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Evaluation of Vertical Effective Stress and Pile Lateral
Capacities Considering Scour-Hole Dimensions
Journal: Canadian Geotechnical Journal
Manuscript ID cgj-2017-0644.R2
Manuscript Type: Note
Date Submitted by the Author: 26-Apr-2018
Complete List of Authors: Lin, Cheng; University of Victoria, Civil Engineering Wu, Randall; University of Victoria, Civil Engineering
Is the invited manuscript for consideration in a Special
Issue? : N/A
Keyword: vertical effective stress, pile lateral capacity, local scour, scour-hole
dimensions, influence depth
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Evaluation of Vertical Effective Stress and Pile Lateral Capacities
Considering Scour-Hole Dimensions
Cheng Lin, Randall Wu
Department of Civil Engineering, University of Victoria, 3800 Finnerty Road, Victoria BC V8P
5C2 Canada,
Abstract
Determination of vertical effective stress along piles is an essential part of calculation of both
pile axial and lateral capacities under scour conditions. However, the current design manuals
including FHWA and API recommend different methods for calculating vertical effective stress.
Moreover, they are effective only for restricted scour-hole dimensions. This study presents an
improved closed-form solution that allows estimation of the vertical effective stress for a wide
range of scour-hole dimensions including scour depth, width, and slope angle. Using the
improved analytical solution for stress, API p-y curves for sand were modified to compute pile
lateral capacity at different scour-hole conditions. Based on a series of parametric analyses for
laterally loaded piles in sand, errors of calculation using the existing methods were quantified
and a simplified method was proposed for practical applications. Effects of different scour-hole
dimensions on both vertical effective stress and pile lateral capacity were also discussed.
Keywords: vertical effective stress, pile lateral capacity, local scour, scour-hole dimensions,
influence depth
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Notation
A = the factor to account for cyclic or static loading condition, equal to 0.9 for cyclic loading, or
�3.0 − 0.8 �� ≥ 0.9 for static loading k= the rate of increase with depth of initial modulus of subgrade reaction, which can be estimated
based on friction angle of sand (API 2011)
D = pile diameter
Ka =coefficient of active lateral earth pressure, tan�(45° − ��� ) Ko=coefficient of lateral earth pressure at rest, 1 − ��� �� for normally consolidated soil p(r) = the overburden effective pressure due to soil above Plane o-r (in Fig. 1)
pu =ultimate lateral resistance per unit length
pus =ultimate lateral resistance per unit length for shallower depths
pud =ultimate lateral resistance per unit length for deep depths
r = the radial distance between applied point load dP and pile (in Fig. 2)
Swt=top width of scour hole
Swb=bottom width of scour hole
Sd = scour depth due to local scour
y= lateral deflection of pile at depth z
zi = influence depth below which the effect of local scour vanishes and the effective stress is
computed from the pre-scour ground level
z = depth below post-scour ground level
α =φ’/2
β = scour-hole slope angle
φ' = friction angle of soil
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γ’ = effective unit weight
θ=angle between wedge failure surface and pile, 45o+φ’/2
σva’ = vertical effective stress after scour
σvb’ = vertical effective stress before scour
σva’/σvb’ =stress ratio, or normalized vertical effective stress
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Introduction
Scour causes loss of soil around bridge or marine foundations, potentially reducing capacity of
foundations in both lateral and axial directions. Therefore, foundations in river or ocean are
required to be designed with adequate axial and lateral capacities against scour (Arneson et al.
2012; API 2011). A key component of the design analysis of pile axial and lateral capacities is
the determination of vertical effective stresses along piles before and after scour in extreme
hydraulic conditions such as floods, hurricanes, etc. Currently, there is generally no accepted
method for considering scour in estimation of pile capacities (API 2011) probably because scour
process changes the stress history in the remaining soil and develops scour holes around piles
(Lin et al. 2014; Lin et al. 2016). To improve the design practices for piles under scour
conditions, it is important to understand the distribution of vertical effective stress along piles
while properly addressing effects of scour-induced changes to soil properties and scour-hole
geometry.
Scour generally consists of general scour (erosion across riverbed) and local scour
(development of scour holes around piles). Both general scour and local scour reduce the
vertical effective stress. In comparison with general scour that uniformly reduces the effective
stress along pile, local scour only alters the effective stress in upper layers of remaining soil near
piles (Qi et al. 2016; Zhang et al. 2017; Tseng et al. 2017). The existing design manuals
including those from US Federal Highway Administration (FHWA) (Hannigan et al. 2006;
Brown and Castelli 2010) and American Petroleum Institute (API) (2011) have outlined methods
to account for local scour in estimation of vertical effective stress along piles. However, these
methods differ from each other, giving rise to confusion in foundation design. Moreover, these
methods are applicable only for certain scour-hole dimensions. Previously, the first author
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presented an analytical solution for calculation of vertical effective stress along piles under
different scour-hole dimensions (Lin 2017), which however did not consider the pile diameter.
This paper aimed to provide an improved analytical solution for calculation of vertical
effective stress based on the solution of Lin (2017), which is applicable to different scour-hole
dimensions and pile diameters. The improved analytical solution (called improved method) was
further utilized to examine limitations of the methods from the design manuals (called existing
methods) when they were used to calculate vertical effective stress for different scour-hole
conditions. Because differences in the calculation of vertical stress directly affect the pile
capacity, errors of calculation using the existing methods were quantified based on the result of
pile lateral capacity. The pile lateral capacity was calculated using a Matlab program that was
developed by the authors to implement modified API p-y curves in sand. The modified p-y
curves were derived from the calculated vertical effective stresses using the improved method
and capable of assessing effects of 3D scour-hole dimensions that conventional p-y curves are
unable to consider. Using the developed program, a series of parametric analyses were
performed to compare results calculated by the existing methods to that by the improved method.
Based on the parametric analyses, a simplified method was proposed for practical applications
and effects of scour-hole dimensions were identified.
Review of Scour-Hole Dimensions Used in Practice
Scour-hole dimensions are important not only for calculation of pile capacities but also for
estimation of quantities of riprap needed to protect foundations against scour. A local scour hole
is typically idealized as an inversed truncated cone in practice (Whitehouse 1998; Arneson et al.
2012) with its dimensions shown in Fig. 1. In reality, it can be in a symmetrical shape, e.g. in
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some marine environment (Whitehouse 1998) or in an irregular shape such as a steep slope in the
upstream side and a gentle slope in the downstream side in bridge foundations (Butch 1996).
For practical applications, FHWA HEC-18 (Arneson et al. 2012) recommends the top width
be twice the scour depth. This corresponds to β = 26.6º and Swb=0. Similar recommendation
(i.e. β = 30º and Swb=0) is also used at marine structures (Whitehouse 1998). A maximum local
scour depth of 2.4D is also used for design (Ettema 1990). However, an actual scour hole can
have other dimensions depending on flow conditions, foundation geometry, and soil conditions.
According to Butch (1996) who collected scour-hole data over 128 piers in New York State, the
average top width was 4.9Sd which corresponded to β = 12º. Large top widths were observed at
sites with debris. Moreover, a bottom width can also be greater than zero for group piles because
the bottom of a scour hole typically extends beyond the periphery of the pile group (Whitehouse
1998).
Existing Methods for Calculation of Vertical Effective Stress
This study reviewed three widely used pile design manuals including FHWA driven piles
(denoted as FHWA-DP) (Hannigan et al. 2006) and drilled shafts (denoted as FHWA-DS)
(Brown and Castelli 2010), and API geotechnical and foundation design manual (denoted as API)
(API 2011). The distribution of vertical effective stress suggested by these three manuals is
illustrated in Fig.1. FHWA-DP assumes that vertical effective stress is not affected by local
scour, so the effective stress is calculated from the pre-scour ground level and its distribution
follows Line AE in Fig. 1. Both FHWA-DS and API consider the effect from local scour by
introducing an influence depth. Below the influence depth, the stress remains identical to that in
pre-scour conditions, but above which the stress follows a linear increase from post-scour ground
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(i.e. Line BC or BD). The preceding procedures can be mathematically written in Eq. 1 and the
stress ratio in Eq. 2. The stress ratio is defined as vertical effective stress after scour divided by
that before scour. FHWA-DS suggests zi =1.5Sd while API suggests zi = (6D-Sd).
���� = ! "�(#$%�&)�& ')*+' < '-.�(/0 + '))*+' ≥ '- (1)
234�235� = !(#$%�&)��&(#$%�) )*+' < '-1.0)*+' ≥ '- (2)
Note that Eq. 1 works only for restricted scour-hole dimensions. For example, pursuant to
FHWA HEC-18, FHWA-DS allows variations of scour depth but only constant bottom width
and slope angle (i.e. Swb=0 and β=26.6º). API is effective only for one scour-hole geometry: Sd
=1.5D, Swb=0, and a constant β (the value of β is unspecified in the manual). As discussed
previously, the true scour-hole dimensions can differ considerably from the above specified. To
address this limitation necessities the development of an improved method that enables
consideration of different scour-hole dimensions. Lin (2017) presents a closed form solution
based on the Boussinesq’s point load solution and the assumption of zero pile diameter, leading
to the following equations. In other words, Eqs. 3 and 4 do not consider the pile diameter, which
is simplified but not fully rigorous.
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���′ = ∆��� + .�' = .�'8999:1 + (;<�=)
>?@ A$B4CD%#E5F� A$B4CD%#E5G%�G
− #E5H#E5G%�GIJKLMMMN (3)
234�235� = ∆2O%"��"�(#$%�) =�8999:P%(Q�RS)
>?@ A$B4CDTAE5FU A$B4CDTAE5VGTOG
W AE5HAE5GTOGIJKLMMMN
(#$%�) (4)
Improved Method
This paper presents an improved method based on Lin (2017) by including the pile diameter.
For completeness, a scour-hole model and some derivation procedures from Lin (2017) are
shown here. Fig. 2 is a scour-hole model modified from Lin (2017) by including the pile
diameter. From Fig. 2, the vertical effective stress induced by soil above Plane o-r can be
computed by integrating the Boussinesq’s point load solution. The vertical effective stress due
to the point load dP (Lin 2017) is
X��′ = Y�Z0[�\(]G%�G)^/G (5)
The vertical effective stress resulting from soils above Plane o-r is termed additional vertical
effective stress ∆σv’. By integrating Eq. 5 with respect to r (as shown in Eq. 6), ∆σv’ at depth z
is given by Eq. 7.
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∆��′ = ` ` a(])Y�Z]�\(]G%�G)G
�\b XcX+d#E5%eG =` fa(])Y�Z](]G%�G)Gg X+d#E5%eG (6)
∆��′ = .�'(;<�=)h #EB%eGH(#EB%eG)G%�G −#E5%eGH(#E5%eG)G%�Gi (7)
The top width can be substituted by scour depth using
/jQ = #$Q�RS + /jk (8)
Then Eq. 7 can be rewritten as
∆��′ = .�'(;<�=)h A$B4CD%#E5%eGH( A$B4CD%#E5%eG)G%�G −#E5%eGH(#E5%eG)G%�Gi (9)
Vertical effective stress after scour is
���′ = ∆��� + .�' = .�' l1 + (;<�=)h A$B4CD%#E5%eGH( A$B4CD%#E5%eG)G%�G −#E5%eGH(#E5%eG)G%�Gim (10)
The stress ratio is
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234�235� = ∆2O%"��"�(#$%�) =�8999:P%(Q�RS)
>?@ A$B4CDTAE5TeGF( A$B4CDTAE5TeG)GTOG
W AE5TeGH(AE5TeG)GTOGIJKLMMMN
(#$%�) (11)
Note that the above-mentioned improved method is a simplification of the actual loading
condition. In reality, the weight of the unscoured soils around the scour hole (i.e., soils above
Plane o-r) can induce not only vertical stress but also horizontal shear stress in soil below the
post-scour ground surface (Savage 1994). The shear stress is also important for evaluation of
both pile axial and lateral capacities. The consideration of shear stress warrants further study,
which however is beyond the scope of this paper because this paper focuses on the vertical
effective stress and the API p-y curves in sand (API 2011) as discussed next consider only
vertical effective stress.
Pile Lateral Capacity
The scour-induced stress changes eventually will alter pile capacities. For demonstration
purpose, lateral capacities of piles in sand were calculated. Using the previously calculated
vertical effective stress, API p-y curves in sand (API 2011) were modified to calculate pile lateral
responses. To apply the calculated stresses to p-y curves, original equations for ultimate lateral
resistance for sand were modified with the original term γ’z substituted by σva’ and z substituted
by z’.
nop = (qP'′ + q�r)���� (12)
no0 = qYr���� (13)
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where qP = (Q�Rs)GQ�Rtuvw(sW��) + x* y ;<��′���stanzs−�′{|*�} + ;<�cz;<��′���c − ;<�}{~
q� = Q�Rcuvw(cW��)− x�
qY = x��(;<�c)� − 1� + x�;<���(;<�c)�
The smaller value of Eqs. 12 and 13 gives the ultimate lateral resistance (pu). In the equations,
σva’ can be obtained by Eq. 1, 3, or 10. The term z’ in Eq. 12 was chosen as z’= z for σva’
<γ’(z+Sd) and z’=z +Sd for σva’ =γ’(z+Sd).
Combining Eq. 1, 3, or 10 with Eqs.12 and 13 resulted in a new series of pu which were then
substituted in Eq. 14 to develop a family of modified p-y curves.
n = � × notanh( �×��×a� �) (14)
The modified p-y curves were able to consider different 3D scour-hole dimensions including
scour depth, scour width, and scour-hole slope angle. Because the widely used commercial
software, LPILE, cannot consider 3D scour-hole dimensions, a Matlab program was developed
to implement the modified p-y curves. The program was validated against LPILE for no-scour
conditions as discussed later. A case used by Lin et al. (2014) was used here. Both pile and soil
parameters are summarized in Table 1. In the table, two friction angles (φ’=28º and 39º)
represented loose and dense condition of sand, respectively. In Lin et al. (2014), the pile
diameter was 0.61 m. To evaluate the effect of pile diameter on pile lateral capacity, a larger pile
diameter (i.e., 1.83 m) was added in Table 1. Overall, a total of 101 cases of simulations were
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conducted for a wide range of scour-hole dimensions (Sd =0 to 5D; Sw=0 to 9D; β=12 to 38º).
From the calculations, relationships between lateral load and lateral deflection at pile head were
obtained. Pile lateral capacity was determined as the lateral load that caused the lateral pile-head
deflection to reach the tolerance limit. In general practice, there is no consensus on the selection
of the limiting pile-head deflection when determining the pile lateral capacity. Depending on the
nature of specific projects, the limiting lateral deflection can vary from 6.2 mm (¼ inch), 12.7
mm (½ inch), to 25.4 mm (1 inch) based on the authors’ experience. The limiting lateral
deflection for bridges is typically between 6.2 mm and 50 mm (0.25 inch-2.0 inches) (Paikowsky
et al. 2004). In this paper, the pile lateral capacity was defined as the lateral load at 25.4 mm
pile-head deflection because a larger deflection corresponded to a greater pile lateral capacity,
which helped identify the differences between the improved method and the existing methods.
Results and Discussion
For comparison purpose, the first set of computations were done for a scour hole with
dimensions of Sd=1.5D, Swb=0, and β=26.6o. These dimensions applied to all the methods
described previously. The calculated vertical effective stress and stress ratio are presented in Fig.
3a and Fig. 3b, respectively. The lateral load-deflection curves at pile head are shown in Fig. 4.
Fig. 3a shows the stress distribution that is similar to those illustrated in Fig. 1. However, the
stress distribution curves in Fig. 3a were less distinct than the stress ratio distribution curves in
Fig. 3b. This indicates that the stress ratio is preferable to the stress for the stress comparison.
As such, stress ratio is used throughout this paper. From Fig. 3b, the stress ratio calculated by
the improved method and the method of Lin (2017) agreed well, with the former producing
slightly smaller stress ratio than the latter. Because FHWA-DP ignores the effect of local scour,
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the stress ratio was equal to 1.0 along pile and its distribution followed a vertical dash line in Fig.
3b. Both API and FHWA-DS were able to reveal the reduced effective stress due to local scour.
However, API’s method yielded more agreeable results with the improved method than FHWA-
DS. In fact, the improved method and API gave the similar area formed by the curves and the
right vertical axis given by:
�� = `(1 − 234�235�)X' (15)
Fig. 4 depicts comparison of the lateral load-deflection at pile head based on different
methods for an assumed friction angle of 39º. The calculation was first completed for the pre-
scour condition in which the Matlab program was validated against LPILE. The results for the
API method were in the best agreement to that of the improved method while the curve for
FHWA-DP deviated most from that of the improved method. The deviation became more
significant at a higher lateral load. The method of Lin (2017) produced slightly smaller lateral
pile-head deflection than the improved method. The pile lateral capacity was identified from the
curves using the limiting deflection of 25.4 mm.
The obtained lateral capacities for post-scour were compared to that for pre-scour, expressed
as a lateral capacity ratio in Table 2. In comparison with the improved method, FHWA-DP
overestimated the lateral capacity by 34%, FHWA-DS by 12%, and API by 2%. Also included
in Table 2 were lateral capacity ratios for sand with φ’=28º. Overall, lateral capacity ratios
calculated using φ’=28º and φ’=39º were the same except for FHWA-DP. As compared with the
improved method, FHWA-DP gave a better prediction of capacity ratio in sand of lower friction
angle than higher friction angle.
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Table 3 summarizes the effect of pile diameter on the pile lateral capacity ratio calculated
using different methods for the scour-hole dimensions of Sd=1.5D, Swb=0, and β=26.6o. It is
shown that the calculated capacity ratio decreased by 32% as the pile diameter tripled. However,
the relative difference in capacity ratio calculated from the different methods was even smaller
for a larger pile diameter. It is important to note that the improved method is developed because
it is more theoretically rigorous than the method of Lin (2017) by incorporating the pile diameter.
The method of Lin (2017) is the special case of the improved method when the pile diameter is
reduced to zero. A close examination indicates that the improved method produced a slightly
smaller capacity ratio than the method of Lin (2017); however, as above discussed, the difference
in calculated capacity ratio between the two methods was not greater for a larger size of pile
diameter. The increase of pile diameter from 0.61 m to 1.83 m caused the ratio of vertical
effective stress calculated by the improved method to that by Lin (2017) to decrease from 83% to
71% but the absolute scour depth to increase by 200% for Sd=1.5D. This indicates the change of
the stress due to the increased pile diameter was insignificant compared with the change of scour
depth. As will be discussed in section effect of scour depth, the relative difference of pile lateral
capacity ratio among different methods was diminishing for a greater scour depth as the
unsupported pile length increased. This may explain why the difference in capacity ratio
obtained from Lin (2017) and the improved method was still minimal for a larger diameter pile.”
Since the differences between Lin (2017) and the improved method were trivial, the method
of Lin (2017) was not included in the further analyses. The focus was to explore the limitations
of the existing prevalent methods such as FHWA DS, FHWA DP, and API. Moreover, in the
further analyses, only the higher friction angle (φ’=39º) and the smaller pile diameter (D=0.61m)
were considered. The capacity ratio was almost independent of friction angle for most methods,
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and the choice of higher friction angle can reflect larger discrepancy of calculation by FHWA-
DP. The smaller pile diameter was chosen for the comparison purpose because of the larger
relative difference among the methods in smaller diameter piles.
Effect of scour depth
Fig. 5 shows the calculated stress ratios using the improved method for Sd ranging from 1D,
3D, to 5D while Swb=0 and β=26.6º. By letting Ae calculated by Eqs.15 and 11 be equal to that
calculated by Eqs.15 and 2, the influence depth (zi) was back-calculated. It was found that the
back-calculated zi was equal to 3.5Sd regardless of variation of Sd. Using zi=3.5Sd, the stress
ratios were calculated in Eq. 2 and plotted in Fig. 5. Note that the use of zi=3.5Sd to compute
vertical effective stress is termed as the proposed simplified method here.
Fig. 6a shows the pile lateral capacity at different scour depths using different methods
including the proposed simplified method. Note API method was not included in Fig. 6 because
it could only consider one scour depth Sd=1.5D. From Fig. 6a, as the scour depth increased, the
lateral capacity decreased substantially. At Sd=5D, the lateral capacity was decreased by 77%.
As compared with the improved method, both FHWA-DP and FHWA-DS overestimated the pile
lateral capacity, especially so at smaller scour depths. Surprisingly, at greater scour depths the
discrepancy of lateral capacity ratios calculated by different methods gradually diminished. This
was attributable to the increased unsupported length of pile at large scour depths. For the
defined limiting deflection (25.4mm), the majority of the deflection resulted from the deflection
in the unsupported length while that in the supported length was relatively small. Therefore, the
soil resistance to pile deflection became less important and thus the distinction for different
methods was small. If the pile was allowed to deflect sufficiently, the difference of calculation
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from different methods became evident, e.g. in Fig.6b. Regardless of changes in scour depth, the
proposed simplified method produced almost the same results as the improved method in Fig. 6a.
This result indicates that a greater influence depth of 3.5Sd is more appropriate than 1.5Sd
suggested by FHWA-DS.
Effect of scour width
Fig. 7 presents lateral capacity ratios for different bottom widths based on the improved
method. Three scour depths (i.e. Sd=1.0, 1.5, and 3.0D) were evaluated but only the results for
Sd=1.5D are presented in Fig. 7 for the comparison purpose. Also included in the figure are
results from FHWA-DS, FHWA-DP, and the proposed simplified method. API method was also
included because Sd was set to1.5D in Fig. 7. Although these methods are only suitable for
estimation of pile lateral capacity at zero bottom width, they might be mistakenly used by design
engineers for other scour widths. The calculated results using these methods are independent of
scour width and thus shown in horizontal lines in the figure. Results from the improved method
indicated that the lateral capacity decreased rapidly with scour width for Sw<2D but slowly for
Sw>2D. The maximum reduction in lateral capacity due to scour width was in the range of 7% to
9% based on the results for Sd=1.0D, 1.5D, and 3.0D. By comparing the improved method to the
other methods for Sd=1.5D, the discrepancy of calculated capacity ratio increased for large scour
widths. For example, FHWA-DS, FHWA-DP, API, and the proposed simplified method
overestimated pile lateral capacity by 46%, 26%, 11%, and 9%, respectively if they were
mistakenly used for design for Sw= 4D but the number was only 34%, 12%, 2%, and 2%,
respectively for Sw= 0.
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Effect of scour-hole slope angle
Fig.8 shows the calculated lateral capacity ratios for β ranging from 0 to 38º and Sd = 1.5D.
Two bottom widths (i.e. Swb=0 and 1.5D) were considered. In this figure, the API method was
also included as Sd = 1.5D. But for other scour depths, the API method would no longer apply.
Note that the upper bound of β should not exceed friction angle of 39º. Fig. 8 reveals that the
lateral capacity decreased linearly with the decrease of β with the maximum decrease in the
lateral capacity up to 12% for Sw=0. The effect of scour-hole slope angle became less evident at
a larger scour width. The lower bound of scour-hole slope angle (i.e. β=12º) was obtained from
the field data (Butch, 1996). If β =26.6º or 30º that is recommended by FHWA or marine
practice were assumed for the lower bound case, the pile lateral capacity would be overestimated
by 40%,17%, 6%, and 5% by FHWA-DP, FHWA-DS, API, and the proposed simplified method,
respectively. This result indicates both FHWA led to unsafe design of pile lateral capacity while
both API and proposed simplified method caused marginal error of calculation.
Conclusions
Based on the analyses in the present study, the following conclusions are drawn.
(1) Compared with the improved analytical solution, FHWA-DP overestimated vertical
effective stress and therefore overestimated pile lateral capacity by 34 to 47% for a typical
scour depth of 1.5D. The overestimation of lateral capacity by FHWA-DS ranged
between 14% and 22% for a typical scour depth of 1.5D. Among all existing methods,
API yielded the most agreeable result with the improved method. However, API method
has limited applications as it is restricted to one scour-hole geometry (Sd=1.5D, Swb=0).
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(2) The change of friction angle (from 39o to 28
o) almost had no effect on the pile lateral
capacity ratio when Sd=1.5D; however, the increase of pile diameter significantly reduced
the pile lateral capacity ratio.
(3) A simplified method was proposed based on the back-calculated influence depth from
stress ratio distribution curves. The influence depth was 3.5Sd which is greater than 1.5Sd
recommended by FHWA-DS. Like FHWA-DS, this simplified method is only suitable
for various scour depths but zero bottom width and a constant scour-hole slope angle of
26.7o. Based on the parametric analyses of pile lateral capacity, it was found that the
simplified method may be used for other scour widths and slope angles, resulting in <10%
error of calculation compared with the improved method.
(4) Scour depth had the most pronounced effect on vertical effective stress and pile lateral
capacity among all scour-hole dimensions. By increasing scour depth to 5D, the pile
lateral capacity was decreased by 77%. The difference of pile lateral capacity computed
by different methods was most evident at small scour depths, but it was diminishing at
large scour depths.
(5) Both scour width and slope angle had less effects on vertical effective stress and pile
lateral capacity than scour depth. The pile lateral capacity decreased with the increased
scour width or the decreased slope angle. The maximum decrease of the lateral capacity
due to scour width was about 9% and that due to slope angle was about 12%.
Acknowledgements
This study was sponsored by Natural Sciences and Engineering Research Council of Canada
(NSERC) Discovery Grant. The author is indebted to the support of NSERC DG.
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References
API RP 2GEO 2011. API Recommended Practice, Geotechnical and Foundation Design
Considerations. American Petroleum Institute, Washington, D.C., USA.
Arneson, L., Zevenbergen, L., Lagasse, P., and Clopper, P. 2012. Evaluating Scour at Bridges,
HEC-18. Report FHWA-HIF-12-003, US Department of Transportation, Federal Highway
Administration,Wahington, D.C., USA,
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Administration,Wahington, D.C., USA.
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Driven Pile Foundation-Volume I. Report FHWA-HI-05-042, US Department of Transportation,
Federal Highway Administration,Wahington, D.C., USA.
Lin, C. 2017. The Loss of Pile Axial Capacities due to Scour: Vertical Stress Distribution. In
Proceedings of International Conference on Transportation Infrastructure and Materials (ICTIM
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Figure Captions
Fig. 1. Scour-hole definition and effective stress distribution (modified from Lin 2017)
Fig.2. Scour-hole model for derivation of stress distribution (modified from Lin 2017)
Fig.3. Comparison of vertical effective stress distribution: (a) stress, (b) stress ratio
(Sd=1.5D, Swb=0, β=26.6o)
Fig.4. Comparison of pile-head deflection computed using different methods (Sd=1.5D,
Swb=0, β=26.7o)
Fig.5. Vertical effective stress ratio based on different scour depths (Swb=0, β=26.6o)
Fig.6. Pile-head responses at different scour depths: (a) load-deflection curves, (b) pile-
head deflection at lateral load of 300 kN (Swb=0, β=26.6o)
Fig.7. Lateral capacity ratio at different scour-hole bottom widths (Sd=1.5D, β=26.6o)
Fig.8. Lateral capacity ratio at different scour-hole slope angles
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Swb
Swt
Sd
D
σv’
Pre-scour ground level
Post-scour ground level
β
1.5Sd
Notation
D= pile diameter or side width;
Sd=local scour depth;
Swt=top width of a scour hole;
Swb=bottom width of a scour hole;
z=depth below post-scour ground;
β = scour-hole slope angle;
σv’= vertical effective stress.
FHWA-DP
z
6D
API
FHWA-DS
A
C
B
D
E
Fig. 1. Scour-hole definition and effective stress distribution (modified from Lin 2017)
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r
z
o
Sd
β
Pile
or
dP
dP
dσv
Swt+D/2
r
z
(a) (b)
Swb+D/2
Swt+D/2Swb+D/2
Fig.2. Scour-hole model for derivation of stress distribution (modified from Lin 2017)
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Fig.3. Comparison of vertical effective stress distribution: (a) stress, (b) stress ratio
(Sd=1.5D, Swb=0, β=26.6o)
0
1
2
3
4
5
6
7
8
9
10
0 25 50 75 100 125D
epth
bel
ow
po
st-g
rou
nd
su
rfac
e (×
D)
σva'
APIFHWA-DPFHWA-DSImproved MethodLin (2017)
(a)
0
1
2
3
4
5
6
7
8
9
10
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Dep
th b
elo
w p
ost
-gro
un
d s
urf
ace
(×D
)
σva'/σvb'
APIFHWA-DPFHWA-DSImproved MethodLin (2017)
(b)
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Fig.4. Comparison of pile-head deflection computed using different methods (Sd=1.5D,
Swb=0, β=26.7o)
0
50
100
150
200
250
300
0 5 10 15 20 25 30 35 40 45 50 55
Appli
ed l
ater
al L
oad
at
pil
e h
ead
(kN
)
Pile-head deflection (mm)
API
FHWA-DS
FHWA-DP
Improved Method
Lin (2017)
Limiting Deflection (1 inch)
LPILE (API Sand)
Prescour
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Fig.5. Vertical effective stress ratio based on different scour depths (Swb=0, β=26.6o)
0
5
10
15
20
25
30
35
40
45
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Dep
th b
elow
po
st-g
rou
nd
su
rfac
e (×
D)
σva'/σvb'
1 (A)
1 (B)
3 (A)
3 (B)
5 (A)
5 (B)
Sd (× D)
A=Improved Method
B=Proposed Simplified Method
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Fig.6. Pile-head responses at different scour depths: (a) load-deflection curves, (b) pile-
head deflection at lateral load of 300 kN (Swb=0, β=26.6o)
0.0
0.2
0.4
0.6
0.8
1.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Lat
eral
cap
acit
y r
atio
Scour depth (×D)
FHWA-DS
FHWA-DP
Improved Method
Proposed Simplfied Method
(a)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 50 100 150 200 250
Sco
ur
dep
th (
×D
)
Pile-head deflection (mm)
Proposed Simplfied Method
Improved Method
FHWA-DS
FHWA-DP
(b)
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Fig.7. Lateral capacity ratio at different scour-hole bottom widths (Sd=1.5D, β=26.6o)
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
0.0 2.0 4.0 6.0 8.0 10.0
Lat
eral
cap
acit
y r
atio
Scour bottomwidth (×D)
API
FHWA-DS
FHWA-DP
Improved Method
Proposed Simplified Method
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Fig.8. Lateral capacity ratio at different scour-hole slope angles
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 10 20 30 40
Lat
eral
cap
acit
y r
atio
Scour-hole slope angle (º)
API
FHWA-DS
FHWA-DP
Improved Method (Swb=0)
Improved Method (Swb=1.5D)
Proposed Simplified Method
Swb=0
Swb=1.5D
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Table 1. Pile and soil parameters
Pile
Length,
L(m)
Outer diameter,
D (m)
Moment of
inertia,
Ip (m4)
Elastic
modulus, Ep (kN/m
2)
21.0 0.61 and 1.83 8.08×10-4
2.02×108
Soil
effective unit
weight,
γγγγ’ (kN/m3)
Friction angle,
φφφφ’ (º) Initial modulus of subgrade
reaction, k (MN/m3)
10 28 and 39 8.76 (for φ’=28º) and
40.4 (for φ’=39º)
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Table 2. Calculated pile lateral capacity ratios for different friction angles (Sd=1.5D,
Sw=0, β=26.7o)
Friction angle,
φ’(º) Pre-scour
Improved
Method
Lin
(2017) API FHWA-DS FHWA-DP
39 1.0 0.68 0.71 0.69 0.76 0.91
28 1.0 0.70 0.72 0.71 0.75 0.81
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Table 3. Calculated pile lateral capacity ratios for different pile diameters (Sd=1.5D,
Sw=0, β=26.7o)
Pile diameter,
D (m)
Improved
Method Lin (2017) API FHWA-DS FHWA-DP
0.61 0.68 0.71 0.69 0.76 0.91
1.83 0.46 0.48 0.47 0.48 0.50
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