Effect of Specimens’ Height to Diameter Ratio on Unconfined Compressive Strength of Cohesive Soil

The cohesive soil specimens were collected from five test pits at a depth of 3 m from the ground level in Jimma Town, Ethiopia (i.e., from Aweytu, Ajip, Mariam Church, Saris, and Jimma Institute of Technology [JIT] campus). According to the Unified Soil Classification System (USCS) soil classification system, the collected cohesive soil from all test pits was fine grained. The fine-grained material collected from the Aweytu test pit was a gray-colored, low-plasticity clay soil (CL). The soil sample collected from the Ajib and JIT campus test pits was a black-colored, high-plasticity clay soil (CH). Moreover, the soil samples collected from Mariam Church and Saris Sefer test pits were red-colored, high-plasticity silty soil (MH).

The soil specimens’ maximum dry density and optimum moisture content were determined using the Proctor compaction test. This study conducted a standard Proctor test for all test pits. The specimens used for this test were air-dried and passed through a sieve of size 4.75 mm. In order to fully wet the specimens, they were soaked for about 4 hours and then compacted by 2.45 kg rammers from a 30.5 cm height of drops in three layers. For each layer, the soil was compacted by dropping the 2.45 kg rammer 25 times using a mechanical compactor machine according to the ASTM D698-07 [22] standard.

The relationship between dry density and moisture content of all test pits is shown in Figure 1. The collected cohesive soils’ maximum dry density and optimum moisture content were determined from the plotted curve. Accordingly, the specimens’ maximum dry densities ranged from 1.27 to 1.51 g/cm³. The optimum moisture content varied from 23% to 39%, as shown in Table 1.

Figure 1

The index properties of the soils, including the classifications according to the American Association of Highway and Transportation Officials (AASHTO) and Unified Soil Classification System (USCS) soil classification standards, are summarized in Table 1.

This research aims to demonstrate the framework of unconfined compression test results affected by the H/D scale ratio. The specimen size selection is usually done according to user preference and past experiences, which are subjective in real-world conditions to apply for practical design, analysis, and modeling. Therefore, these thought triggers are investigated in the subsequent section. This experiment was designed to evaluate the impact of the specimen's H/D ratio on the UCSs of cohesive soils. The diameters of compacted (remolded) sample specimens were selected to be 38, 50, and 100 mm. The diameters of the specimen were chosen as per ASTM D 2166 [4] and BSI 1377-7 [7] as well as the availability of these size on the market. Each specimen's diameter had H/D ratio of 1.00, 1.25, 1.50, 1.75, 2.00, 2.25, 2.50, 2.75, and 3.00. The test was conducted on a compacted (remolded) sample specimen. The remolded specimens were prepared based on their respective maximum dry density and optimum moisture content according to ASTM D2166 [6]. A compacted soil specimen is more homogeneous and has minor defects and voids. Accordingly, it gives a uniform UCS and deformations.

To evenly wet all the soil particles, the samples were soaked for roughly 24 h at their optimum moisture content. The soaked soil materials were covered by plastic to protect them from water evaporation. The soil samples were remolded at their maximum dry density after being uniformly wet.

The unconfined compression soil test specimens were remolded using their respective specimens’ diameters of molds (i.e., 38, 50, and 100 mm specimen diameters). Trials were used to determine the number of layers and blows required to remold the sample specimens.

The remolded specimens were extruded from the lubricated molds using a hydraulic extruder and their height was trimmed according to their H/D ratio, as shown in Table 2. The dry density and the moisture content of the remolded specimens were checked. The difference between the remolded specimens’ water content and their optimum moisture content varied from 0.56% to 0.75%. Also, the difference between the remolded specimens’ dry density and their maximum dry density was from −0.02 to 0.02 g/cm³. However, since the difference was slight, it was considered negligible [3]. The strain rate of the unconfined compression testing was adopted according to earlier studies [1, 16]. The strain rate was taken at 1% per minute as stated in the Japanese geotechnical standard [5] for all specimen heights to decrease the strain rate effect on the unconfined compression test result.

As shown in Table 2, the unconfined compressive test was performed at the H/D ratio of 1.00, 1.25, 1.50, 1.75, 2.00, 2.25, 2.50, 2.75, and 3.00 for each specimen's diameter of 38 mm, 50 mm, and 100 mm. The height of the specimens for each diameter ranged from 38 to 300 mm. Accordingly, the UCS values for the remolded cohesive soil specimens were determined from the five test pits at three different soil specimen diameters and nine H/D ratios for their respective diameter.

The dry density and the moisture content of the remolded soil specimens prepared at different H/D ratios were compared with the optimum moisture content and maximum dry density. The soil specimens’ dry density, water content, diameter, and height before and after the test were similar with a negligible variance. Then, the determined UCS value corresponding to its H/D ratio was appropriated for the data analysis. For the test results having a wide gap between those control points, another trial was conducted until the variance was reduced.

The optimum aspect ratio was determined by analyzing the UCS values and stress-strain curves of the remolded cohesive soil specimens for the different specimen diameters with their corresponding H/D ratios. The recommendation of an appropriate aspect ratio of specimens was evaluated according to consistency peak UCS values among the series H/D ratio of 38, 50, and 100mm diameters. When the aspect ratio of specimens increases, the peak UCS value difference between the successive aspect ratios decreases and becomes more stable [3,18]. The change in UCS value among the successive H/D ratio of the specimens is greater for too small and too large aspect ratios of the specimens. Therefore, an appropriate H/D ratio was selected according to the UCS uniformity. For the unconfined compression test sample specimen, the inclined failure planes do not intersect each other along the entire length of the sample specimens of the appropriate specimen size [2]. However, the failure pattern varies with the H/D ratios of the test sample specimens. For a small H/D ratio, the whole sample is restrained by the friction of the end-loading plates [11].

Consequently, the bulging failure mechanism occurs [19]. On increasing the aspect ratio, stress distribution inside the sample will become more uniform [3]. Therefore, the failure mechanism will be changed. The buckling effect is another issue if the H/D ratio increases due to the slenderness effect [11]. As a result, a complex failure mechanism will happen [1]. Accordingly, the failure mechanism of the specimens was assessed to determine the appropriate H/D ratio of UCS values. Then, according to the failure mechanism, the UCS value uniformity, the characteristics of the stress–strain graph, axial strains of the peaks, and the UCS values of the H/D ratios for each diameter were evaluated and validated with previous studies done in similar soil types.

A single linear regression analysis was conducted to evaluate the effect of the H/D ratio on the UCS of the cohesive soils using Microsoft Excel-2016, OriginPro-2021, and SPSS-25 data modeling software. UCS equations were then derived for the selected H/D ratio for specimens’ sample diameters, which applies to the study area. A Statistical Distributions test, Shapiro-Wilk normality test, scatter plot, and Pearson correlation coefficient (R) were used to evaluate the quality of the data collected.

Figure 2 shows the effect of the H/D ratio on the UCS test, varying the H/D of the soil specimens. From the result, it is observed that as the height and diameter of the soil specimen increase, the UCS of the soil decreases. With H/D ratios from 1.00 to 1.75 and from 2.5 to 3, the difference in UCS value of the cohesive soil specimen between consecutive H/D ratios was steeply decreased. Compared to the other consecutive H/D ratios, the difference between the UCS values of the specimens measured from the H/D ratio of 1.75–2.25 was considerably smaller. This was also similar for all the sample specimens’ diameters, as shown in Figure 3, which is the same as [1] investigated earlier. The peak UCS value of all test pits at a small H/D ratio was the highest because the whole specimen is restrained by the friction of the end-loading plate and develops the potential for the interference of failure planes, which increases the UCS of a soil sample by preventing the formation of the weakest failure plane. From an H/D ratio of 2.50 to 3, the peak UCS values rapidly decreased and attained the smallest values due to the buckle effect, developing bulging local failures.

Figure 2

Figure 3

The peak value of UCS for each consecutive H/D ratio decreased as the diameter of specimens increased. Micro-defects and voids increased as the specimen's diameter increased. Compaction homogeneity and moisture content uniformity also started to decline. For these reasons, an increase in specimen diameter results in a fall in the UCS value. Despite the difficulty in transporting and drilling, large-sized soil sample specimens might represent the actual soil specimens in the field. This difference in the UCS value of the cohesive soil from the smallest specimen diameter to the largest specimen diameter was relatively smaller than that mentioned in [14, 20]. Both studies were conducted on specimen size effects using the triaxial test. The effect of confining pressure can explain the observed difference.

Figure 3 shows the variation in percentage for the peak UCS in each H/D ratio from their mean or average values of 38 mm, 50 mm, and 100 mm specimen diameter of all test pits. The sample specimen's UCS value of 2.0 H/D ratio was the one that comes closest to the average value for all specimens’ diameter. However, the difference in the average value of UCS increased as the H/D ratio was far from the H/D ratio of 2 to both 1 and 3. The polynomial fit curve trend lines illustrated that, generally, the closest UCS value of the specimen to the mean value was at a 2 H/D ratio for all test pits. This property was also mentioned in [3], and the result was similar. According to the laboratory test result in the study, the UCS value is stable from 1.75 to 2.25 H/D ratio. The end platen and slenderness (buckling) effect decrease among these H/D ratios. Hence, the test result becomes close to the mean value of UCS for the cohesive soils tested at different specimen sizes.

Figures 4–8 show the relation of stress–strain of unconfined compression test results for the test pits of Ajib, Aweytu, JIT, Mariam Church, and Saris Sefer, respectively. The peak UCS values were attained at the significant axial strain in the smallest H/D ratio. However, for a small H/D ratio, the specimen's stress–strain curve experienced small axial stresses at the early axial strains. When the height of the specimen was too short, the whole specimen was restrained by the friction of the end-loading plates [11]. This reveals that the axial stress grows to a peak and is slightly constant.

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

However, as the specimen's H/D ratio increased (from 1.75 for 38 mm and 1.50 for 50 mm specimen diameter), the curve was slightly linear at the initial axial strain, and then the slope decreased until the peak reached the UCS value. Having reached the peak UCS value, the curve rapidly dropped as the H/D ratio was increased. Specifically, from the H/D ratio of 2.50, the stress–strain curve was slightly linear, with less steeply slope until the peak strength was attained and the curve became sharp. Hence, the endplate effect was reduced by the specimen's height starting from 1.5 to 1.75 H/D ratios and above. However, the axial stresses rapidly dropped from 2.25 to 2.50 H/D ratios due to the increase in local defects and buckling effects. This is similar to that reported in previous studies [1,3,11].

The effect of specimen's diameter for a stress–strain curve is shown in Figures 5–9. As the H/D ratio increased, the axial strain of peak UCS decreased, and the sharpness of the curve increased for 38 mm specimen diameter. However, 50 and 100 mm specimen diameters showed relatively minor differences compared to the 38 mm diameter of the specimen.

Figure 9

The characteristics of the stress–strain curves in the successive specimens’ H/D ratio becomes consistent as increased as the specimen's diameter. For instance, the 38 mm diameter specimen's peak UCS strain varied from 11.5% to 4.4%, while the strain value varied from 6% to 2% and from 4.7% to1.8% for specimen diameters of 50 and 100 mm, respectively. The peak UCS stress–strain curve of 38 mm specimen diameter was a smooth curve for an H/D ratio from 1.00 to 1.75 for all test pits. In contrast, it was a sharp curve for an H/D ratio from 2.5 and above. The stress–strain curves were sharp for 50 and 100 mm diameter, starting from H/D ratios of 2. Therefore, the highest diameter specimen exhibited complex stress–strain curves compared to those of smaller diameter specimens. In this study, the stress–strain curve of 38 mm diameter experienced both ductile and brittle behaviors, while those of 50 and 100 mm specimen diameters possessed a brittle failure with localized shear failures before the development of one or more failure planes. Accordingly, the effect of the endplate decreased on increasing both the specimen diameter and H/D ratios. Thus, the behavior of the stress–strain curves of the unconfined compression test changed from ductile to brittle behavior as the H/D ratio and diameter of the specimen increased.