evaluation of vertical effective stress and pile lateral

Draft

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

https://mc06.manuscriptcentral.com/cgj-pubs

Canadian Geotechnical Journal

Draft

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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Paikowsky, S.G., Birgisson, B., McVay, M., Nguyen, T., Kuo, C., Baecher. G., Ayyub, B.,

Stenersen, K., O’Malley, K., Chernauskas, L., and O’Neill, M. 2004. Load and Resistance Factor

Design (LRFD) for Deep Foundations. National Cooperative Highway Research Program Report

507, Transportation Research Board, National Research Council, Washington, D.C.

Qi, W. G., Gao, F. P., Randolph, M. F., and Lehane, B. M. 2016 Scour Effects on p-y Curves for

Shallowly Embedded Piles in Sand. Geotechnique, 66(8):648-660.

Savage, W.Z. 1994. Gravity-Induced Stresses in Finite Slopes. International Journal of Rock

Mechanics and Mining Sciences & Geomechanics Abstracts, 31(5): 471-483.

Tseng, W. C., Kuo, Y. S., and Chen, J. W. 2017. An Investigation into the Effect of Scour on the

Loading and Deformation Responses of Monopile Foundations. Energies, 10(8): 1190.

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Telford, London, UK.

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Zhang, H., Chen, S., and Liang, F. 2017. Effects of Scour-Hole Dimensions and Soil Stress

History on the Behavior of Laterally Loaded Piles in Soft Clay under Scour Conditions.

Computers and Geotechnics, 84:198-209.

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Draft

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

Page 22 of 33



Draft

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)

Page 23 of 33



Draft

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)

Page 24 of 33



Draft

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)

Page 25 of 33



Draft

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

Page 26 of 33



Draft

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

Page 27 of 33



Draft

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)

Page 28 of 33



Draft

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

Page 29 of 33



Draft

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

Page 30 of 33



Draft

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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Draft

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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Draft

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

Page 33 of 33



evaluation of vertical effective stress and pile lateral

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