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Pseudo-Static Analysis of Soil Nailed Excavations

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Abstract

In this paper, a pseudo-static analysis has been presented to investigate the stability of soil nailed vertical/nearly vertical excavations. The failure surface is assumed as the arc of log-spiral passing through the toe of the excavation and intersecting the ground at right angle. The horizontal and vertical seismic forces are taken in terms of horizontal and vertical seismic coefficients. The internal failure mode of the nailed cut is considered either by pull-out or rupture or excessive bending whichever is critical. Expression for the factor of safety is derived using moment equilibrium method. Results have been arranged in tabular form considering ranges of the design parameters usually occur in practice. A typical table for the design of nailed excavation with driven nails is presented in the paper. Analytical results have been compared with the findings of model tests and reasonably good agreement has been observed.

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Abbreviations

A s :

Area of nail = π/4 d 2

c :

Cohesion acting along the surface of sliding wedge bd

C′:

Is a constant and considered as C′ = 4 for the plastic analysis (Jewell and Pedley 1990)

d :

Diameter of the driven nail

f*:

Apparent coefficient of friction between nail and soil. It is obtained from pull out tests

f y :

Yield strength of steel nail

i :

Number of nail, It varies from i = 1 to i = N

K a :

\( \frac{1 - \sin \,\phi }{1 + \sin \,\phi } \)

le i :

Length of the ith nail behind the failure wedge

l si :

Shear width = \( \sqrt {\frac{{8M_{\text{p}} }}{{\sigma_{\text{b}} }} \times \frac{1}{d} \times \left( {1 - \frac{{T_{i} }}{{T_{\text{P}} }}} \right)} \)

M 1 :

Moment of force W 1 along the center of log-spiral i.e., point ‘o’

M 2 :

Moment of W 2 along the point ‘o’

M 3 :

Moment of W 3 along the point ‘o’

M 4 :

Moment of W 4 along the point ‘o’

M 5 :

Moment of W 1αh along the point ‘o’

M 6 :

Moment of W 2αh along the point ‘o’

M 7 :

Moment of W 3αh along the point ‘o’

M 8 :

Moment of W 4αh along the point ‘o’

M QV :

Moment of Q (1 ± αv) about the point ‘o’

M QH :

Moment of Q αh about the point ‘o’

M C :

Moment of cohesion force c about the point ‘o’

M T :

Moment of nail axial force T i of the ith nail about the point ‘o’

M Tc :

Moment of the mobilised shear force Tc i acting normal to the axis of nail

M P :

Fully plastic bending moment of nail varying with shape of nail

N :

Total number of nails in a single column of nails

P i :

Perimeter of the ith nail (i.e., π d)

q :

Applied surcharge intensity on the ground surface

Tc i :

Mobilised shear in the ith nail which acts normal to the axis of nail at its intersection with slip surface, Jewell and Pedley (1990)

T p :

Fully plastic axial force = f y × A s

W 1 :

Weight of the soil wedge obd

W 2 :

Weight of the soil wedge oed

W 3 :

Weight of the soil wedge eab

W 4 :

Weight of the soil wedge aba′

\( \sigma_{{n_{i} }} \) :

Normal stress at the mid depth of ith nail in the length le i

\( \sigma_{{n_{i} }} \) :

\( \frac{{\sigma_{y} \,\cos^{2} \theta - \sigma_{x} \,\sin^{2} \theta }}{{\left[ {\cos 2\theta \, + \,\sin 2\theta \,\tan \delta } \right]}} \)

σy :

\( \left[ {\gamma (i - 0.5)\,S_{{{\upnu}}} + q} \right] \)

σb :

Soil bearing pressure

σv :

\( \gamma (i - 0.5)S_{{{\upnu}}} \)

ω:

Log spiral angle

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Acknowledgments

Authors wish to thank Council of Scientific and Industrial Research (CSIR), New Delhi, India, for providing financial support for undertaking this research work.

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Authors and Affiliations

  1. Department of Civil Engineering, College of Technology, G.B. Pant University of Agriculture and Technology, Pantnagar, Distt. UdhamSingh Nagar, Uttarakhand, 263 145, India

    Gosavi Meenal, Swami Saran & Satyendra Mittal

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  1. Gosavi Meenal
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  2. Swami Saran
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  3. Satyendra Mittal
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Correspondence to Gosavi Meenal.

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Meenal, G., Saran, S. & Mittal, S. Pseudo-Static Analysis of Soil Nailed Excavations. Geotech Geol Eng 27, 571–583 (2009). https://doi.org/10.1007/s10706-009-9258-z

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