Keywords

1 Introduction

The shear strength of sand is usually characterized by the peak friction angle, \( {\upvarphi }_{\text{max} }^{\prime } \), and the critical state friction angle, \( {\upvarphi }_{\text{crit}}^{\prime } \). The latter is considered when the sand is shearing at constant volume conditions and is generally lower than the former, especially in the case of high relative density, Dr. Bolton (1986) investigated the effect of Dr on the dilatancy related component of strength, \( {\upvarphi }_{ \text{max} }^{\prime } \) - \( {\upvarphi }_{\text{crit}}^{\prime } \), of clean sands and suggested simple correlations for the estimation of the friction angles. The purpose of the work presented in this paper is to clarify the effect of sand grains characteristics and fines type and content as well as relative density on the shear strength parameters of sands by means of direct shear tests, which were carried out in the Laboratory of Geotechnical Engineering of University of Thessaly.

2 Tested Soils and Testing Procedure

The tested soils fall into three groups: clean sands of similar grading (group 1), sands containing non-plastic fines (group 2) and sands containing plastic fines (group 3). Sands A and B are comprised totally of quartz whereas sand C is comprised of 77% quartz and 23% feldspar. Only sand B consists of angular grains. Both group 2 and group 3 were prepared by mixing the same clean sand A with a non-plastic sandy silt with D50 = 0.04 mm and Cu = 6 (group 2), or kaolin with PI = 18% (group 3). Table 1 summarizes the physical properties of the tested soils.

Table 1. Physical properties of tested soils
Full size table

The specimens had dimensions of D = 62.5 mm and H = 25 mm, and were prepared at optimum moisture content directly into the shear box using the undercompaction method (Ladd 1978). Specimens of uniform structure at various densities were prepared from each soil and tested in the direct shear apparatus at a range of normal stresses \( \upsigma_{v}^{\prime } \) = 50–400 kPa under drained conditions according to ASTM D3080 (2011). The strength parameters at both peak and critical state were determined in order to evaluate the dilatancy of the tested sands.

3 Results

Due to the space restriction, the results only at \( \upsigma_{v}^{\prime } \) = 100 kPa are presented in Figs. 1, 2 and 3 for soil groups 1, 2 and 3 respectively. The results show the variation of peak angle, \( {\upvarphi }_{ \text{max} }^{\prime } \), and critical angle, \( {\upvarphi }_{\text{crit}}^{\prime } \), of soil resistance as well as the dilatancy related component of strength, \( {\upvarphi }_{ \text{max} }^{\prime } \) - \( {\upvarphi }_{\text{crit}}^{\prime } \), with relative density, Dr. The values of φ΄ were determined based on the results for the whole range of the applied \( \upsigma_{v}^{\prime } \) (50–400 kPa) using the Mohr – Coulomb criterion. The linear correlations between the above parameters are also given. For soil group 3 (sands with plastic fines) the variation of cohesion, c΄, and shear stress, τ, with relative density, Dr, is also presented.

Fig. 1.
figure 1

Variation of (a) peak friction angle, \( {\upvarphi }_{ \text{max} }^{\prime } \), (b) critical friction angle, \( {\upvarphi }_{\text{crit}}^{\prime } \), and (c) \( {\upvarphi }_{ \text{max} }^{\prime } \) - \( {\upvarphi }_{\text{crit}}^{\prime } \) with relative density, Dr, for soil group (1) at \( \upsigma_{v}^{\prime } \) = 100 kPa (Apostolaki 2016).

Full size image
Fig. 2.
figure 2

Effect of non-plastic fines on the variation of (a) peak friction angle, \( {\upvarphi }_{ \text{max} }^{\prime } \), (b) critical friction angle, \( {\upvarphi }_{\text{crit}}^{\prime } \), and (c) \( {\upvarphi }_{ \text{max} }^{\prime } \) - \( {\upvarphi }_{\text{crit}}^{\prime } \) with relative density, Dr, for soil group (2) at \( \upsigma_{v}^{\prime } \) = 100 kPa (Tyri 2016).

Full size image
Fig. 3.
figure 3

Effect of plastic fines on the variation of (a) peak friction angle, \( {\upvarphi }_{ \text{max} }^{\prime } \), (b) peak cohesion, \( c_{{\text{max}}}^{\prime } \), (c) peak shear strength, τmax, (d) critical friction angle, \( {\upvarphi }_{\text{crit}}^{\prime } \), (e) critical cohesion, \( c_{{\text{crit}}}^{\prime } \), and (f) critical shear strength, τcrit, with relative density, Dr, for soil group (3) at \( \upsigma_{v}^{\prime } \) = 100 kPa (Koulaouzidou 2016).

Full size image

4 Conclusions

The following conclusions can be drawn from the results presented herein:

  1. (a)

    Simple correlations between Dr and \( {\upvarphi }_{\text{max} }^{\prime } \), \( {\upvarphi }_{\text{crit}}^{\prime } \) and \( {\upvarphi }_{ \text{max} }^{\prime } \) - \( {\upvarphi }_{\text{crit}}^{\prime } \) are supported for the tested soils, showing the increase of φ΄ values with the increasing Dr, especially in the case of \( {\upvarphi }_{ \text{max} }^{\prime } \) - \( {\upvarphi }_{\text{crit}}^{\prime } \).

  2. (b)

    The differences among the φ΄ values of the tested clean sands at the same level of Dr are small due to their similar gradings and may be attributed to the effect of grain angularity and soil mineralogy, e.g. the higher values are pertaining to sand containing portions of feldspar or angular grains.

  3. (c)

    For the mixtures of sand with non-plastic fines, an increase of φ΄ values is observed with the increase of FC and Dr, except for \( {\upvarphi }_{\text{crit}}^{\prime } \) value which remains constant.

  4. (d)

    For the mixtures of sand with plastic fines, a development of cohesion, c΄, which depends on Dr, is observed in both peak and critical states but in an opposite way, whereas φ΄ values increase with increasing Dr. The effect of FC on strength components, c΄ and φ΄, is not clear.