Design of Embankments over Piles to BS 8006
Accompanying Document to Design Spreadsheet
Officine Maccaferri Spa Via Agresti, 6 40123 Bologna tel. +39-051-6436000 fax. +39-051236507 www.maccaferri.com
March 2008
1
Introduction The piled embankment technique allows embankments to be constructed to unrestricted heights at any construction rate with subsequent control of postconstruction settlements. Basal reinforcement is used to bridge across the top of piles to distribute the load and maximize the economic benefits of piles installed in soft foundations. BS 8006 assumes that all of the embankment loading will be transferred through the piles down to a firm stratum. Consequently, the performance of the embankment, and the characteristics of the soft foundation soil have to be considered only with regard to the type of piles used and their installation. Reinforcement spanning across the pile caps is used to transfer the embankment loading onto the piles. The reinforcement permits the spacing of the piles to be increased and the size of the pile caps to be reduced. The reinforcement also counteracts the horizontal thrust of the embankment fill and the need for raking piles along the extremities of the foundation can be eliminated. BS 8006 considers the following ultimate limit states: — Pile group capacity, — Pile group extent, — Vertical load shedding onto the pile caps, — Lateral sliding stability of the embankment fill, — Overall stability of the piled embankment (this limit state is not discussed in this document and is not included in the design spreadsheet). The serviceability limit states to be considered are: — Excessive strain in the reinforcement, — Settlement of the piled foundation (this limit state is not discussed in this document and is not included in the design spreadsheet). The maximum ultimate limit state tensile load T r per metre run, in the reinforcement should be the following: (a) In the direction along the length of the embankment the maximum tensile load should be the load needed to transfer the vertical embankment loading onto the pile caps, T rp, (b) In the direction across the width of the embankment the maximum tensile load should be the sum of the load needed to transfer the vertical embankment loading onto the pile caps, T rp, and the load needed to resist lateral sliding, T ds. Partial factors of safety BS 8006 is a limit state code of practice and as such partial factors are applied to the loads, soil unit mass and strength parameters. The partial factors specified by BS 8006 for use in the design of piled embankments are summarised in Table 1.
2
Table 1. Summary of partial factors used in BS 8006 for piled embankment design. Partial factors Ultimate limit Serviceability state limit state f fs = 1.3 f fs = 1.0 Load factor Soil unit mass External dead loads f f = 1.2 f f = 1.0 f q = 1.3 f q = 1.0 External live loads f ms = 1.0 f ms = 1.0 Soil material factors To be applied to tan φ CV ' Soil/reinforcement interaction factors
Sliding across surface of reinforcement Pull-out resistance of reinforcements
f s = 1.3
f s = 1.0
f p = 1.3
f p = 1.0
A partial material factor to take account of the long-term reinforcement strength is also specified in BS 8006. The over partial material factor, f m, is calculated as follows: f m = f m11 f m12 f 21 f 22
Where: f m11 is a partial material factor related to the consistency of manufacture of the reinforcement and how strength may be affected by this and possible inaccuracy in assessment, f m12 is a partial material factor related to the extrapolation of test data dealing with base strength, f m21 is a partial material factor related to the susceptibility of the reinforcement to damage during installation in the soil, f m22 is a partial material factor related to the environment in which the reinforcement is installed.
The effects of long-term creep are accounted for in design by limiting the load in the reinforcement to prevent creep-rupture of the reinforcement over the design life. A partial creep factor, f cr , is introduced which accounts for the reinforcement reaching creep-rupture during the design life of the structure. The partial creep factor is not part of BS 8006, which uses a creep limited strength, CLS, to account for creep. The partial creep factor used in the spreadsheet is the inverse of the creep limited strength and is therefore compatible with BS 8006. Values for the partial material and partial creep factors for ParaLink appropriate for use in piled embankments with a 120 year design life and a design temperature of 20 0C are presented in Table 2. For other design conditions please refer to the Maccaferri Technical Data Sheet for ParaLink Geogrids.
3
Table 2. Partial material and creep factors for ParaLink in piled embankments where the design life is 120 years and a design temperature of 20 0C. Partial material factor Condition Value f m11 1.05 f m12 1.05 f m21 ParaLink 200-250 1.10 ParaLink 300-450 1.05 > Paralink 500 1.05 f m22 1.10 2.0 ≤ pH ≤ 4.0 1.03 4.1 ≤ pH ≤ 8.9 1.10 9.0 ≤ pH ≤ 9.5 f cr 1.38 In addition, BS 8006 accounts for the economic ramifications of failure of the piled embankment by specifying a partial factor for the ramifications of failure, f n. The magnitude of this partial factor is dependent on the type of structure and the design life. For piled embankments the ramifications of failure are high resulting in f n = 1.1. The design strength, P d , of the reinforcement in the direction along the embankment is determined as follows: P d = T rp f m f n f cr
The design strength, P d , of the reinforcement in the direction across the embankment is determined as follows: P d = (T rp + T ds ) f m f n f cr
Where, T rp is the maximum limit state tensile force to be resisted by the basal T ds
reinforcement due to arching, is the maximum limit state tensile force to be resisted by the basal reinforcement along the embankment length due to direct sliding.
Pile group capacity The load carrying capacity of the pile group should be designed to an appropriate design code and should include any reduction in pile capacity due to group action. Where the piles are installed on a square grid the maximum centre-tocentre pile spacing, s, is given by: s =
Q P f fs γ H + f q w s
4
Where: Q p is the allowable load carrying capacity of each pile in the pile group; f fs is the partial factor for soil unit weight, γ is the unit weight of the embankment fill, H is the height of the embankment, f q is the partial load factor for external applied loads, w s is the external surcharge loading. Pile group extent The piled area should extend to a distance beyond the edge of the shoulder of the embankment to ensure that any differential settlement or instability outside the piled area will not affect the embankment crest. The edge limit of the outer pile cap is given by: L P = H ( n − tan θ p )
Where: LP is the horizontal distance between the outer edge of the outside pile cap and the toe of the embankment, n is the side slope of the embankment, θ P is the angle, to the vertical, between the outer edge of the outside pile cap and the shoulder of the embankment. Vertical load shedding It is necessary for the vertical embankment loads to be transferred onto the pile caps. To ensure localised differential deformations cannot occur at the surface of embankments (which can be a problem with shallow embankments) it is recommended that the relationship between embankment height and pile cap spacing be maintained to, Figure 1: H ≥ 0.7( s − a)
Where: a is the size of the pile cap. BS 8006 assumes that the pile caps are square and that the reinforcement material is in direct contact with the top of the pile cap. Where circular pile caps are used it is suggested that the diameter of the circular pile cap be divided by 1.15 to arrive at an appropriate pile cap size, a , for use in design. Where a 0.5 m layer of fill is placed between the pile caps and the reinforcement the size of the pile cap can be multiplied by 1.2 to arrive at an appropriate pile cap size, a , for use in design.
5
Figure 1. Outer limit of pile caps for vertical load shedding. Because of the significant differences in deformation characteristics that exist between the piles and the surrounding soft foundation soil, the vertical stress distribution across the base of the embankment is non-uniform. Soil arching between adjacent pile caps induces greater vertical stresses on the pile caps than on the surrounding foundation soil. The ratio of the vertical stress exerted on top of the pile caps to the average vertical stress at the base of the embankment, p C ' , is estimated in BS 8006 by use of Marston’s formula for positive projecting σ V ' subsurface conduits:
C a = C σ V ' H p C '
2
Where, pc ’ is the vertical stress on the pile caps, σ v ’ is the factored average vertical stress at the base of the embankment, C C is the arching coefficient. Values for the arching coefficient C C are shown in Table 3. Table 3. Values for the arching coefficient, C C. Pile arrangement End-bearing piles (unyielding) Friction and other piles (normal)
Arching coefficient H C C = 1.95 − 0.18 a H C C = 1.5 − 0.07 a 6
The distributed load, W T, carried by the reinforcement between adjacent pile caps can be determined from: For H > 1.4( s − a) : W T =
1.4 sf fs γ ( s − a ) 2 2 p C ' s a − σ ' s 2 − a 2 V
For 0.7( s − a ) ≤ H ≤ 1.4( s − a) : W T =
s( f fs γ H + f q w s ) 2 2 p C ' s a − σ ' s 2 − a 2 V
but W T = 0 if
s
2
a
2
≤
pC ' σ V '
.
The tensile load, T rp, per metre run generated in the reinforcement resulting from the distributed load W T is: T rp =
W T ( s − a) 2a
1+
1 6ε
Where: ε is the strain in the reinforcement. The above equations have two unknowns T rp and ε . It is solved for T rp by taking into account the maximum allowable strain in the reinforcement and by an understanding of the stress-strain characteristics of the reinforcement. The tensile load in the reinforcement develops as the reinforcement deforms under the weight of the embankment. This normally occurs during embankment construction but in situations where the reinforcement cannot deform during construction the reinforcement will not carry the applied loads until the foundation settles. Lateral sliding The reinforcement should resist the horizontal force due to lateral sliding. This reinforcement tensile load should be generated at a strain compatible with allowable lateral pile movements thereby eliminating the need for raking piles. The reinforcement tensile load, T ds, needed to resist the outward thrust of the embankment is: T ds = 0.5 K a ( f fs γ H + 2 f q w s ) H
7
Where: K a is the active earth pressure coefficient K a = tan 2 (450 −
φ CV 2
),
φ CV is constant volume angle of internal friction.
To generate the tensile load T ds in the reinforcement the embankment fill should not slide outwards over the reinforcement. To prevent this horizontal sliding the minimum reinforcement bond length, Le, should be, Figure 2: Le =
0.5 K a H ( f fs γ H + 2 f q w s ) f s f n
α ' tan φ CV ' f ms
γ h
Where: f s is the partial factor for reinforcement sliding resistance, f n is the partial factor for the economic ramifications of failure, f ms is the partial material factor applied to tan φ CV ' , h is the average height of the embankment fill above the reinforcement length, Le, is constant volume angle of internal friction under effective stress φ CV ' conditions, α ’ is the interaction coefficient relating the soil/reinforcement bond angle to tan φ CV ' , Reinforcement bond The reinforcement should achieve an adequate bond with the adjacent soil at the extremities of the piled area. This is to ensure that the maximum limit state tensile loads can be generated (across the width and along the length of the embankment) between the outer two rows of piles. Across the width of the embankment the reinforcement should extend a minimum distance beyond the outer row of piles given by: Lb ≥
f n f p (T rp + T ds )
α 1 ' tan φ CV 1 '
γ H
f ms
+
α 2 ' tan φ CV 2 ' f ms
Where: is constant volume angle of internal friction under effective stress φ CV 1 ' conditions on one side of the reinforcement, α 1’ is the interaction coefficient relating the soil/reinforcement bond angle to tan φ CV 1 ' on one side of the reinforcement,
8
is constant volume angle of internal friction under effective stress
φ CV 2 '
conditions on the other side of the reinforcement, α 2 ’ is the interaction coefficient relating the soil/reinforcement bond angle to tan φ CV 2 ' on the other side of the reinforcement. Along the length of the embankment the reinforcement should extend a minimum distance beyond the outer row of piles given by, Figure 2: Lb ≥
f n f p T rp
α 1 ' tan φ CV 1 '
γ H
f ms
+
α 2 ' tan φ CV 2 ' f ms
Depending on the geometry of the embankment it may be difficult to achieve an adequate bond length at the extremity of the piles by maintaining the reinforcement in a horizontal alignment. One solution to this problem is to use a row of gabions as a thrust block along the top of the outer row of piles. The reinforcement is extended around the row of gabions and returned into the embankment fill to develop the necessary bond length.
Figure 2. Required length of reinforcement after outer row of pile caps to provide bond length and resist lateral sliding. Reinforcement strain The maximum allowable strain in the reinforcement εmax should be limited to ensure differential settlements do not occur at the surface of the embankment. This can be a problem with shallow embankments where the soil arch cannot develop fully within the embankment fill. The initial tensile strain in the reinforcement is needed to generate a tensile load. BS 8006 imposes a practical upper limit of 6 % strain to ensure all embankment loads are transferred to the piles. With shallow embankments this upper strain limit may have to be reduced
9
to prevent differential movements at the surface of the embankment. The longterm strain (due to creep) of the reinforcement should be kept to a minimum to ensure that long-term localised deformations do not occur at the surface of the embankment. BS 8006 restricts the maximum creep strain over the design life of the reinforcement to 2 %. Note: Compatibility between the assumed and calculated design strains is made with reference to the short-term stress-strain curve for ParaLink. The spreadsheet allows a ± 10 % variation between the calculated loads and that determined from the stress-strain curve based on the initially assumed design strain. Operation of the design spreadsheet The design parameters are entered in the back boxes, Figure 3. Design parameters required are: Embankment height, Traffic load, Unit weight of embankment fill, Friction angle of embankment fill and subsoil, Piled load and pile type, Reinforcement design strain, Average height of the embankment, across and along the embankment, and for horizontal sliding. The red values on this sheet are calculated values and should not be altered. The design strain and partial material factors are inputted in the yellow boxes on page two, Figure 4. By scrolling down the page intermediate calculations can be viewed. The spreadsheet automatically makes the following checks: 1. A check on the pile and embankment geometry, 2. A check on strain compatibility in the longitudinal and transverse directions, 3. A check on creep strain over the design life. The spreadsheet will indicate where the checks have not been satisfied and appropriate corrective action should be taken. The following are suggested actions: 1. In the case of the geometry check: the spacing of the piles and/or the pile cap size should be adjusted, 2. In the case of strain compatibility: the design strain should be altered. Typically a design strain in the range 4 % - 6 % is suitable for use with ParaLink,
10
3. In the case of creep strain over the design life: the long-term creep strain for the material should be checked. The creep strain of ParaLink for a 120 year design life satisfies the requirements of BS 8006. Notes are also provided in the spreadsheet on the lateral thrust issue, Figure 5, and on calculating the bond length under the side slope of the embankment, Figure 6.
11
Figure 3. Page one of the design spreadsheet.
12
Figure 4. Page two of the design spreadsheet.
13
Figure 5. Notes on lateral thrust issues.
Figure 6. Notes on calculating the bond length under the embankment side slope.
14
