11 Theory of a vertically loaded Suction Pile in CLAY Mainly based on the et Norske Veritas NV-RP-E303 1. Convention Water COG h L Soil COG t Figure 1 Suction Pile Figure 2 Suction pile with main parameters Possible forces: Main parameters: Total resistance of suction pile (R d ) - Water depth (h) Vertical load force (T d ) - Pile or caisson length (L) (Submerged) Self weight caisson (W ) - Pile or caisson diameter () Effective overburden pressure (P 0 ) - Pile thickness (t) Penetration resistance (Q tot ) - Penetration depth () Side shear along the side wall (Q side ) - Center of grity (CoG) The bearing capacity at the skirt tip (Q tip ) Necessary underpressure ( u n ) 1
22 2. Soil conditions For the calculation of the holding capacity or resistance R the most important variable is the SS (irect Simple Shear test) cyclic shear strength τ f, cy. With this the shear strength between the pile and the soil can be determined. The cyclic shear strength is associated by the characteristic storm and the equivalent number of cycles it produces N eq. This can be done using an empirically determined graph. τ f, cy τ With the graph the value of can be determined with the normalied shear stress a S u consisting of the erage shear stress τ a divided by the static undrained shear stress S u. S u,, Figure 3 Cyclic SS shear strength of clay for various N eqv The erage shear stress can be calculated by: τ When hing determined f, cy S u τ = a 0 S d, from this the cyclic SS strength can be determined. u pile 2
33 In short, for the suction pile calculation in offshore clay the following variables are needed with their ranges: Cyclic SS strength of the intact clay, τ f, cy 0 100 kpa Plasticity index, I p 20% - 100% Static undrained shear stress, S u 5 100 kpa Soil sensitivity, S t 1-8 Effective unit weight of soil, γ 9 11 kn/m 3 Average shear stress, τ a The soil sensitivity S t is a factor to show the strength of the soil after it s been remoulded, determined from laboratory tests; Su St = S remoulded The Plasticity index Ip is also determined in by laboratory tests and is determined by the difference between the liquid limit and the plastic limit of the soil. 3. esign Limit state design For the general design criterion is the following, Where R is the design value of the resistance of the pile and T is the tension in the mooring line, both at the depth of the pad-eye; the connection point between the suction pile and the mooring line. The tension will be determined as follows: Where 3
44 In the following figure the case is described that, with horiontal loading, the tension in at the pad-eye T ( ) differs from the tension at the dip-down point T ( P ). Figure 4 - Change of tension and uplift angle between dip-down point and padeye depth. The resistance is determined as follows:, where In this resistance the submerged weight of the suction pile is included and determined by the cyclic shear strength. The γ depends on the limit state; the ultimate limit state ULS or the accidental damage limit state. These are put in line in this table: Table 1 the various factors depending on the limit state The limit state design is a general requirement for calculating the eventual required resistance. As the process will be done by iteration, it is recommended to start with the preliminary design by means of rules of thumb. Preliminary design For the preliminary design, there are two rules of thumb for determining the dimensions suction pile in clay: L/d = 3 to 6 d/t = 100 to 250 Where L is the total length of the pile, d the diameter and t the wall thickness. The first rule of thumb is determined by the behior of the suction piles with general soil properties of clay and the second by the elasticity and buckling ranges of the caisson. 4
55 After assuming the variables, the bearing capacity can be calculated, knowing the soil conditions, and be compared to the maximum load on the suction piles. This is a process of iteration to achieve the desired results. Calculation of the resistance The resistance can be calculated as the sum of the shear force along the outside of the pile and the inside of the pile. For suction piles in clay there are two optional cases for which the shear strength and thus the total resistance can be calculated, depending on the type of installation; the shear strength for the suction pile installed by penetration by self weight and by penetration by underpressure. Firstly the set-up factor for both methods of installation has to be determined. Set-up factor The ratio between the shear strength at the interface between clay and outside skirt wall and the original shear strength is referred to as the shear strength factor or set-up factor: With this factor, the determining shear strength for the bearing capacity calculation of the suction pile can be calculated. The set-up factor depends on the type of installation, as in penetration by self weight or by underpressure. For self weight penetration, the factor is determined as follows: The set-up factor in this case can be calculated by the following formulae, with a plasticity index of the clay of I p >20%: Where P 0 S u effective overburden pressure static undrained shear stress The effective overburden pressure is the overburden pressure (=ρg) minus the pore pressure at the depth. P = ρ g ρ g = ρ g 0 ' grain, wet water pile grain, dry pile The self weight penetration depth will be determined later. 5
66 For penetration by underpressure, the set-up factor will be calculated using the method described below. Here, the set-up factor needs to be determined by an empirically determined table, depending on the plasticity index I p and the soil sensitivity S t of the clay: Table 2 the lower bound set-up factor α (after consolidation) Resistance along skirts penetrated by self weight With the earlier calculated set-up factor for self weight installation and the known original cyclic SS strength of the clay the shear strength S rr between the skirt and soil can be calculated. If this is integrated over the surface A skirt of the skirt, the holding capacity or resistance R can be calculated: R = S A = α τ A rr skirt f, cy skirt The surface of the skirt is on the outside of the skirt over the self weight penetration depth. The set up factor that is used is the one calculated earlier for the self weight penetration. Shear strength along skirts penetrated by underpressure Keeping in mind the earlier determined set-up factor for penetration by underpressure, the formula for the resistance can be applied again: R = S A = α τ A rr skirt f, cy skirt The surface of the skirt A skirt is on the outside of the skirt over the penetration depth. 4. Installation For installation there are two types or phases; self weight penetration and installation by underpressure. In general, a suction pile will be installed with two methods combined. The pile will penetrate first into the soil by its own submerged weight where after the pumping installation will penetrate. In this case the bearing capacity will be calculated by the method of the underpressure. 6
77 Self weight penetration depth The submerged self weight (W ) penetration depth can be calculated by assuming the weight to be equal to the penetration resistance Q tot. This is the total penetration resistance resulting of the side shear along the side wall Q side plus the bearing capacity at the skirt tip Q tip. Where: A wall skirt wall area (sum of inside and outside) A tip skirt tip area α shear strength factor or set-up factor (normally assumed equal to the inverse of the sensitivity; if the skirt wall is painted or treated in other ways, this must be taken into account in the α-factor) S erage SS shear strength over penetration depth S erage undrained shear strength at skirt tip level (erage of triaxial γ' N c tip compression, triaxial extension and SS shear strengths) effective unit weight of soil bearing capacity factor, plane strain conditions skirt penetration depth The bearing capacity factor N c varies from 6.2 to 9, calculated by the following formula: The erage SS shear strength over penetration depth S and the erage undrained shear strength at skirt tip level can be calculated using: S C E τ f, cyd = and τ + τ + τ S,,, u, tip = 3 swpd f cy f cy f cy 7
88 Installation by underpressure For installation by underpressure, the most important variable is the required underpressure. The necessary underpressure u n, needed for the finaliation of the installation or penetration, depends on the self weight penetration depth and the total resistance for the penetration Q tot : Where: W submerged weight during installation A in plan view inside area of the pile where underpressure is applied 8