# Determination of c-φ Properties of Lightly Stabilized Soils from Conventional Tensile and Compressive Testing

Mario Castaneda-Lopez, Thomas Lenoir, Luc Thorel, Jean-Pierre Sanfratello

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Mario Castaneda-Lopez, Thomas Lenoir, Luc Thorel, Jean-Pierre Sanfratello. Determination of c-φ Properties of Lightly Stabilized Soils from Conventional Tensile and Compressive Testing. 5th International Conference on Transportation Geotechnics (ICTG) 2024, Nov 2024, Sydney, Australia. pp.77 - 85, 10.1007/978-981-97-8237-6_8. hal-04815149

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# Determination of c-φ properties of lightly stabilized soils from conventional tensile and compressive testing

Mario Castaneda-Lopez¹[0000-0002-7406-8046], Thomas Lenoir¹[0000-0003-4539-9417], Luc Thorel¹[0000-0002-0218-4144], Jean-Pierre Sanfratello²

¹ University Gustave Eiffel, F-44344 Bouguenais, France

² DTRD, COLAS SA, 78771 Magny-les-Hameaux, France

mario-alexander.castaneda-lopez@univ-eiffel.fr

**Abstract.** Cement stabilization of soils is a common technique to enhance engineering and mechanical properties of in situ soils in the field of road geotechnics. Usually, moderate quantities of cement are used, around 5 to 10% of the dry material. However, cement manufacturing is one of the biggest sources of greenhouse gas emissions, specifically carbon dioxide. For this reason, reducing cement content by a few percent in geotechnical structures made with cement stabilized soils (CSS) has a high environmental interest, particularly in view of the involved volumes of material. This work aims to contribute to a better understanding of the mechanical characteristics of lightly stabilized soils. First, the mechanical behavior of a clayey and a sandy soil treated with 3% cement was studied for several curing times. Next, measured mechanical features were correlated. Finally, these measurements were used to characterize the Mohr-Coulomb failure criterion and compared with a conventional approach. Results point out that mechanical enhancement can be quantified in terms of cohesion. Friction angle seems to be independent of curing time. The proposed approach can be used to determine geotechnical structures design parameters.

**Keywords:** Earthworks, Cement-stabilized Soils, Correlation Analysis, Mohr-Coulomb.

## 1 Introduction

Cement stabilization of soils is a common technique to enhance the engineering and mechanical properties of in situ soils according to stress rates imposed by civil engineering projects [1]. Use of cement-stabilized soils (CSS) cover a wide range of civil engineering applications such as embankments, foundations, slope protection, pavements and rail construction [2].

CSS constitute an intermediate class of geomaterials whose mechanical behavior is at the boundary between soil mechanics and rock mechanics [3, 4]. Compressive and tensile strength are widely employed as indicators of stabilization. Whereas compressive strength is linked to granular packing and bonding compounds, tensile strength is more related to the amount of cementitious compounds [5]. However, these
characteristics represent a defined state of stresses and don't necessarily match with the service state of stresses of structures.

It is generally accepted that the mechanical failure of CSS can be represented with the Mohr-Coulomb (MC) criterion [3]. Use of compressive and tensile properties to determine MC parameters for design purposes have been related in literature [4, 6, 7]. However, a direct measurement of these parameters has never been done.

Using direct and indirect measurements, the present work investigates the shear strength of two lightly stabilized soils.

# 2 Materials and Methods

## 2.1 Materials

**Soils.** Two soils named A and B are studied. Soil A is cut from the covering soil of an aggregate quarry at Soignies, Belgium (50° 34′ 25.759″ N, 4° 2′ 16.476″ E). Soil B is a quarry tailing from Chauvé, France (47° 8′ 22.886″ N, 2° 0′ 45.934″ W). The grain size curves are shown in Fig. 1.

<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Particle-size distribution. F: fine, M: medium, C: coarse. PL: plastic limit, LL: liquid limit, PI: plastic index and ρs specific mass.</figcaption></figure>

Following the AASHTO (M 145-91), USCS (ASTM D2487-17) and GTR (NF P11-300) classification systems in this order, soil A is classified as A-6 (11), CL and A2 and soil B is classified as A-2-6(0), SM-SC and A2. The clay activity (A=PI/clay content) is 0.29 for soil A and 1.3 for soil B.

**Soil treatment.** Soils were treated with 3% of cement (weight of dry material) CEM II/A-LL 42.5 R (NF EN 197-1.). Lime pre-treatment was not needed due to the suitable
workability of both mixtures. The Optimum Moisture Content (OMC) and Maximum Dry Density (MDD) were determined following the standard Proctor compaction tests (NF P94-093). For mixture A, OMC = 15.5% and MDD = 1.79 g/cm³. For mixture B, OMC = 10.0% and MDD = 1.98 g/cm³. Reference values for sample preparation are 96% of MDD at OMC. Samples were tested after several curing times (CT): 7, 28, 90, 180 and 360 days. For curing, samples were stored in a room with temperature regulated at 20 °C in plastic bags to keep constant water content

## 2.2 Experiments

Experimental program is summarized in Table 1. For Unconfined Compression Strength test (UCS), Direct Tensile Strength test (DTS) and Indirect Tensile Strength test (ITS), tests are carried out on a Zwick/Roell Z150 press. Crosshead speed was 0.1 mm/min for UCS and DTS and 0.3 mm/min for ITS.

**UCS.** Vertical stress, $\sigma_{zz}$ is calculated using Eq. (1) with $\sigma$ in MPa, F in N and D in mm. Its maximum value, corresponding to the failure load, is equal to the UCS. As $\sigma_{zz}$ is a compressive load, its value is positive (Fig. 2(a)).

$$ \sigma_{zz} = 4F/\pi D^2 \quad (1) $$

**DTS.** Equation for DTS calculations is the same than for UCS (Eq.(1)). As vertical load is a traction load, its value is negative (Fig. 2 (b)). Minimal value of $\sigma_{zz}$ corresponds to the DTS.

**ITS.** Horizontal $\sigma_{zz}$ and vertical stresses $\sigma_{xx}$ are calculated using Eq. (2) with $\sigma$ in MPa, F in N, D and H in mm. Its minimum value, corresponding to the failure load, is equal to the ITS. Vertical compressive (positive) load $\sigma_{zz}$ follows the eq. (3) with $\sigma_{xx}$ negative (traction) (Fig. 2 (c)).

$$ \sigma_{xx} = -2F/\pi HD \quad (2) $$

$$ \sigma_{zz} = -3\sigma_{xx} \quad (3) $$

**Direct Shear test (DS).** Tests were carried out in a machine Sheartest VJT following the standard NF EN ISO 17892-10. Shear rate was 0.12 mm/min. Based on normal (N) and tangential (T) forces (in N), and the contact area, normal ($\sigma$) and shear ($\tau$) stress are calculated following eq. (4) and (5) with A (in mm²) corrected shearing area [8]. Levels of N varied between 2 and 250 kPa.

$$ \sigma = N/A \quad (4) $$

$$ \tau = T/A \quad (5) $$
<table><caption>**Table 1.** Experimental program for each mixture</caption><thead><tr><th>Test</th><th>Standard</th><th>D (mm)</th><th>H (mm)</th><th>CT (days)</th><th>Testes Samples</th><th>Tested samples, total</th></tr></thead><tbody><tr><td>UCS</td><td>EN 13286-41:2021</td><td>100</td><td>200</td><td rowspan="4">7, 28, 90, 180 and 360</td><td>3</td><td>15</td></tr><tr><td>DTS</td><td>NF EN 13286-40</td><td>100</td><td>200</td><td>3</td><td>15</td></tr><tr><td>ITS</td><td>NF EN 13286-42</td><td>100</td><td>100</td><td>4</td><td>19</td></tr><tr><td>DS</td><td>NF EN ISO 17892-10</td><td>60</td><td>35</td><td>15</td><td>75</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Characteristics of mechanical tests employed: (a) UCS, (b) DTS, (c) ITS</figcaption></figure>

## 3 Results and discussion

For UCS, DTS and ITS, mean values and standard deviation (SD) are presented in Table 2. For DS, conventional linear regressions parameters *c* (cohesion) and *φ* (friction angle) corresponding to the MC criteria are presented for each CT with the coefficient of determination, R². R² is higher than 0.93 for 3 out of 5 CT for mixture A and higher than 0.85 for 4 out of 5 CT for mixture B, which suggest the suitability of this model to represent the failure characteristics of both materials.

<table><caption>**Table 2.** Experimental results</caption><thead><tr><th rowspan="2">Mix.</th><th rowspan="2">CT (days)</th><th colspan="2">UCS (MPa)</th><th colspan="2">DTS (MPa)</th><th colspan="2">ITS (MPa)</th><th colspan="3">DS</th></tr><tr><th>Mean</th><th>SD</th><th>Mean</th><th>SD</th><th>Mean</th><th>SD</th><th>c (MPa)</th><th>φ (°)</th><th>R²</th></tr></thead><tbody><tr><td rowspan="5">A</td><td>7</td><td>1.53</td><td>0.05</td><td>0.13</td><td>0.02</td><td>0.14</td><td>0.02</td><td>0.24</td><td>50.2</td><td>0.942</td></tr><tr><td>28</td><td>1.65</td><td>0.15</td><td>0.15</td><td>0.01</td><td>0.15</td><td>0.01</td><td>0.35</td><td>36.3</td><td>0.568</td></tr><tr><td>90</td><td>2.41</td><td>0.01</td><td>0.18</td><td>0.03</td><td>0.18</td><td>0.01</td><td>0.37</td><td>55.9</td><td>0.933</td></tr><tr><td>180</td><td>1.77</td><td>0.11</td><td>0.26</td><td>0.07</td><td>0.23</td><td>0.01</td><td>0.33</td><td>41.7</td><td>0.485</td></tr><tr><td>360</td><td>2.11</td><td>0.02</td><td>0.25</td><td>0.04</td><td>0.22</td><td>0.03</td><td>0.34</td><td>62.0</td><td>0.936</td></tr><tr><td rowspan="5">B</td><td>7</td><td>0.91</td><td>0.03</td><td>0.12</td><td>0.02</td><td>0.12</td><td>0.01</td><td>0.20</td><td>49.7</td><td>0.998</td></tr><tr><td>28</td><td>1.20</td><td>0.03</td><td>0.16</td><td>0.03</td><td>0.17</td><td>0.01</td><td>0.27</td><td>53.1</td><td>0.849</td></tr><tr><td>90</td><td>1.53</td><td>0.18</td><td>0.21</td><td>0.06</td><td>0.21</td><td>0.01</td><td>0.39</td><td>49.5</td><td>0.943</td></tr><tr><td>180</td><td>1.72</td><td>0.07</td><td>0.23</td><td>0.05</td><td>0.26</td><td>0.01</td><td>0.43</td><td>32.3</td><td>0.927</td></tr><tr><td>360</td><td>1.91</td><td>0.04</td><td>0.37</td><td>0.05</td><td>0.31</td><td>0.01</td><td>0.42</td><td>61.4</td><td>0.345</td></tr></tbody></table>
Linear regressions are used to represent UCS, DTS, ITS and cohesion as a function of CT [9] following the eq.(6). Results, shown in Table 3, reveal a good agreement, especially between traction and CT for mixture A. For mixture B, it is obtained a noteworthy agreement for all the presented features. For $\phi$, regressions reveal a poor correlation for mixture A ($R^2$=0.15) and mixture B ($R^2$=0.00). When comparing the magnitude of coefficients $a$ between both materials, it is identified a higher effect of CT for the mixture B for UCS, DTS and cohesion. Measured values of UCS, DTS and ITS are in general higher for mixture A, as presented in Table 2, and this fact is confirmed when comparing the magnitude of coefficients $b$.

$$y = a \log_{10}(CT) + b \quad (6)$$

<table><caption>**Table 3.** Regression models for experimental results.</caption><thead><tr><th rowspan="2">Test</th><th colspan="3">Mixture A</th><th colspan="3">Mixture B</th></tr><tr><th>a</th><th>b</th><th>R<sup>2</sup></th><th>a</th><th>b</th><th>R<sup>2</sup></th></tr></thead><tbody><tr><td>UCS (MPa)</td><td>0.338</td><td>1.281</td><td>0.403</td><td>0.593</td><td>0.381</td><td>0.995</td></tr><tr><td>DTS (MPa)</td><td>0.077</td><td>0.053</td><td>0.840</td><td>0.133</td><td>-0.022</td><td>0.830</td></tr><tr><td>ITS (MPa)</td><td>0.063</td><td>0.074</td><td>0.842</td><td>0.010</td><td>0.115</td><td>0.923</td></tr><tr><td>c (MPa)</td><td>0.050</td><td>0.238</td><td>0.473</td><td>0.144</td><td>0.081</td><td>0.925</td></tr></tbody></table>

A comprehensive correlation between studied parameters was done (Fig. 3). Results agree with the linear correlation between Log<sub>10</sub>CT and the strength enhancement for both materials, in particular for mixture B, which exhibit a noteworthy correlation. Correlation matrix also reveals the low relationship of CT with measured values of $\phi$.

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Correlation matrix of the dataset for mixture A (left) and mixture B (right)</figcaption></figure>

DTS and ITS are highly correlated ($R_{DTS-ITS}$ is 1.00 for mixture A and 0.96 for mixture B). The ratio DTS/ITS is 1.04±0.09 and 1.00±0.12 for mixture A and B respectively. For practical purposes this ratio is normally assumed as 0.8 [10]. A high correlation is also identified between UCS and cohesion ($R_{UCS-c(A)}$ = 0.73 and $R_{UCS-c(B)}$ = 0.96). Correlation between the tensile strength (either DTS or ITS) and the MC parameters is
higher for cohesion. In this case, the degree of correlation is moderated for mixture A ($R_{DTS-c} = 0.39$, $R_{ITS-c} = 0.43$) and high for mixture B ($R_{DTS-c} = 0.79$, $R_{ITS-c} = 0.90$).

Mean results after 7 days of cure for both mixtures are displayed in a {σ - τ} space in Fig. 4 for both materials. Here, principal stresses in the failure, i.e., the couple ($σ_3$, $σ_1$), are used to represent Mohr semi-circles for UCS in blue (0, UCS), DTS in orange (DTS, 0) and ITS in green (ITS, -3ITS) [11]. Direct shear results, in red, are depicted as both the couple ($σ$, $τ$) of individual tests (scatterplot) and the MC envelope (linear regression).

<figure><img src="image_5.png" /><figcaption>Fig. 4. Mean results after 7 days of cure for mixture A (above) and mixture B (below). UCS (blue), DTS (orange), ITS (green) and Direct shear (red)</figcaption></figure>

Results suggests a link between MC envelope and UCS and ITS values as reported in the literature. This approach [6] states that the envelope of Mohr-Coulomb's failure corresponds to the tangent to the ITS and UCS semi-circles. Mathematically, it relies on either UCS or ITS, and the ratio $\xi = ITS/UCS$. This ratio varies within quite a narrow range for both materials: $\xi_A = 0.10 \pm 0.02$ and $\xi_B = 0.15 \pm 0.01$.
In Table 4, this approach is applied to the experimental dataset and compared to the measured values from DS test. Results are in good agreement. When comparing the ratio between estimated and measured values of cohesion, it varies between 0.84 and 1.22 with a mean of 1.07 for mixture A, and between 0.95 and 1.31 with a mean of 1.10 for mixture B. For $\varphi$, this ratio varies between 0.77 and 1.40 with a mean of 1.03 for mixture A and between 0.50 and 1.07 with a mean of 0.77 for mixture B.

It is interesting to remark that $\varphi_{\xi}$ is close to a constant value (49.4±5.5° and 36.0±3.5° for mixture A and B respectively). It confirms that addition of cement has an effect on friction angle. However, it seems that CT doesn't have effect on friction angle.

<table><caption>**Table 4.** Measured ($c, \varphi$) and estimated ($c_{\xi}, \varphi_{\xi}$) MC parameters</caption><thead><tr><th rowspan="2">Mixture</th><th rowspan="2">CT (days)</th><th rowspan="2">ξ</th><th colspan="2">Estimated</th><th rowspan="2">c<sub>ξ</sub>/c</th><th rowspan="2">φ<sub>ξ</sub>/φ</th></tr><tr><th>c<sub>ξ</sub> kPa)</th><th>φ<sub>ξ</sub> (°)</th></tr></thead><tbody><tr><td rowspan="5">A</td><td>7</td><td>0.09</td><td>271.0</td><td>51.0</td><td>1.11</td><td>1.02</td></tr><tr><td>28</td><td>0.09</td><td>293.4</td><td>50.9</td><td>0.84</td><td>1.40</td></tr><tr><td>90</td><td>0.07</td><td>368.8</td><td>56.0</td><td>0.99</td><td>1.00</td></tr><tr><td>180</td><td>0.13</td><td>402.9</td><td>41.0</td><td>1.22</td><td>0.98</td></tr><tr><td>360</td><td>0.10</td><td>405.0</td><td>48.0</td><td>1.18</td><td>0.77</td></tr><tr><td rowspan="5">B</td><td>7</td><td>0.13</td><td>212.8</td><td>39.9</td><td>1.06</td><td>0.80</td></tr><tr><td>28</td><td>0.15</td><td>304.6</td><td>36.0</td><td>1.13</td><td>0.68</td></tr><tr><td>90</td><td>0.14</td><td>369.8</td><td>38.5</td><td>0.95</td><td>0.78</td></tr><tr><td>180</td><td>0.15</td><td>453.2</td><td>34.5</td><td>1.04</td><td>1.07</td></tr><tr><td>360</td><td>0.16</td><td>541.8</td><td>30.9</td><td>1.31</td><td>0.50</td></tr></tbody></table>

## CONCLUSIONS

This work shows that investigated properties, UCS, DTS, ITS and cohesion of a clayey and a sandy soil, are linearly correlated with curing time. This correlation is particularly higher for the sandy soil. For tensile strength, in this study, DTS~ITS for both materials. DTS exhibit higher SD. The ITS/UCS ratio is 0.10 ± 0.02 for mixture A and 0.15 ± 0.01 for mixture B.

A high relationship is also identified between UCS and MC parameters. The alternative method for estimating MC parameters for CSS based on ITS and UCS is successfully checked. Results point out the mechanical enhancement with CT in terms of cohesion. Friction angle is modified with the addition of cement but seems to be independent from CT.

## ACKNOWLEDGEMENTS

The authors would like to thank the Gustave Eiffel University - Materials and Infrastructures Department (MAST) for the technical support and laboratory facilities to carry out this research.
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