schna id 2010

DISCUSSIONS AND CLOSURES

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Discussion of “Active Earth Pressure onRetaining Wall for c-� Soil Backfill underSeismic Loading Condition” by S. K.Shukla, S. K. Gupta, and N. SivakuganMay 2009, Vol. 135, No. 5, pp. 690–696.DOI: 10.1061/�ASCE�GT.1943-5606.0000003

Venanzio R. Greco1

1Dept. of Structural Engineering, Univ. of Calabria, 87036 Rende �Cs�,Italy. E-mail: [email protected]

The authors’ paper is welcome because it makes up for a lack inthe original method of Coulomb and renders it applicable to c�-��soil backfills. Such a backfill type could be studied with themethod of Rankine but this does not have the versatility of Cou-lomb’s method for analyzing thrust wedges with various geo-metrical shapes and subject to surcharges. Therefore, the paper isvery important for geotechnical engineering practice.

However, the formulation is limited to backfills with a hori-zontal profile ��=0�, walls with a vertical backface ��=� /2�, andno friction between backfill and wall backface ��=0�. Moreover,it does not take the presence of tension cracks, which are prob-ably present in a cohesive soil subjected to a reduction in thelateral stress, into account. This discussion aims to contribute tothe approach followed by the authors by extending the field ofapplicability of the method to:1. Backfills with an inclined profile ��0�, walls with an in-

clined backface �� /2�, and a friction angle � betweenwall and backfill soil; and

2. Backfills with tension cracks up to a depth of zc.

Formulation for Inclined Backfill and Wall Backface

With reference to Fig. 1, where the geometry of the thrust wedgeABC and the forces acting on it are shown, the equilibrium con-ditions of forces lead to the following relation for the thrust Pae

Pae = W1 � kv

cos �

sin�� − � + ��sin�� + � + �� − ��

−C cos ��

sin�� + � + �� − ��1�

where W=weight of the thrust wedge ABC

W =1

2h2sin�� − ��sin�� − ��

sin2 � sin�� − ��2�

and C=force on AC due to cohesion

C = c�h

sin �

sin�� − ��sin�� − ��

�3�

Introducing Eqs. �2� and �3� in Eq. �1�, we have

Pae =1

2h2a2 tan2 � − a1 tan � + a0

d2 tan2 � − d1 tan � + d0�4�

where

JOURNAL OF GEOTECHNICAL AND GEOE

J. Geotech. Geoenviron. Eng.

a2 = p cos � cos�� − �� + q �5a�

a1 = p sin�� + �� − �� 5b�

a0 = p sin � sin�� − �� + q �5c�

d2 = cos�� + � + ��cos � �6a�

d1 = sin�� + � + �� + �� 6b�

d0 = sin�� + � + ��sin � �6c�

with

p =1 � kv

cos �

sin�� − ��sin2 �

�7a�

q =2c�

h

sin�� − ��sin �

cos �� 7b�

and, using Eq. �22� of the original paper, we can write

q

p= 2

c�

h

cos �

1 � kvcos �� sin � = 2m cos �� sin � �7c�

Because Eq. �9� of the original paper is equivalent to the condi-tion

dPae

d tan �= 0 �8�

the thrust Pae is maximized for that value of � solving the qua-dratic equation

�a1d2 − a2d1�tan2 � − 2�a0d2 − a2d0�tan � + �a0d1 − a1d0� = 0

�9�

which gives the critical value of the inclination angle � maximiz-ing the thrust Pae in general geometrical conditions.

Pa

W

εA

B

C

α

h

β R

φ'π/2−α

δβ−π/2

CkhW

kvW

Fig. 1. Cross section of a wall and the thrust wedge ABC withouttension cracks

NVIRONMENTAL ENGINEERING © ASCE / NOVEMBER 2010 / 1583

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Obviously, if �=� /2, �=0, and �=0 as in the original paper,the value of �c given by Eq. �9� is equal to that given by Eq. �11�of the original paper. In this case, in fact, the coefficients of Eq.�9� becomes

a1d2 − a2d1 = − p�sin �� cos�� − �� + 2m cos2 �� 10a�

a0d2 − a2d0 = − p�cos �� sin�� − �� + m sin 2�� 10b�

a0d1 − a1d0 = p�cos �� sin�� − �� + 2m cos2 �� 10c�

and the solution of Eq. �9� is given by Eq. �11� of the originalpaper.

The influence of the angles �, �, and � on the values of �c andPae is relevant. For example, in the specific case of ��=24°, c�=5 kPa, H=5 m, =20 kN /m3, �=80°, �=15°, �=12°, kh=0.2and kv=0.1, Eq. �9� gives �c=32.5° and Pae=137.4 kN /m �Eq.�4��, while the inappropriate use of Eqs. �11� and �14� of theoriginal paper leads to �c=48.0° and Pae=121.6 kN /m.

Soils with Tension Cracks

If we suppose that tension cracks are vertical �as shown by theapplication of Rankine’s method to materials not resistant to trac-tion� and extended up to depth zc, the thrust wedge is limited bythe slip surface CA �inclined at �� and by the tension crack AA�.Therefore the thrust wedge is the quadrilateral B�CAA� and itsweight is given by

W = −1

2zc

2cos � cos �

sin�� − ��+ zchc

cos �

sin �

sin�� − ��sin�� − ��

+1

2hc

2sin�� − ��sin�� − ��sin2 � sin�� − ��

�11�

Pa

εA'

B'

C

α

h

β Rφ'

π/2−αδ

β−π/2

CA

B"

B

zczc

crackedsoil

)sin(cossin

c ε−βεβz

hcW

khW

kvW

Fig. 2. Cross section of a wall and the thrust wedge B�CAA� withtension cracks

where �Fig. 2�

1584 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGIN


hc = h − zc

sin � cos �

sin�� − ��. �12�

In the second member of Eq. �11�, the first term represents theweight of the triangle B�BB�, the second that of the parallelogramB�BAA� �B� is on the vertical crossing point B�, and the third thatof the triangle BCA.

The force C acting on CA is given by

C = c�hc

sin �

sin�� − ��sin�� − ��

�13�

Introducing Eqs. �11�–�13� in Eq. �1�, we have

Pae =1

2hc

2b2 tan2 � − b1 tan � + b0

d2 tan2 � − d1 tan � + d0�14�

where

b2 = �p0 cos � + p1 cos ��cos�� − �� + q �15a�

b1 = p0 sin�� + �� − �� + p1 sin�� + �� − �� 15b�

b0 = �p0 sin � + p1 sin ��sin�� − �� + q �15c�

with

p0 =1 � kv

cos �� zc

hc�2cos � cos �

sin�� − ��16a�

p1 =1 � kv

cos ��2

zc

hc

cos �

sin �+

sin�� − ��sin2 �

� �16b�

q =2c�

hc

cos ��

sin �sin�� − �� 17�

Eq. �8� leads to the quadratic equation

�b1d2 − b2d1�tan2 � − 2�b0d2 − b2d0�tan � + �b0d1 − b1d0� = 0

�18�

which gives the critical value of the inclination angle �c in thepresence of tension cracks up to depth zc. In absence of tensioncracks, p0=0, p1= p and Eq. �18� reduces to Eq. �9�.

With the previous numerical data, if we calculate the depth zc

of the tension cracks with the equation zc= �2c� /�cos �� /�1-sin��, we have zc=0.77, hc=4.19 m, �c=30.8°, and Pae

=143.4 kN /m. In this case, the tension crack presence leads to anincrease of 4% in the value of Pae, but if c�=10 kPa, this increasebecomes 17%.

EERING © ASCE / NOVEMBER 2010

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Closure to “Active Earth Pressure onRetaining Wall for c-� Soil Backfill underSeismic Loading Condition” by S. K. Shukla,S. K. Gupta, and N. SivakuganMay 2009, Vol. 135, No. 5, pp. 690–696.DOI: 10.1061/�ASCE�GT.1943-5606.0000003

Sanjay Kumar Shukla1

1Assoc. Prof. and Program Leader, Discipline of Civil Engineering,School of Engineering, Edith Cowan Univ., 270 Joondalup Dr., Joon-dalup, WA 6027, Australia. E-mail: [email protected]

The writer thanks the discusser for finding our paper very impor-tant for geotechnical engineering practice. The discusser has ex-tended our expression for the total active earth pressure for itsapplicability to backfills with inclined profile, walls with inclinedbackface, friction angle between wall and backfill soil, and back-fills with tension crack. The discusser is greatly appreciated forthis highly valuable contribution. Derivation of Eqs. �1� to �18�presented by the discusser has been checked carefully, and theyhave been found to be correct. However, readers should note thecorrections as mentioned below:1. Eq. �1� contains � and ��, which refer to the effective angle

of shearing resistance; it should contain only ��.2. In Eq. �10b�, cos �� should be replaced by sin ��.3. In Eqs. �15a-c�, q should be replaced by another symbol, say

q0, because q refers to a different expression in Eq. �7b�.It should be noted that we have explained through Eq. �24� in

the original paper how one can use our analytical expression forestimating active earth pressure on a retaining wall from the c-�soil backfill under seismic loading condition, considering tensioncrack. It appears that the discusser has not noticed this fact; how-ever, the approach adopted in the discussion is appreciated.

One of the interesting observations is that Eq. �9� and Eq. �18�can be expressed in the determinant form, respectively, as follows

tan2 � 2 tan � 1

a0 a1 a2

d0 d1 d2 = 0 �1�

and

tan2 � 2 tan � 1

b0 b1 b2

d0 d1 d2 = 0 �2�

The above determinant form of equations can easily be re-membered by the readers for their use while making the calcula-tion for the total active force. The readers should also note thefollowing:1. The symbol � used in the equations of the discussion is given

by Eq. �21� of our paper.2. The discusser has suggested to use the expression for the

depth of tension crack

zc = �2c�

�� cos ��

1 − sin �� 3�

without any reference. This value is based on Rankine’sanalysis of active earth pressure from the c-� soil backfill
under static condition �Lambe and Whitman 1979; Das


2008�. Alternatively, one can use its value obtained from thefield observations.

References

Das, B. M. �2008�. Fundamentals of geotechnical engineering, 3rd Ed.,Thomson, Mason, Ohio.

Lambe, T. W., and Whitman, R. V. �1979�. Soil mechanics, SI Version,Wiley, New York.

Discussion of “Use of SPT Blow Counts toEstimate Shear Strength Properties ofSoils: Energy Balance Approach” byH. Hettiarachchi and T. BrownJune 2009, Vol. 135, No. 6, pp. 830–834.DOI: 10.1061/�ASCE�GT.1943-5606.0000016

Fernando Schnaid1; Edgar Odebrecht2; andBianca O. Lobo3

1Assoc. Prof., Dept. of Civil Engineering, Federal Univ. of Rio Grande doSul, Av. Osvaldo Aranha, 99–3° andar-90035-190 Porto Alegre, RioGrande do Sul, Brazil. E-mail: [email protected]

2Asst. Prof., Dept. of Civil Engineering, State Univ. of Santa Catarina,Rua Machado de Assis, 277-Ap. 602-89204-390-Joinville, SantaCatarina, Brazil. E-mail: [email protected]

3Asst. Prof., Dept. of Civil Engineering, Federal Univ. of Santa Catarina,Servidão Corintians, 97-Ap. 704-88040-100-Florianópolis, SantaCatarina, Brazil. E-mail: [email protected]

The authors proposed approach for interpretation of SPT test re-sults appears to have the right framework given the fact that en-ergy concepts have been incorporated to the prediction of soilproperties. However, the approach relies on a number of assump-tions that the writers find difficult to accept. In particular it hasbeen argued that possible loss of wave energy in a long rod couldbe partially compensated by the extra weight added by the longrods, leading to the assumption that energy losses are negligible.

This hypothesis emerges from a recent ASCE paper publishedby Odebrecht et al. �2005� that states that “the sampler energy canbe conveniently expressed as a function of nominal potential en-ergy E*, sampler final penetration, and weight of both hammerand rods. The influence of rod length produces two opposite ef-fects: wave energy losses increase with increasing rod length andin a long composition of rods the gain in potential energy fromrod weight is significant and may partially compensate measuredenergy losses.” This conclusion is directly derived from the sys-tem energy delivered to the sampler Esampler by considering thecombined effects of the hammer potential energy �Eh� and rodpotential energy �Er�

ESampler = 3�1Eh + 2Er� = 3�1�H + ��Mhg + 2��Mrg�

�1�

where Mh=hammer weight; Mr=rod weight; g=gravity accelera-tion; ��=sampler penetration; H=height of fall; and 1, 2, and3=efficiency coefficients. In this proposed equation, both ham-mer and rod potential energies are a function of �� and the lengthof the rod in addition to the Mh and H, whereas efficiency is not
affected by ��. These principles have been extensively evaluated

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by numerical analysis to demonstrate that energy losses fromwave propagation cannot be entirely compensated by the rod po-tential energy �Odebrecht et al. 2005�, which is illustrated in Fig.18 of the original paper.

This effect is demonstrated in Fig. 1, in which errors intro-duced by the misinterpretation of energy balance are related torod length. The error is defined as

Error =�Esampler

rod − 0.6E*�0.6E*

100 �2�

where Esamplerrod =3�2��Mrg� is the contribution of the rod energy

and E� the nominal potential energy corrected to the referencevalue of 60%. Note that Fig. 1�a� relates to American standardswhereas Fig. 1�b� refers to Brazilian standards. From these figuresit is observed that a 30-m-long rod in loose sand �Nspt = 3�

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"

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#!

$

$!

" # $ % !

&''(' *+,

-./

01*2

, " #

" $

" %&

" '&

Fig. 1. �a� Rod energy losses error �American sta

!

"

#!

#"

$!

$"

"!

""

! %! ! #! $! "! &! '! (! )! %!! %%! % ! %#!*+%,&! . /0102030 4 56789:0 *%))&,

*+%,&! . ;<7=>?1 *%)(),*+%,&! . /<1190?078789 4 @?=A2 * !!),

φφφφB

C02: CD 02: CD.CE

C02: F9GG *CD 1= CE,

CE D9<:H=21

/0102030 4 56789:0 *%))&,

;<7=>?1 *%)(),

/<1190?078789 4 @?=A2 * !!),

Fig. 2. Peak friction angle of sands from SPT resistance



yields an error of about 40% �i.e., the contribution of the rodenergy is larger than losses produced by wave propagation�. Onlyin dense sand �Nspt = 40� the error is negligible.

The authors could argue that despite simplified considerations,the angle of internal friction �� is derived with reasonable accu-racy. The database adopted to validate the method might partiallyexplain this apparently successful application. Friction anglesfrom Tables 1 and 3 �of the original paper� fall in a very narrowband �from 28° to 35°�, despite the wide range of associated SPTblow counts �7 N60 97�. These adopted values are signifi-cantly lower than reported data published by the U.S. Bureau ofReclamation �De Mello 1971� and by Hatanaka and Uschida�1996�, as illustrated in Fig. 2 �after Schnaid et al. 2009�. Toenable a direct comparison to published data, the blow count N60

used by the authors had to be corrected to �N1�60 adopting thevalue of CN �= �100 /�v��

0.5� proposed by Liao and Whitmann�1986�.

Since the database shows some discrepancy with precedingexperience, there appears to be enough evidence to question theproposed approach and to suggest caution in using the method forengineering works until proven by practical experience.

References

De Mello, V. F. B. �1971� “The standard penetration test.” Proc., 4th PanAmerican Conference on Soil Mechanics and Foundation Engineer-ing, Vol. 1, Puerto rico, 1–87.

Hatanaka, M., and Uchida, A. �1996�. “Empirical correlation betweenpenetration resistance and effective friction of sand soil.” Soil Found.,36�4�, 1–9.

Liao, S. S. C., and Whitman, R. V. �1986�. “Overburden correction fac-

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#!

$

$!

" # $ % !

&''(' *+,

-./

01*2

,

" #

" $

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�; �b� rod energy losses error �Brazilian standard�

ndard

tors for SPT in sand.” J. Geotech. Engrg., 112�3�, 373–377.


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Odebrecht, E., Schnaid, F., Rocha, M. M., and Bernardes, G. P. �2005�.“Energy efficiency for standard penetration test.” J. Geotech. Geoen-viron. Eng., 131�10�, 1252–1263.

Schnaid, F., Odebrecht, E., Rocha, M. M., and Bernardes, G. P. �2009�.“Prediction of soil proprieties from the concepts of energy transfer indynamic penetration tests.” J. Geotech. Geoenviron. Eng., 135�8�,1092–1100.

Closure to “Use of SPT Blow Counts toEstimate Shear Strength Properties ofSoils: Energy Balance Approach” byH. Hettiarachchi and T. BrownJune 2009, Vol. 135, No. 6, pp. 830–834.DOI: 10.1061/�ASCE�GT.1943-5606.0000016

Hiroshan Hettiarachchi11Asst. Prof., Dept. of Civil Engineering, Lawrence Technological Univ.,

21000 West Ten Mile Rd., Southfield, MI 48075. E-mail:[email protected]

The writers wish to thank discussers for their interest in this paperand also for the constructive criticism. The discussers’ commentsopened up a discussion on the importance of incorporating SPTrod weight into the formulation of energy balance equations.

It may be true that the proposed equations could have beenimproved by incorporating SPT rod weight. However, the writersare skeptical about the degree of improvement it can make. Thediscussers suggest that the proposed equations may cause 40%error for 30-m-long rod in loose sand �with N=3�, but agree thatfor the same depth, the error may be negligible in dense sand. Ifa 30-m-long rod is used during an SPT, obviously the test musthave been conducted at least at a depth greater than 25 m. Atdeeper depths �such as 25 m�, it is rare to find sand that can giveblow counts as low as 3. According to the error analysis presentedby the discussers �Fig. 1�, shallower depths produce relatively lowerror for a wide range of N values. Fig. 1 also suggests that atdeeper depths the proposed equations produce considerable erroronly for very low N values. Therefore, Fig. 1 indirectly supportsthe practical level of accuracy produced of the proposed equationseven in their current forms.

The writers also have a concern about the way the discussersdefine error. If they are attempting to quantify the error due to theomission of rod weight, it is more meaningful to define the erroras the energy difference between the two methods �with rod en-ergy and without rod energy� compared to the energy given by themore detailed method �with rod energy�. It is not clear why thediscussers would define the error as the difference between therod energy and hammer energy.

The discussers’ argument on predicting a narrow 28°–35° fric-tion angles from 7 to 97 wide range of SPT blow counts is alsomisleading. It is true that the writers used a 7–92 wide range ofSPT blow counts to estimate the model parameters. However, theblow count data used in the verification was only limited to 11–69and it produced a reasonable range of 28°–35° friction angles. Asdiscussed in the paper, one of the attractive features of the pro-posed model is its ability to slightly underpredict. While fewother widely used models are overpredicting friction angles, theproposed model provided more conservative answers. This is also
clearly indicated in Fig. 2 provided by the discussers. In Fig, 2,


the discussers compare the results produced by the proposedmodel with data from published literature and two other models.For blow counts in the range of 20–40 the proposed model pro-duces friction angles from 28°–32°. For the same range of blowcounts, other data/methods provide friction angles as high as 46°.

The authors are in agreement with the discussers about usingcaution in using the proposed equations until they are proven byexperience. In addition the writers also believe that the proposedmodel parameters may have to be fine-tuned for different types ofmaterial.

Discussion of “Reliability-BasedEconomic Design Optimization of SpreadFoundations” by Y. WangVol. 135, No. 7, July 1, 2009, pp. 954–959.DOI: 10.1061/�ASCE�GT.1943-5606.0000013

Sarat Kumar Das1 and Manas Ranjan Das2

1Assoc. Prof., Civil Engineering Dept., National Institute of TechnologyRourkela, Orissa-769008, India. E-mail: [email protected];[email protected]

2Asst. Prof., Dept. of Civil Engineering, ITER, SOA Univ., Orissa-769008, India. E-mail: [email protected]

The author has proposed reliability-based economic design opti-mization framework of spread foundation comprising of reliabil-ity based design methodology, construction cost estimate and costoptimization. The author has discussed the economically opti-mized design in the line proposed in available literature �Wangand Kulhawy 2008�. Both in this paper and in Wang and Kulhawy�2008�, the approach is expressed as a constrained optimizationprocess, in which the objective is to minimize the total construc-tion cost. Design parameters, such as the dimensions of the foun-dations have been treated as variables, which vary in the rangesconstrained by design requirement including ultimate limit state�ULS� and serviceability limit state �SLS� requirements. The op-timization model has been set up in a Microsoft Excel spreadsheetand has been solved using the Excel function solver. As the aboveproblems are nonlinear it is solved using generalized reduced gra-dient �GRG� algorithm in solver. The GRG method is a directmethod of solving a constrained optimization problem, unlike theLagrange multiplier method that is solved as a sequential uncon-strained optimization problem. The GRG method is based on theprinciples of elimination of variables using equality constraint�Deb 2005�. The optimization method is a numerical method and

Table 1. Comparison of Spread Footing Designs

Designoption

Design variableOptimized

value Constraints

Width�B��m�

Length�L��m�

Depth�D��m�

Cost�USD�

Factor ofsafetyagainstbearing

Settlement�mm�

Optimized�Wang andKulhawy2008�

1.86 2.30 1.38 1086.00 2.97 25.01

Present study 2.06 2.12 0.50 959.10 3.00 25.00


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depends upon the initial value �guess� of the design variable.As it is very much difficult to predict global optimum of such

points it is required that the problems should be checked withdifferent initial point. Another important aspect of the constrainedoptimization problem is constraint violation, which needs to bechecked for the optimized value. However, such a study is neitherdiscussed in Wang and Kulhawy �2008� nor in this paper. Thediscussers have made such a study based on the results of Wangand Kulhawy �2008� and observed different trends in the obtainedresults in terms of optimized values and the design parameters.The results are shown in Table 1 and it can be seen that theobtained optimized value is less than that given in Wang andKulhawy �2008�. The constraint violations are also better and thedepth of the foundation is more practical considering it as a rein-forced concrete foundation. This also shows that it is very much
important to consider different initial point to arrive at optimized


value. The discussers have also faced similar difficulties whileoptimizing the problems using MS Excel solver.

As discussed above both the constraints are the inequality typeand the GRG method is based on the principle of elimination ofvariable using equality constraint. Hence the discusser would re-quests the author to verify the constraint violation of the resultsfor their problem and also should be checked with different initialpoint before drawing their conclusions.

References

Deb, K. �2005�. Optimization for engineering design algorithms and ex-amples, PHI Pvt. Ltd., New Delhi, India.

Wang, Y., and Kulhawy, F. H. �2008�. “Economic design optimization of
foundations.” J. Geotech. Geoenviron. Eng., 134�8�, 1097–1105.

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