcement bar shall not be less than 12 mm.
The diameter of the lateral ties shall be not less than one-fourth of the diameter of the largest longitudinal bar, and in no case less than 5 mm. The spacing of the transverse reinforcement shall not be more than the least of the following distances:
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However, large scale cracking is not acceptable because of its ugliness and the resultant ingress of moisture and eventual corrosion.
A dense concrete with adequate cover to the reinforcement can protect it during the entire useful life of the structural component. But cracking permits the ingress of carbon dioxide, chlorides, etc. thus initiating corrosion. Direct and indirect financial losses due to corrosion runs to several millions of rupees in India and hence the limit state of clacking is included as one of the important design limit states. Concrete cracks even when there is no external load applied on a structure, mainly due to shrinkage and temperature effects. Tension members of reinforced concrete have cracks penetrating right through the cross section and steel reinforcement is the only connecting link between the various parts. Such cracks are called as separation cracks. On the other hand, the reinforced concrete member subjected to pure flexure has cracks in the tensile zone only and they penetrate the cross section of the member up to the neutral axis. These flexural cracks are of primary concern to the designers.
For purposes of crack control, it is essential to define the admissible crack width. As per IS 4651 (Part IV)- 1989 the crack width should be less than 0.004 times the cover provided. Many research organizations and codes like CEB/FIP, ACI Code, Russian Code, DIN Code, British Code, IRC Code etc., have recommended various formulae for the calculation of crack width. Many of these formulae are arrived at conducting experiments on rectangular beams subjected to bending moment only. Consequently the expressions derived have included the width of the section as a parameter. Only IRC formula appears to be applicable for circular piles because it involves only stress in steel and effective cover concrete.
The formulae given by CEB/FIP, IRC and SP24 are given below. 6.5.3.1 CEB/FIP Formula
CEB/FIP recommends the following formula to calculate the crack width (Cw),
Cw = (1.5 C + 16φ/Pf) (σs - 3000/Pf) x 10-6 (6.42)
Where
C = Effective cover
φ = Diameter of the reinforcing bar
σs = Stress in tensile steel Pf = (100 Ast)/(0.25 bh)
Ast = Area of tensile steel
b = Breadth of the section h = Depth of the section 6.5.3.2 IRC Formula
The IRC formula is given for bridge like structures to calculate the crack width. As berthing structures are also subjected to truck loads such as class AA etc., the formula given by IRC has been used to calculate the crack width. The formula given by IRC to calculate crack width, Cw is as follows:
Cw = (3.3 fst dc)/(m Ec) (6.43)
where
fst = Stress in steel
dc = Effective cover m = Modular ratio
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Cmin = Minimum cover to the longitudinal bar εm = Average strain at the level considered D = Overall depth of the member
x = Depth of neutral axis
The average strain at the level at which cracking is being considering is given by
3 s st t 1 m x10 f ) x d ( A ) x ' a ( D b 7 . 0 − − − − ε = ε (6.45) Where
ε1 = The strain at the level considered ignoring the concrete in the tension zone bt = The width of the section at the centroid of the tension steel
a’ = The distance from the compression face to the point of the crack Ast = The area of tension steel
fs = Service stress in tension reinforcement which may be taken as
= provided A required A f 58 . 0 st st y× (6.46)
The above formulae can be used provided the strain in tension reinforcement does not exceed 0.8 fy/Es. The negative value of εm indicates that the section is uncracked. In
assessing the strains, the modulus of elasticity of concrete shall be taken as 280/3σcbc as given in elastic theory to account for creep.
6.5.4 Computer Aided Design
Since the design of berthing structures involves analysis of various configurations considering nonlinear behaviour of soil, and, codal provisions for crack width calculations, computer aided design of berthing structures has become necessary (Ranga Rao & Sundaravadivelu (1994).
6.6 MARINE FENDERING SYSTEMS
6.6.1 General
The purpose of the marine fendering system is to prevent damage to both the vessel and berth, during the berthing process and while the vessel is moored. As the vessel approaches a berth it possess kinetic energy by virtue of its displacement and motion. As the vessel contacts the berth and is brought to stop this kinetic energy must be dissipated. Fendering systems that is being berthed are provided to absorb or dissipate the kinetic energy of the ship.
6.6.2 Types of Fendering Systems
The different types of fendering systems are as follows: 1. Standard pile fenders
2. Rubber fenders 3. Pneumatic fenders 4. Gravity type fenders 6.6.2.1 Standard Pile Fenders
This system is generally used for low energy absorption. The piles made of timber, steel. RCC and PSC are driven in front of the berthing structure to absorb the energy from the ship by direct compression and flexure. The energy capacity depends on the size, shape and length of the pile. Wooden piles does not have long life while the RCC piles have low energy absorption. Steel piles and PSC piles with rubber buffers are used for larger depths.
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used for jetties and berths also because of its good performance. The pneumatic fender is an inflated rubber bag and dimensions vary from 0.5m to 4.5 m in dia and 1m to 12 m in length. The fender bag is protected by wire or chain net with tyres or rubber sleeves. The energy absorption does not decline at inclined compression for these fenders.
6.6.2.4 Gravity Type Fenders
These are generally made of concrete blocks suspended from a heavily constructed wharf work. the Impact energy is absorbed by moving and lifting the heavy concrete block.
6.6.3 Selection Criteria of Fendering Systems
The selection of a optimum fender for a given service depends on the following factors : 1. The type, size, draft and allowable hull pressure of a vessel.
2. Berthing velocity and angle.
3. Distance between the berthing point and the vessels gravity centre measured along the face of the pier.
4. Water level, tidal range, wind velocity, direction of wind, direction and velocity of currents.
5. Behaviour and installation pitches of Dock fender 6. Structure and strength of Berthing facilities 7. Certain human factors involved in berthing.
6.6.4 Berthing Energy of a Vessel
The design of fenders depends very much on the energy to be absorbed by the fenders during berthing. When a ship strikes the fender, it transfers some part of the kinetic energy to the fender and the other part gets dissipated to the motion of ship in water. Some part of the energy absorbed by the fender is transferred back to the ship, after the ship has come to rest, by the fender trying to recoil back to its normal shape. This process of exchange of energies between fender, ship and the loss of energy in water motion continues till the whole of the kinetic energy of ship is dissipated in water motion. The different methods that are used in determining the maximum amount of energy to be absorbed by the fender is given below :
6.6.4.1 Quinn Method
In this method fifty percent of the energy of the ship calculated on the basis of the velocity of the ship normal to berthing structure is assumed as the energy absorbed by the fender.
4 V G W E 2 = (6.47) 6.6.4.2 Woodruff Method
In this method the following empirical equation is used to calculate the berthing energy.
E = W(0.004 - W x 10-8 (6.48)
Where W is in tons and E is in ton feet. 6.6.4.3 Vasco Costa Method
Vasco Costa has given the following analytical solution, for a ship moving with translatory velocity u and angular velocity w, having no slip along the berth.
E = (WV2/2g) (1 + 2D/B) (K2 + r2 Cos2r / K2 + r2) (6.49)
Where v Distance P= u + aw
The value of k can be taken as 0.2 L to 0.29 L. The following three coefficients are to be considered along with equation.