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One-dimensional compression behavior of granular soils around virgin compression line (VCL)

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Abstract

The aim of this study was to investigate the effects of initial values of soil mean grain size (\({\mathrm{d}}_{{50}_{0}}\)) and soil uniformity coefficient (\({\mathrm{C}}_{{\mathrm{u}}_{0}}\)) on the one-dimensional compression behavior of granular soils. Soil samples consisting of equant-shaped, calcerous origin, crushed individual grains with a grain size range of 2.00–25.00 mm were examined in the laboratory tests. The yield stress, the initial and final stresses of the virgin compression line (VCL), and the hardening stress of soil samples during one-dimensional compression behavior were determined. Results indicated that an increase in the soil’s initial mean grain size and a decrease in the soil’s initial uniformity coefficient led to an increase in the value of these oedometric stresses. Soil samples reached the virgin compression line at an axial deformation \(\left({\varepsilon }_{a\left(VCL-i\right)}\right)\) of 10–13% and passed this line at an axial deformation \(\left({\varepsilon }_{a\left(VCL-f\right)}\right)\) of 26–30%. It was observed that the instantaneous index void ratio values \(\left({\mathrm{e}}_{{\mathrm{min}}_{\mathrm{i}}} \, {\mathrm{and}} \, {\mathrm{e}}_{{\mathrm{max}}_{\mathrm{i}}}\right)\) of the soil samples decreased linearly with a slope \(\left({\alpha }_{e}\right)\) of 0.10 in the \(e-\mathrm{ln}{\sigma }_{V}\) plane during one-dimensional compression. The curve of the soil’s instantaneous minimum void ratio \(\left({\mathrm{e}}_{{\mathrm{min}}_{\mathrm{i}}}\right)\) values during one-dimensional compression was proposed as a lower boundary for the one-dimensional compression curve of granular soils.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Abbreviations

\(\Delta {F}_{c}\) :

Increase in fine-grain content

\(\Delta S\) :

Miura and O-Hara (1979) grain breakage factor

B:

Grain breakage factor, the amount of grain breakage

\({B}_{{\sigma }_{f\left({d}_{50}\right)}}\) :

Sefi and Lav (2022) grain breakage factor

\({\mathrm{B}}_{10}\) :

Lade et al. (1996) grain breakage factor

\({\mathrm{B}}_{15}\) :

Lee and Farhoomand (1967) grain breakage factor

\({\mathrm{B}}_{\mathrm{f}}\) :

Nakata et al. (1999) grain breakage factor

\({\mathrm{B}}_{\mathrm{g}}\) :

Marsal (1967) grain breakage factor

\({\mathrm{B}}_{\mathrm{t}}\), \({\mathrm{B}}_{\mathrm{p}}\), \({\mathrm{B}}_{\mathrm{r}}\) :

Hardin (1985) grain breakage factors

BBI:

Indraratna and Salim (2005) grain breakage factor

\({\mathrm{C}}_{\mathrm{c}}\) :

Colliat-Dangus et al. (1988) grain breakage factor

\({\mathrm{C}}_{{\mathrm{u}}_{0}}\) :

Soil initial uniformity coefficient

\({\mathrm{C}}_{\mathrm{u}}\) :

Coefficient of uniformity

\({\mathrm{d}}_{{50}_{0}}\) :

Soil initial mean grain size

\({\mathrm{d}}_{0}\) :

Distance between the two plates

\({\mathrm{d}}_{1}\), \({\mathrm{d}}_{2}\), \({\mathrm{d}}_{3}\) :

Longest, intermediate, and shortest orthogonal axis length of a grain

\({\mathrm{d}}_{10}\) :

Soil effective grain size

\({\mathrm{d}}_{15}\) :

Soil filter grain size

\({\mathrm{d}}_{50}\) :

Soil mean grain size

\({\mathrm{d}}_{\mathrm{av}}\) :

Average size of the grain sub-groups

\({\mathrm{d}}_{\mathrm{m }{\mathrm{cubic}}}\) :

Single cubic grain mean size

\({\mathrm{d}}_{\mathrm{m}}\) :

Single grain mean size

\({\mathrm{d}}_{\mathrm{major}}\) :

Major axis length of the optimal ellipse

\({\mathrm{d}}_{\mathrm{max}}\) :

Soil maximum grain size

\({\mathrm{d}}_{\mathrm{min}}\) :

Soil minimum grain size

\({\mathrm{D}}_{\mathrm{r}}\) :

Relative density

\({\mathrm{d}}_{\mathrm{sta}}\) :

Average length of tested all cubes

\({\mathrm{e}}_{{\mathrm{max}}_{0}}\) :

Soil initial maximum void ratio

\({\mathrm{e}}_{{\mathrm{max}}_{\mathrm{i}}}\) :

Soil instantaneous maximum void ratio

\({\mathrm{e}}_{{\mathrm{min}}_{0}}\) :

Soil initial minimum void ratio

\({\mathrm{e}}_{{\mathrm{min}}_{\mathrm{i}}}\) :

Soil instantaneous minimum void ratio

\({\mathrm{e}}_{{\mathrm{VCL}}_{\mathrm{i}}}\) :

Soil void ratio at the initial stress of the VCL

\({\mathrm{e}}_{0}\) :

Initial void ratio

\({\mathrm{e}}_{\mathrm{i}}\) :

Instantaneous void ratio

\({\mathrm{e}}_{\mathrm{max}}\) :

Maximum void ratio

\({\mathrm{e}}_{\mathrm{min}}\) :

Minimum void ratio

\({\mathrm{F}}_{\mathrm{f}}\) :

Single grain crushing load

\({\mathrm{G}}_{\mathrm{s}}\) :

Specific gravity

m1, m2, C1, C2 :

Material constants for C-parameter

\({\mathrm{M}}_{\mathrm{f}}\) :

Final stiffness value of soil

M i :

Initial stiffness value of soil

α v :

Slope of the instantaneous index void ratios in the e-ln σv plane

\({\alpha }_{e-int}\) :

Slope of the instantaneous index void ratios after the stress of \({\sigma }_{v-int}\)

\({\varepsilon }_{a}\) :

Axial strain

\({\sigma }_{\left({\mathrm{sp}}\right){\mathrm{i}}}\) :

Instantaneous tensile stress acting on the soil mean sized grains

\({\sigma }_{{\mathrm{VCL}}_{\mathrm{f}}}\) :

Final oedometric stress of the virgin compression line

\({\sigma }_{{\mathrm{VCL}}_{\mathrm{i}}}\) :

Initial oedometric stress of the virgin compression line

\({\sigma }_{{\mathrm{v}}_{\mathrm{i}}}\) :

Instantaneous oedometric stress

\({\sigma }_{{\mathrm{v}}_{\mathrm{max}}}\) :

Maximum oedometric stress

\({\sigma }_{\mathrm{f (}{\mathrm{d}}_{50}\mathrm{)}}\) :

Single grain crushing strength of mean-sized grains of a soil

\({\sigma }_{\mathrm{f}}\) :

Single grain crushing strength

\({\sigma }_{\mathrm{h}}\) :

Hardening stress

\({\sigma }_{\mathrm{v}}\) :

Axial stress, oedometric stress

\({\sigma }_{\mathrm{v-int}}\) :

Oedometric stress at the middle part of the VCL

\({\sigma }_{\mathrm{y}}\) :

Yield stress

A :

Material parameter

B :

Material parameter

C :

Material parameter

EI:

Elongation index

FI:

Flatness index

\({\mathrm{n}}\) :

Absorption value

VCL:

Virgin compression line

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Acknowledgements

The authors would like to thank Prof. İskender Atilla Reyhancan and MSc. M. Sahip Kızıltaş for their support in the Istanbul Technical University (ITU) Energy Institute Radiography Laboratory. The authors also would like to thank Prof. Hakan Nuri Atahan, Prof. Hasan Yıldırım, and MSc. Hasan Nuri Türkmenoğlu for their support in the ITU Construction Materials Laboratory.

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Authors and Affiliations

  1. Department of Civil Engineering, Istanbul Technical University, Maslak, Istanbul, Turkey

    Faruk Sefi & Musaffa Ayşen Lav

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  1. Faruk Sefi
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  2. Musaffa Ayşen Lav
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Correspondence to Faruk Sefi.

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Sefi, F., Lav, M.A. One-dimensional compression behavior of granular soils around virgin compression line (VCL). Bull Eng Geol Environ 82, 227 (2023). https://doi.org/10.1007/s10064-023-03229-w

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