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Article

Effects of the Properties of Fines on the Pore Water Pressure Generation Characteristics of Sand–Silt–Clay Mixtures during Cyclic Loading

by
Darn-Horng Hsiao
* and
Chung-Chieh Lin
Department of Civil Engineering, National Kaohsiung University of Science and Technology, 415 Chien Kung Road, Kaohsiung 80778, Taiwan
*
Author to whom correspondence should be addressed.
Appl. Sci. 2023, 13(14), 8126; https://doi.org/10.3390/app13148126
Submission received: 19 May 2023 / Revised: 11 July 2023 / Accepted: 11 July 2023 / Published: 12 July 2023
(This article belongs to the Special Issue Advances in Geotechnologies in Infrastructure Engineering)
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Abstract

:
To investigate the effects of the properties of plastic fines on the pore water pressure generation characteristics of fine-grained soils during cyclic loadings, we used 29 sets of test data from the literature and prepared another 21 reconstituted specimens with different types of fines and fine contents (FCs) for cyclic triaxial testing. Two types of undisturbed soil specimens and three types of reconstituted soil specimens were also included for testing. The results indicated that under cyclic loading, the pore water pressure (PWP) ratios of clean sands increased slowly, stagnated, then finally accelerated until initial liquefaction, whereas those of the plastic soils containing fines with a plastic index (PI) value of >5 increased sharply in the initial stage. In addition, the cyclic stress ratio of specimens containing mudstone (PI = 12.4) and kaolinite (PI = 32.0) fines increased by 1.5–3.0 times more than non-plastic fines if the cyclic number chosen was 100. The range of the upper and lower limits of the PWP curves of the specimens with an FC of 30% were smaller that of the limits of the PWP curves of the specimens with an FC of 15%. The above results were further analyzed using a mathematical model. This paper systematically uses both the literature and laboratory test data to demonstrate that plastic fines and non-plastic fines have significantly different effects on water pressure generation under cyclic loading conditions, and a mathematical model also demonstrated the same trends. These findings are able to clarify previous unclear arguments. Thus, the model results developed in this study could also provide the field of engineering with a complete advanced calculation, requiring analysis only via software.

1. Introduction

Earthquakes frequently cause disasters worldwide. Located at the boundary between the Philippine Sea Plate and the Eurasian Plate, Taiwan experiences earthquakes frequently. Disasters such as building tilting and soil subsidence are therefore common. A primary cause of these disasters is soil liquefaction. Although many studies have explored liquefaction, few have accounted for water pressure generation characteristics, which serve as key indicators of liquefaction, plastic index (PI) values, and mathematical models. Studies have obtained inconsistent results regarding the effect of fines content (FC) on liquefaction. Because the properties of fines in silt and clay soils differ drastically, the present study added fines with different PI values to soils to understand their effect on the liquefaction resistance and pore water pressure (PWP) excitation of soils under cyclic loading. Thevanayagam et al. [1,2] demonstrated that, in soil structure (fabric), fines may significantly influence relevant dynamic and static properties. Seed et al. and Tokimatsu and Yoshimi [3,4] reported that, among field soils with the same N values obtained from the standard penetration test, those containing a higher FC exhibit greater resistance to liquefaction. Dobry et al. [5] used a centrifuge to measure the liquefaction, subsidence, and PWP of saturated clean Ottawa sand, focusing on partially drained conditions rather than undrained conditions and pore pressure dissipation. Some researchers have reported that when the FC of soil increases, the liquefaction resistance decreases. According to Hsiao et al. [6,7], the liquefaction resistance of a mixture can increase or decrease as the FC of the mixture increases in the laboratory.
Fines in soils can be divided into three categories: non-plastic fines, low-plasticity fines, and high-plasticity fines. Non-plastic and low-plasticity fines have been widely studied [8,9,10,11]. Belkhatir et al. [12] studied the effect of the grading characteristics of the liquefaction resistance of sand–silt mixtures in laboratory conditions. Regarding laboratory research, some papers [13,14,15,16,17] have investigated PWP in the liquefaction process by using different models and equipment. Gobbi et al. [18] conducted a series of monotonic and cyclic triaxial tests and resonant column tests to assess the packing configuration of coarse and fine particles in terms of the equivalent intergranular void ratio. Hsiao et al. and Porcino and Diano [6,7,19] performed extensive experiments to study the behavior of sand–silt mixtures under cyclic loading. Takch et al. [20] performed cyclic ring-shear tests on samples and reported that, when excess PWP (Ru) comprised 0.6–0.7 and the shear strain (γ) was 4–7%, Ru quickly reached 0.8 as γ continued to increase. Xenaki and Athanasopoulos [21] investigated the dynamic properties of clay soil and gravelly soil in an earthfill dam. Stamatopoulos et al. [22] analyzed the effect of preloading on liquefaction resistance by analyzing variables such as FCs, prestress ratios, densities, and vertical stresses.
Gratchev et al. [23] estimated shear resistance during the liquefaction of a mixture of clay soil and sandy soil and discovered that the addition of bentonite decreased the resistance the most. This finding may explain the occurrence of natural landslides. Kim et al. [24] and Tsai et al. [25] inspected the behavior and strength of clay soils both under cyclic loading and during earthquakes. Wijewickreme et al. [26] examined riverside soils, and their results indicated that the liquefaction resistance of the soil specimens with a PI of 34% and non-plastic specimens were the highest and lowest, respectively, and that the liquefaction resistances of the undisturbed specimens were stronger than that of the reconstituted specimens. Mominul et al. [27] collected samples of sandy soil near the Piyain River in Bangladesh and subjected mixtures with different contents of non-plastic silt to cyclic triaxial tests. Prakash and Sandoval [28] collected silt specimens with a PI value of 1.7 and added 5% and 10% kaolinite to increase the PI values to 2.6 and 3.4, respectively. The results of the axial strain test also revealed that the axial strain of the low-plasticity soils increased as the PI value increased. Guo and Prakash [29] and El Hosri et al. [30] investigated the correlation between PI values and liquefaction resistance. Kaya and Erken [31] compared specimens with different PI values (PI = 0–40). When the cyclic number (N) was 20, the strain of the specimen with a PI = NP reached approximately 2.8%, whereas that of the specimen with a PI of 40 was approximately 1.3%. When the SPT-N was 15, the Ru of the specimen with a PI = NP was 1.0, indicating initial liquefaction, whereas the excess PWP ratio (Ru) of the specimen with a PI of 40 was only 0.8. Accordingly, increases in PI were associated with increases in liquefaction resistance. Papadopoulou and Tika [32] and Azzouz et al. [33] also studied the effect of plasticity fines and clay on monotonic and cyclic behaviors in undrained tests. Nong et al. [34] demonstrated that the liquefaction resistance of sand increases with the increase in cyclic loading frequency using cyclic direct simple shear tests. Cabalar and Hasan [35] investigated the compressional behavior of various size/shape sand–clay mixtures with different pore fluids. Johari et al. [36] presented an analysis and the probabilistic modeling of liquefaction, which has also been applied to parameter quality. Although mixture theory is very complicated, Kokusho and Tsai et al. [37,38] applied it to a case study in the field.
Regarding PWP curves, Chiaradonna et al. [39] calculated the liquefaction potential of an integral index using PWP, a method that can also be used to calculate LSN. Chiaradonna et al. [40,41] also applied PWP in field research and proposed that the β value in the model proposed by Booker et al. [42] was correlated with the FC, relative density (Dr), and cyclic stress ratio (CSR). Zhang et al. [43] proposed a PWP model applicable for randomly distributed fibers. Porcino and Diano [19] discovered that when the FC of a sand–silt mixture was less than 20%, the β value in the model proposed by Booker et al. [42] ranged from 0.6 to 1.0, whereas when the FC was less than 35%, the β value varied considerably, ranging from 0.69 to 1.41. Li et al. [44] used shear strain to obtain an ascending PWP curve. El Hosdri et al. [30] subjected clean sand and silty clay soils to cyclic triaxial tests and discovered that the PWP generation mode of non-plastic sandy soils differed from that of plastic silty clay soils. Using a shaking table, Kalatehjari and Bolarinwa [45] demonstrated that samples mixed with lower clay content produced the highest excess PWP, with higher tendencies of contraction and liquefaction properties. However, soil samples with a higher percentage of clay yielded the lowest PWP, with softening and dilative properties. Other researchers [46,47] have also investigated PWP in relation to layered sites and waste materials, such as fly ash and tire rubber.
Based on the discussion of the above literature, the past researchers have not reached an agreement regarding plastic and non-plastic fine specimens and the rising trend of pore water pressure under undrained cyclic loading. In addition, specimens cannot successfully complete an entire loading process, mostly likely due to smaller cyclic stress ratios. The purpose of the present study was to collect the results of experiments performed on fines with and without plasticity from the relevant literature. The normalized relationship between the PWP ratio and CSR was used to assess the effect of plasticity on PWP generation, and model analysis was performed in order to obtain the model parameters. To expand upon previous research, argillaceous soils were mixed with fines with different levels of plasticity and were subjected to cyclic triaxial tests. According to Høeg et al. [48], specimen preparation methods can affect experimental results. Therefore, the specimens used in the cyclic triaxial tests were all prepared using the wet tamping method, enabling a comparison between the experimental results and results published in the relevant literature. Fines with different PI values (i.e., Liugui sand from Kaohsiung, Taiwan; Mudstone from Tainan, Taiwan; and Kaolinite) were added to the specimens to investigate the effect of the addition of fines with different PI values on the liquefaction resistance and PWP generation modes of the soil specimens under dynamic loading.

2. Study Methods and Tests Materials

2.1. Study Methods

Figure 1 shows a flowchart of the step-by-step interpretation process of all the usable data obtained from the experimental works found in the literature. After carefully collecting relevant experimental data from the past literature, it was found that many papers focused only on the study of non-plastic and low-plastic fine soils, while there was a lack of research systematically discussing different PIs and fine materials. There are some papers on the rising trend of the pore water pressure of the test specimen that have reported high PI fines under dynamic loadings [31,32]. Because the CSR applied by the dynamic load was small, some of the specimens were not able to achieve the initial liquefaction, and the Ru was 0.85–0.9 when the process ended. Through inspective observation, the cyclical number was normalized, and the analysis results were collected if they met the preliminary requirements. Table 1 shows the detailed description of the databases used in this study. This paper compiled four papers with a total of 29 sample sets, including two groups of undisturbed and two groups of reconstituted samples. Moreover, a total of 29 sets of new, reconstituted samples were analyzed separately. The plastic PI and fine content of the fine material are also provided in the table.

2.2. The Model of Booker et al. (1976)

The model proposed by Booker et al. [42] is an empirical model derived from a series of experiments that were used to predict changes in the excess PWP ratio (Ru) under cyclic loading. This can be expressed as shown in Equation (1):
R u = 2 π sin − 1 ⁡ N N L 1 2 β
where N is the cyclic number, NL is the cyclic number required to reach initial liquefaction, Ru is the ratio of excess PWP to the effective confining pressure, and β is the parameter of the curve of the model. In the model developed by Booker et al. [42], β is the key parameter that influences the curve of the model. Towhata [49] also described β as an empirical parameter that is dependent on the soil type, effective stress, or the rate of cyclic loadings [40,50]. Figure 2 presents curves mapped according to different β values. When β was 0.45–2.0, the curves corresponded more closely to the three stages of the WP excitation of non-plastic sandy soils (i.e., the initial excitation stage, stable excitation stage, and the accelerated excitation stage) [6,7,19]. When β was 20–250, the curves corresponded to the PWP excitation behavior of plastic soils described by El Hosdri et al. [30]. The PWP increased sharply in the initial stage and leveled off until the initial liquefaction. Of the various models of PWP excitation under dynamic loading, the mathematical model of PWP developed by Zhang et al. [43] can be used to predict fiber content in sandy soils. In contrast to the model developed by Booker et al., the model proposed by Zhang et al. [43] accounts for factors such as Dr, FC, FL, and CSR and integrates cubic curve functions. Chiaradonna et al. [40,41] identified a polynomial relationship between Ru and normalized damage. Li et al. [44] introduced a general logarithmic model. Polito et al. [51] demonstrated that Dr, FC, and CSR must be considered when calculating β values. Overall, although the model developed by Booker et al. [42] is relatively easy to understand, it may be insufficient for the analysis of multiple parameters.

2.3. Test Materials

In this study, cyclic triaxial testing was performed on Liugui sandy soil specimens from Kaohsiung, Taiwan. A gradation curve of Liugui coarse aggregates was developed. The applied particle size distribution curve is illustrated in Figure 3. Subsequently, Liugui sand from Kaohsiung, mudstone from Tainan, Taiwan, and kaolinite were added at 15% and 30% by weight to the soils as a replacement for the coarse aggregate. All the experimental results were compiled and analyzed using the mathematical model proposed by Booker et al. [42]. First, a sieve analysis was conducted on the sandy soil specimens retrieved from Liugui District, Kaoshiung. The mudstone was collected from Tainan. According to Hsiao and Hsieh [52], mudstone was first discovered in Renwu District, Tainan, which is located in the southernmost region Taiwan. The specimens were all produced with a fixed dry soil unit weight of γd = 16.58 kN/m3. The tests conducted are listed as follows: (1) ASTM D422 for grain size distribution curve [53]; ASTM D854 for specific gravity test [53]; ASTM D423, D424, and D4318 for Atterberg limits [53]; ASTM D2487 for the Unified Soil Classification System (USCS); ASTM D2216 for soil moisture content [53]; and ASTM D4253 and ASTM 4254 for maximum and minimum density [53].
The soil gradation parameters and general physical properties of interest are listed in Table 2. When γd was 16.58 kN/m3, the specimens with FCs of 0%, 15%, and 30% had relative densities of 14.7%, 10.2%, and 19.7%, respectively. The appearances of the three types of fines are depicted in Figure 4. The Atterberg limits of the fines and the USCS classification results are presented in Table 3. The kaolinite had the highest PI value (32), followed by the mudstone (12.4) and Liugui sand (5.7). The plasticity data, namely the Atterberg limits, PI values, and liquid limits, are presented in Figure 5. The USCS results of the three fines were all above the A line on the Casagrande plasticity chart. The USCS classifications of Liugui sand, Mudstone fines, and Kaolinite were CL-ML, CL, and CH with respect to the fine contents.
A British standard geotechnical digital system (the GDS Enterprise Level Dynamic Triaxial Testing System) was used to perform cyclic triaxial tests on the soil specimens. Loading was repeatedly applied through load control, and the PWPs within the specimens were measured simultaneously during the tests. The tests performed were triaxial consolidated undrained tests. The required amounts of the test soils were determined according to the grain size gradation curves, and the soil specimens were each divided into five groups for mixing. After the base of the triaxial chamber was wiped clean and a porous stone and filter paper were placed on the top of the sample base, the rubber mold used to hold the specimens and the split mold were placed on the base. Two O-rings were used to set the rubber mold, and expansion rings were used to lock the split mold to the outside of the rubber mold. The specimens were reconstituted through wet tamping. The five samples of sandy soils were mixed with water in concentrations of 8–14% according to their distinct properties. The specimens were tamped into five layers. Subsequently, a scraper was used to scrape vertically and horizontally interlaced lines of 0.25 mm in length on the surface of each layer to avoid weak, discontinuous surfaces.
After the five layers were tamped, the filter paper and porous stone were placed on the tamped surfaces of the soil specimens, and a piece of transparent acrylic was used to cover the porous stone. Eventually, each specimen was wrapped in the rubber mold and fixed using the two O-rings, and the initial preparation of the specimen was thus completed. Subsequently, air extraction equipment was used to detect holes in the rubber mold. A container with a pressure gauge was filled with water, and a negative pressure of 10–12 kPa was applied within the container. The tubes of the container were connected to the upper part of the specimen in order to extract as much air from the specimen as possible, enabling the specimen to be saturated when placed in the triaxial chamber. The average diameter and height of the specimens were set to approximately 7.1 and 14.2 cm, respectively. After the specimens were prepared, carbon dioxide was injected at the bottom of each specimen, and the upper valve of the specimen was opened to discharge excess air. The injection process took approximately 30 min. The injection rate was maintained at an appropriate level to ensure that the flushing mold would not expand.
Vylastic sleeves, the inner walls of which were covered in an electrical insulating compound to prevent liquid from entering, were used to place the specimen in the triaxial chamber. The screws in the top cover of the triaxial chamber were tightened, and the chamber was fixed to the machine. Subsequently, computer software was used to control the loading process. An axial load of 0.005 kN was repeatedly applied until the Vylastic sleeve and the top cover of the chamber fit together. Water was then poured into the triaxial chamber until the water level reached 90% of the height of the chamber. An air compressor was used to apply the confining stress of the specimen in the remaining space in the chamber. Thereafter, the de-aired water was injected at the bottom of the specimen. This injection process took 20–40 min depending on the properties of the specimens; if the added fines were plastic soils, less time was required. Before each specimen was compressed, the saturation state of the soils in the specimen was determined. The process of measuring the saturation state involved increasing the confining pressure to 350 kPa and maintaining the WP. A total of 10 min later, when the Skempton PWP parameter (B) was stable, the saturation value was obtained. In this study, a B value of greater than 0.96 indicated a saturated state. When the specimen was compressed, the confining pressure was set to 390 kPa, and the reverse WP was 290 kPa. The drain valve at the bottom of the specimen was opened. The compression was completed when the water draining rate was less than 1 mm3/min. The time required for compression was also related to the soil properties. The compression of the pure sandy soil specimens required approximately 20–30 min, whereas that of the specimens with higher PI values required 1–4 h. After the compression process was completed, a cyclic triaxial consolidated undrained compression test was performed. Before the tests, the valves (except for the WP gauge) were closed tightly. Computer software was used for dynamic loading. The loading was performed in sinusoidal stress waves of 1 Hz. Variables, including the amplitude, soil stiffness, and cyclic number, were adjusted. When the set target was reached, the machine automatically stopped cyclic loading. The computer automatically read and recorded all the values involved in the experimental process for subsequent analysis.

3. Results and Discussion

3.1. Normalization of Experimental Results from the Literature and Model Analysis

First, the experimental results reported by Hsiao et al. [6,7] were inspected. The experiment of Hsiao et al. was conducted using clean sand obtained during a sieve analysis of Liugui sandy soils from Kaohsiung. The initial soil specimens did not contain fines. Instead, fines were added to obtain specimens with FCs of 0–60%. The specimens with different FCs were controlled at the same relative density (Dr), void ratio (e), and peak deviator stress (290 kPa) to facilitate comparisons. The effect of low-plasticity fines on WP excitation was reflected in the PWP data. Furthermore, the changes in PWP in the plastic soils under repeated loading were compared with the results of the studies conducted by Sanin [54], Derakhshandi et al. [55], and Kaya and Erken [31], in which different PI values, FCs, confining pressures, strain controls, and CSR were applied. The present study analyzed the characteristics and differences in the PWP excitation of plastic soils according to the mathematical model developed by Booker et al. [42]. The experimental results and the model results were compared to obtain the WP range and model parameters of plastic and non-plastic soils. Finally, the reconstituted soil specimens produced in the present study were compared to those described in the literature to investigate the effect of plastic fines on WP excitation.

3.1.1. Low-Plasticity Soils

To assess the PWP excitation mode of low-plasticity sandy soils, the experimental results reported by Hsiao et al. [7] were first inspected. Clean sands obtained through a sieve analysis of sandy Liugui soil from Kaohsiung were used in the experiment. Fines were added to the clean sand to obtain specimens with FCs of 0–60%, and the void ratio, relative density, and peak deviator stress were controlled at 0.589, 30%, and 270 kPa, respectively, to facilitate comparison. The effects of plastic fines on WP excitation were assessed according to the PWP data. The experimental results are given in Figure 6. The focus of the present study was the increase in the PWP of plastic sandy soils. As indicated in Figure 6a–c, the PWP of the low-plasticity sandy soils increased in a fixed pattern under different conditions, and the excitation occurred in three stages. Therefore, in the present study, 15 sets of data were compiled, the upper and lower limits were identified, and the PWP excitation range of low-plasticity sandy soils in cyclic triaxial tests was assessed, as shown in Figure 6d. Because numerous sets of data were included, the ranges of the upper limit and the lower limit were large.
After the PWP excitation range of the low-plasticity sandy soils in the cyclic triaxial tests was mapped, the WP curves of the non-plastic soils were illustrated. Subsequently, the experimental curves of the low-plasticity sandy soils and non-plastic soils were compared to the curves produced using the model developed by Booker et al. [42] to identify which β value corresponded most closely to the excitation range in the experiment. The calculation revealed that when β was 2.0, the curve produced by the model was closest to the experimental curve at the upper limit, indicating that the model results were consistent with the experimental results. When β was 0.45, the curve produced by the model was closest to the experimental curve at the lower limit, which also indicated that the model results were consistent with the experimental results. Accordingly, when low-plasticity sandy soils are tested, the β value in the model developed by Booker et al. [42] should be between 0.45 and 2.0 (Figure 7).

3.1.2. Plastic Soils

The results of repeated triaxial tests on soil plasticity performed in the studies by Kaya and Erken [31], Sanin [54], and Derakhshandi et al. [55] were used to assess the PWP excitation modes of plastic soils. In the three aforementioned studies, different PI values, FCs, confining pressures, strain controls, and CSRs were used. The present study inspected the characteristics and differences in the PWP excitation of plastic soils. According to the experimental results, the PWP of the non-plastic sandy soils rapidly reached the level of initial liquefaction, suggesting that the liquefaction resistance of the soils was relatively low. However, when the cyclic number exceeded 20, the high-plasticity specimens did not reach initial liquefaction, indicating that the liquefaction resistance increased with increasing plasticity. The PWP data of plastic specimens approaching the initial liquefaction obtained from the three studies were normalized. If initial liquefaction was not reached, the cyclic number was adjusted accordingly until initial liquefaction was reached. First, to examine the behavior of low-plasticity soils under repeated loading, Sanin [54] collected undisturbed soil specimens from the Fraser River in Canada and subjected them to cyclic triaxial testing. The specimens were silty sandy soils with PI values of 7. The water contents of specimens FRS-100-017, FRS-100-020, FRS-100-029, FRS-300-015, FRS-300-017, and FRS-400-015 were 36.8%, 36.2%, 38.7%, 40.3%, 40.1%, and 40.1%, respectively, and their initial void ratios were 0.990, 0.974, 1.041, 1.083, 1.078, and 1.078, respectively. The soils with higher water contents had higher void ratios. The numbers 100 and 300 in the names of the specimens were used to distinguish specimens with an experimental compaction stress of approximately 100 and 300 kPa, respectively. Different repeated shear ratios and confining stresses were used in the experiments. The PWP data were consistent with the WP excitation mode of plastic soils. The Ru and normalized N/NL values are shown in Figure 8a. To explore the effect of plastic fines on changes in PWP during vibration, Derakhshandi et al. [55] subjected samples of mixed Monterey soils and kaolinite to cyclic triaxial tests. Kaolinite fines were added at concentrations of 10%, 20%, and 30% by weight. The Gs, LL, PL, and PI values of the kaolinite were 2.58, 41.7%, 26.2%, and 15.5, respectively. The grain size of 70% of the kaolinite fines was smaller than 5 μm, and the USCS classification of the kaolinite was CL/ML. Shear strains of 0.1% and 0.3% were used. The Ru and normalized N/NL values are mapped in Figure 8b.
To investigate the stress–strain and PWP behavior of soils in Adaparzari, Turkey during earthquakes, Kaya and Erken [24] collected undisturbed soil specimens from ten boreholes in eight different locations in Adaparzari and subjected them to repeated triaxial tests. The failure criterion was set to a strain of 2.5% or an Ru value of 1. The 10 specimens included non-plastic soils with a PI = NP and plastic soils with a PI of 40. The experimental results revealed the effects of plastic fines on PWP at roughly the same CSR. The Ru and normalized N/NL values are mapped in Figure 8c. The basic parameters and soil classifications of the four thin-tube specimens were as follows: (1) T5-1 (thin tube number): PI = 40%, CSR = 0.40, and CH; (2) T6-3 (thin tube number): PI = 39%, CSR = 0.41, and CH; (3) S6-1 (thin tube number): PI = 23%, CSR = 0.42, and CH; and (4) T7-1 (thin tube number): PI = 19%, T7-1, CSR = 0.40, and CL. The curve shifted toward the lower right as the PI value decreased. Figure 8a–c was compiled into 8d, in which the PWP ratios and normalized N/NL¬ values are mapped for comparison. As indicated in the normalized graph, the increase in PWP was consistent with the WP generation mode of plastic soils. The curves increased sharply in the initial stage and leveled off until initial liquefaction, and the curves corresponding to higher PI values shifted more toward the upper left corner; that is, the curve corresponding to the specimen with a PI of 40 increased more sharply in the initial excitation stage.
After the WP generation range of plastic soils was obtained, the model developed by Booker et al. [42] and the experimental results from the literature presented in Figure 8 were analyzed. The adjusted β values were compared with the range obtained from the experimental results. When β was 250, the curve produced by the model was closest to the experimental curve at the upper limit; however, when β was 20, the curve produced by the model was closest to the experimental curve at the lower limit. Therefore, when testing soil specimens containing plastic fines, the β value in the model developed by Booker et al. [42] should be between 20 and 250 (Figure 9).

3.2. Experimental Results and Analysis

3.2.1. Results of Cyclic Triaxial Tests

To assess the feasibility of applying the aforementioned results from the literature in practical settings, a series of tests were performed on the specimens of sandy soil containing fines with three different PI values (i.e., Liugui fines from Kaohsiung, mudstone, and kaolinite). The fines were added at 15% and 30% by weight to replace the same weights of the original soils. The liquefaction resistance and PWP curves of the non-plastic, low-plasticity, and high-plasticity soils were obtained from the experimental results. In the experiment, kaolinite (PI = 32), mudstone (PI = 12.4), and Liugui fines (PI = 5.7) were added to the Kaohsiung Liugui sandy soils at 15% and 30% by weight to replace the same weights of the original soils. Reconstituted specimens were produced through wet tamping and with a fixed dry soil unit weight (γd) of 16.57 kN/m3. The repeated triaxial tests were conducted under the same effective confining pressure (100 kPa). Initial liquefaction was reached when the PWP ratio (Ru) reached 1.0. Table 4 lists the results of the experiments performed using different specimens. Sand-0x is used to denote clean sand specimens, and S, M, and K are used to denote specimens containing Liugui fines, mudstone, and Kaolin, respectively. FC15 and FC30 are used to denote weight percentages of 15% and 30%, respectively. The cyclic numbers (No.) corresponding to each excess PWP ratio (Ru) are also listed in Table 4.
Figure 10 plots the CSRs against the cyclic numbers from Table 3 (Ru = 1.0). As indicated in the figure, regardless of the types of fines in the specimens, when the added fines were all plastic fines, the curves of the specimens with FCs of 30% were above those of the specimens with FCs of 15%. This suggests that increasing the plastic FC of soil can strengthen its liquefaction resistance. Among the specimens with FCs of 15%, specimens containing mudstone and Liugui fines had corresponding cyclic resistance curves similar to the curves of the clean sand specimens. By contrast, the curves of the specimens containing kaolinite fines shifted significantly upward. Therefore, when the fines had low PI values and the FCs of the specimens were low, the fines in the specimens did not effectively increase the liquefaction resistance of the specimens. However, when the fines had high PI values, they increased the liquefaction resistance of the specimens.
As seen in the figure, the curves of the specimens shifted upward as the PI values of the fines increased. Under the same cyclic number, the pure sandy soils and kaolinite required the lowest and highest cyclic shear ratios, respectively, to reach initial liquefaction. This suggests that the liquefaction resistance is proportional to the PI value of soils. The liquefaction resistance of the specimens varied widely, and the differences in the viscosity of the specimens could be easily noticed during the reconstitution process. In addition, as indicated in Figure 10, when the mudstone FC was 30% and the kaolinite FC was 15% or 30%, the CSR must reach 0.30 or higher to reach initial liquefaction, or if the CSR was 0.24, the initial cyclic number had to be at least 168. When the mudstone FC was 15% and the Liugui FC was 15% or 30%, the CSR had to be 0.15–0.25.
Kim et al. [24] conducted repeated triaxial tests on clay soils. Regardless of whether the cyclic loading frequency was 0.1 or 0.01 Hz, when the cyclic number was between 3 and 100 and the required CSR was approximately 0.26–0.41, the specimen demonstrated higher liquefaction resistance. Kaya and Erken [31] used Shelby tubes to perform cyclic triaxial tests on Adapazari soil specimens. For specimens with high FCs, a CSR of approximately 0.360–0.380 was applied. Nevertheless, the specimen with a PI value of 33 had a PWP ratio of only 0.5 at the end of the tests, and the ratio seemed unlikely to increase. For specimens with low FCs, a CSR of approximately 0.40–0.42 was used. Among specimens with PI values of 19–40, the specimen with a PI value of 36 had a PWP ratio of only 0.5 at the end of the tests, whereas the specimen with a PI value of 39 had a PWP ratio of approximately 0.85. Wijewickreme et al. [26] collected undisturbed specimens from a conventional mud-rotary drill hole in British Columbia, Canada through fixed-piston tube sampling. The specimen with a PI value of 34 had a cyclic number between 1 and 100 when the CSR was 0.25–0.39, whereas the specimens with PI values of 4–7 had cyclic numbers between 1 and 100 when the CSR was approximately 0.14–0.28. The results in the literature are thus similar to the results of the experiments performed in the present study. These findings indicate that the data in Figure 10 are reasonable. The specimens with a Liugui FC of 15% or a mudstone FC of 15% were able to reach initial liquefaction when the CSR was lower than 0.30, but the specimens containing kaolinite fines were only able to reach initial liquefaction when the CSR was higher than 0.30, indicating that the PI values of the soils greatly affected their liquefaction resistance. In addition, the cyclic stress ratio of specimen containing mudstone (PI = 12.4) and kaolinite (PI = 32.0) fines increased by 1.5–3.0 times over the non-plastic fines if the cyclic number chosen was 100. Even though the cyclic number was limited to 10–20 when an earthquake occurred, this study is still important for sand–silt–clay mixtures with high cyclic numbers.
Figure 11 illustrates the process of liquefaction as the PWPs of the specimens increased during repeated triaxial testing. The test results of the three clean sand specimens are presented in Figure 11a. According to Table 4, the three specimens required a cyclic number of ≤92 to reach initial liquefaction. Therefore, a cyclic number of 100 was used in the analysis. The CSRs of the three specimens were low (0.14, 0.18, and 0.22, respectively). The WP excitation processes of the specimens each consisted of an initial excitation stage, a stable excitation stage, and an accelerated excitation stage. Figure 11b illustrates the normalized relationship between the PWP ratios and cyclic numbers of the specimens with Liugui FCs of 15% and 30%. The curves of S-FC15-01, S-FC15-02, and S-FC15-03 in the initial stage were shifted to the right. As indicated in Table 4, when Ru was 0.5, the cyclic numbers of S-FC15-01, S-FC15-02, and S-FC15-03 were 10, 7, and 5, respectively, which were all greater than the cyclic numbers of the specimens with FCs of 30%. The cyclic numbers increased until Ru reached 0.9, at which point the cyclic numbers of some of the specimens with FCs of 30% were higher. When Ru was 1.0, the cyclic numbers of the specimens with FCs of 30% were all higher. Figure 11c presents the results of the tests performed on the specimens containing mudstone fines. As in the tests performed on the specimens containing Liugui fines, the curves of M-FC15-01, M-FC15-02, and M-FC15-03 in the initial stage were shifted to the right. As indicated in Table 3, when Ru was 0.5, the cyclic numbers of M-FC15-01, M-FC15-02, and M-FC15-03 were 17, 8, and 4, respectively, all of which were greater than the cyclic numbers of specimens with FCs of 30%. When Ru was 1.0, the cyclic numbers of specimens with FCs of 30% were all higher. The required cyclic number of M-FC30-01 and M-FC15-01 were 168 and 83, respectively, and the cyclic numbers of M-FC30-02 and M-FC15-02 were similar.
Figure 11d presents the results of the tests performed on the six specimens containing kaolinite fines. The results in Table 3 indicate that the effects of the fines were not obvious in the initial stage. Nevertheless, when Ru was 0.5, the cyclic numbers of the specimens with FCs of 30% were greater and remained so until Ru reached 1.0. Furthermore, the liquefaction resistance and required cyclic numbers of the specimens with kaolinite FCs of 30% were considerably higher than those of the other specimens, suggesting that kaolinite is extremely resistant to liquefaction. El Hosdri et al. [30] mentioned that in repeated triaxial tests, plastic and non-plastic specimens exhibit different PWP excitation behaviors. Therefore, four types of specimens were used in the present study. The first type was clean Liugui sand. The PWPs of the non-plastic sandy soils under dynamic loading were obtained from the results of the repeated triaxial tests, whereas those of specimens containing Liugui fines, mudstone, and kaolinite were obtained from the results of testing low-plasticity soils to high-plasticity soils. The results of the tests performed on Sand-02, S-FC30-02, M-FC30-01, and K-FC30-01 are compiled in Figure 12. As indicated in the figure, the PWP excitation behavior of the non-plastic sandy soils (FC = 0%) differed considerably from those of the specimens with FCs of 30%, which was consistent with the results reported by El Hosdri et al. [30]. Wijewickreme et al. [26] used a direct simple shear device to perform repeated loading tests. When the CSR was 0.2, the cyclic numbers were 0–5, and the PWP ratio reached 0.7–0.8. When the CSR was 0.15, the cyclic numbers were 35–40, and the PWP ratio decreased to 0.4–0.6. By performing strain-controlled cyclic triaxial tests, Derakhshandi et al. [55] discovered that when the cyclic number of specimens with an FC 20% was 50, the PWP ratio reached 0.56.
As indicated in Figure 11, each specimen had a different CSR and required a different cyclic number to reach initial liquefaction. Therefore, the figure reveals the distinct trends in the PWP of each specimen. However, the complete WP excitation behavior of all the specimens could not be determined. The data from all the tests performed in the present study were therefore normalized. The PWP ratios (Ru) and cyclic ratios (N/NL) are compiled in Figure 13. Wang et al. [56] indicated that the bentonite content in the constituted specimens increased the excess pore water pressure at a slower rate, and the total excess pore water pressure decreased at the end of the cyclic loadings. One of the reasons for this was that the specimen with the higher plasticity index had higher compressibility, resulting in less excess pore water pressure under cyclic loading in undrained conditions. The difference between the MRV silt and specimens modified with bentonite might be related to soil permeability and drainage. The results of the tests performed on the specimens containing the three types of fines were examined separately. The specimens with Liugui FCs of 0%, 15%, and 30% were analyzed first. The PWP curves of Sand-01, Sand-02, and Sand-03 with a CSR of 0.14–0.22 are presented in Figure 13a. The WP curves of the pure sand specimens were sometimes higher or lower than each other. The normalized relationship between the PWP ratios and cyclic numbers of the specimens with a Liugui FC of 15% is illustrated in Figure 13b. The increasing trends of the nine curves were similar. The curves of K-FC15%-01, K-FC15%-02, and K-FC15%-03 increased the fastest. The remaining six curves of the specimens containing mudstone and Liugui fines were comparable. Figure 13c illustrates the normalized relationship between the PWP ratios and cyclic numbers of the specimens with plastic FCs of 30%. The curves were denser; however, the curves of the specimens containing kaolinite fines increased the fastest. Figure 13d illustrates the normalized relationship between the PWP ratios and cyclic numbers of the clean sands and specimens containing fines with PI values >5.7. The data of the cleans sand specimens differed significantly from those of the specimens with PI values >5.7.

3.2.2. Model Analysis of the Experimental Results

As mentioned previously, according to the experimental results reported by Hsiao et al. [7], the β values of non-plastic sandy soils were 2 and 0.45. Figure 14 presents the PWP data of Sand-01, Sand-02, and Sand-03. The results in Figure 14 were compared with those obtained using the model developed by Booker et al. [42]. The PWP data of the Liugui specimens were consistent with the results produced by the model. Almost all the PWP values were within the model range. Accordingly, when the PWPs of nonplastic sandy soil specimens are examined, the β value in the model developed by Booker et al. [42] should be 0.45–2, which corresponds to the results in Figure 7.
In Figure 15a, the PWPs of specimens with plastic FCs of 15% are compared with those obtained using the model developed by Booker et al. [42]. The PWP excitation speed of the specimens with plastic FCs of 15%, particularly those containing fines with low PI values, was slower in the initial stage. Most of the PWP values in the initial stages were not within the designated range of the model; only those in the later stage fell within the designated range. A possible reason for this is that the plastic fines only accounted for 15% of the specimens, and the fines had lower PI values. Therefore, the model might be less applicable to soils with low PI values or FCs. A comparison between the PWPs of the specimens with FCs of 30% and the range of the model are presented in Figure 15b. The normalized results of the nine sets of data indicate that different types of fines exert different effects on the WP excitation trends of plastic soils. The curves of the specimens with FCs of 30% increased faster than those of the specimens with FCs of 15%. Most of the PWP curves increased sharply in the initial stage; only the WP values of a few specimens were not within the range of the model. The PWP curves were generally similar to the curve produced by the model. Therefore, the results of the present study suggest that when plastic soils with high FCs are inspected, the β parameter in the model developed by Booker et al. [42] should be set at 20 to 250, which is consistent with the results in Figure 8.

4. Conclusions

The previous literature demonstrates that researchers still have no agreement regarding plastic and non-plastic fine specimens and the rising trend of pore water pressure under cyclic loading. In addition, specimens cannot successfully complete the entire loading process, most likely due to a smaller cyclic stress ratio. On the basis of the literature review and the results of the cyclic triaxial tests, the following conclusions were drawn. The experimental results accompanied with the reports by Hsiao et al. (2015) [7], Sanin (2010) [54], Derakhshandi et al. (2008) [55], and Kaya and Erken (2015) [31], whose studies included two types of undisturbed soil specimens and three types of reconstituted soil specimens, were normalized. The results indicated that under dynamic loading, the PWP curves of clean sands increased slowly, stagnated, and finally increased until initial liquefaction, whereas the curves of plastic soil containing fines with a PI value of >7 increased sharply in the initial stage. This difference may be related to soil permeability or drainage. The changes in the liquefaction resistance of the soils containing Liugui fines were minimal; however, the CSRs of the soils containing mudstone and kaolinite fines increased considerably. The PWP data were consistent with those reported in the literature. The upper and lower limits of the curves of the clean sand were close to each other, but the upper and lower limits of the curves of specimens with FCs of 30% were closer to each other than to those of the curves of specimens with FCs of 15%. Finally, all the results were reanalyzed using the model developed by Booker et al. (1976) [42], according to which the β parameters for plastic and non-plastic soils should be 20–250 and 0.45–2, respectively. This paper systematically used both literature and laboratory test data sets to demonstrate that plastic fines and non-plastic fines display significant differences in water pressure generation under cyclic loading conditions, and a mathematical model also proved the same trend. These findings can clarify previously unclear arguments.

Author Contributions

D.-H.H., project administration, experimental plan, supervision, writing—review and editing; C.-C.L., experimental work and analysis, validation, writing—original draft preparation. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

All the data are available upon request.

Acknowledgments

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Flowchart of the step-by-step interpretation process involving experimental works and the utilization of research and experimental data from the literature.
Figure 1. Flowchart of the step-by-step interpretation process involving experimental works and the utilization of research and experimental data from the literature.
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Figure 2. Curves mapped according to different β values based on the model proposed by Booker et al. (1976) [42].
Figure 2. Curves mapped according to different β values based on the model proposed by Booker et al. (1976) [42].
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Figure 3. Particle size gradation curve of soils with different fine contents.
Figure 3. Particle size gradation curve of soils with different fine contents.
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Figure 4. The appearances of the three types of fines. (a) Liugui sand, (b) mudstone, (c) kaolinite.
Figure 4. The appearances of the three types of fines. (a) Liugui sand, (b) mudstone, (c) kaolinite.
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Figure 5. Plasticity data, plastic index, and liquid limits of the three fines.
Figure 5. Plasticity data, plastic index, and liquid limits of the three fines.
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Figure 6. PWP ratios with their respective to N/NL contents based on the test results of Hsiao et al. [5] for low-plasticity soils. (a) Same void ratio 0.582, (b) same deviator stress 270 kPa, (c) same relative density 30%. (d) Ru and normalized N/NL values are mapped between two color lines for low plastic soils.
Figure 6. PWP ratios with their respective to N/NL contents based on the test results of Hsiao et al. [5] for low-plasticity soils. (a) Same void ratio 0.582, (b) same deviator stress 270 kPa, (c) same relative density 30%. (d) Ru and normalized N/NL values are mapped between two color lines for low plastic soils.
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Figure 7. The β value in the model developed by Booker et al. [42] should be between 0.45 and 2.0 in comparison with experimental data between red and blue solid lines.
Figure 7. The β value in the model developed by Booker et al. [42] should be between 0.45 and 2.0 in comparison with experimental data between red and blue solid lines.
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Figure 8. PWP ratios and normalized N/NL values from previous works are shown and redrawn. (a) Sanin (2010) [54], (b) Derakhshandi et al. (2008) [55], (c) Kaya and Erken (2015) [31]. (d) Ru and normalized N/NL values are plotted between two color lines for plastic soils.
Figure 8. PWP ratios and normalized N/NL values from previous works are shown and redrawn. (a) Sanin (2010) [54], (b) Derakhshandi et al. (2008) [55], (c) Kaya and Erken (2015) [31]. (d) Ru and normalized N/NL values are plotted between two color lines for plastic soils.
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Figure 9. The β value in the model developed by Booker et al. [42] should be between 20 and 250 with comparison with experimental data between red and blue soild lines.
Figure 9. The β value in the model developed by Booker et al. [42] should be between 20 and 250 with comparison with experimental data between red and blue soild lines.
Applsci 13 08126 g009
Applsci 13 08126 g010 550
Figure 10. CSRs plotted against the cyclic numbers from the data in Table 3 (Ru = 1.0).
Figure 10. CSRs plotted against the cyclic numbers from the data in Table 3 (Ru = 1.0).
Applsci 13 08126 g010
Applsci 13 08126 g011 550
Figure 11. The process of liquefaction as the PWPs of the specimens increased during cyclic triaxial testing. (a) Clean sands. (b) Liugui fines. (c) Mudstone fines. (d) Kaolinite fines.
Figure 11. The process of liquefaction as the PWPs of the specimens increased during cyclic triaxial testing. (a) Clean sands. (b) Liugui fines. (c) Mudstone fines. (d) Kaolinite fines.
Applsci 13 08126 g011
Applsci 13 08126 g012 550
Figure 12. The process of liquefaction as the PWPs of the specimens increased during cyclic triaxial testing for non-plastic and plastic soils.
Figure 12. The process of liquefaction as the PWPs of the specimens increased during cyclic triaxial testing for non-plastic and plastic soils.
Applsci 13 08126 g012
Applsci 13 08126 g013 550
Figure 13. PWP ratios and normalized N/NL values are compared for different fine contents. (a) Clean sands. (b) FC = 15%. (c) FC = 30%. (d) Effect of PI on the curve.
Figure 13. PWP ratios and normalized N/NL values are compared for different fine contents. (a) Clean sands. (b) FC = 15%. (c) FC = 30%. (d) Effect of PI on the curve.
Applsci 13 08126 g013
Applsci 13 08126 g014 550
Figure 14. Test results in the article were analyzed using the Booker et al. (1976) [42] model.
Figure 14. Test results in the article were analyzed using the Booker et al. (1976) [42] model.
Applsci 13 08126 g014
Applsci 13 08126 g015 550
Figure 15. Test results in the article were analyzed using the Booker et al. (1976) [42] model for different fine contents.
Figure 15. Test results in the article were analyzed using the Booker et al. (1976) [42] model for different fine contents.
Applsci 13 08126 g015
Table
Table 1. Detained description of the databases used in the study.
Table 1. Detained description of the databases used in the study.
SoilsFinesUndisturbed/
Reconstituted Sample		Set for TestingFC (%)/PI (Fines)Refs.
Fraser River, Canada-Undisturbed6PI = 7%Sanin 2015 [49]
Monterey soilsKaoliniteReconstituted4PI = 15%, FC = 10, 20%Derakhandi, et al., 2008 [50]
Adaparzari, Turkey-Undisturbed4PI = 19, 23, 39, 40%Kaya and Erken, 2015 [31]
Liugui sands, TaiwanLiugui finesReconstituted6Same void ratio 0.582, FC = 0, 15, 30, 40, 50, 60% (PI = 0, 3.1, 5.0, 5.9, 6.7, 7.0)Hsaio, et al., 2015 [7]
Liugui sands, TaiwanLiugui finesReconstituted6Same deviate stress 270 kPa, FC = 0, 15, 30, 40, 50, 60% (PI = 0, 3.1, 5.0, 5.9, 6.7, 7.0)Hsaio, et al., 2015 [7]
Liugui sands, TaiwanLiugui finesReconstituted3Same relative density, FC = 0, 15, 30% (PI = 0, 3.1, 5.0)Hsaio, et al., 2015 [7]
Liugui sands, TaiwancleanReconstituted3FC = 0%, PI = noneThis study
Liugui sands, TaiwanLiugui finesReconstituted6FC = 15, 30%, PI = 5.7This study
Liugui sands, TaiwanMudstoneReconstituted6FC = 15, 30%, PI = 12.4This study
Liugui sands, TaiwanKaoliniteReconstituted6FC = 15, 30%, PI = 32This study
Table
Table 2. Soil gradation parameters and general physical properties of soils with different fine contents.
Table 2. Soil gradation parameters and general physical properties of soils with different fine contents.
FC (%)D60
(mm)		D50
(mm)		D30
(mm)		D10
(mm)		CuCdemaxeminγdmax
(kN/m3)		γdmin
(kN/m3)
00.520.40.20.114.730.700.680.3320.2416.05
150.450.280.150.067.500.830.860.4817.8914.24
300.30.190.0740.0466.520.400.910.4518.2613.87
Table
Table 3. Atterberg limits of the fines and their USCS classification results.
Table 3. Atterberg limits of the fines and their USCS classification results.
FinesLL (%)PL (%)PIUSCS
Liugui sand23.517.85.7CL-ML
Mudstone28.816.412.4CL
Kaolinite56.324.332.0CH
Table
Table 4. List of the results of the experiments performed using different specimens.
Table 4. List of the results of the experiments performed using different specimens.
SpecimenFC (%)CSRNo. (Ru = 0.2)No. (Ru = 0.5)No. (Ru = 0.7)No. (Ru = 0.9)No. (Ru = 1.0)
Sand-0100.14752788592
Sand-020.18226465155
Sand-030.2218121516
S-FC15-01150.17210193360
S-FC15-020.2137102645
S-FC15-030.262581632
S-FC30-01300.1912823139
S-FC30-020.2325122369
S-FC30-030.271381548
M-FC15-01150.15617223583
M-FC15-020.1948122256
M-FC15-030.241471842
M-FC30-01300.2413522168
M-FC30-020.291241774
M-FC30-030.3411.53.51526
K-FC15-01150.311.5349187
K-FC15-020.35126.54088
K-FC15-030.420.10.624.511
K-FC30-01300.4113990215
K-FC30-020.4512.3816107
K-FC30-030.491.3592959
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Hsiao, D.-H.; Lin, C.-C. Effects of the Properties of Fines on the Pore Water Pressure Generation Characteristics of Sand–Silt–Clay Mixtures during Cyclic Loading. Appl. Sci. 2023, 13, 8126. https://doi.org/10.3390/app13148126

AMA Style

Hsiao D-H, Lin C-C. Effects of the Properties of Fines on the Pore Water Pressure Generation Characteristics of Sand–Silt–Clay Mixtures during Cyclic Loading. Applied Sciences. 2023; 13(14):8126. https://doi.org/10.3390/app13148126

Chicago/Turabian Style

Hsiao, Darn-Horng, and Chung-Chieh Lin. 2023. "Effects of the Properties of Fines on the Pore Water Pressure Generation Characteristics of Sand–Silt–Clay Mixtures during Cyclic Loading" Applied Sciences 13, no. 14: 8126. https://doi.org/10.3390/app13148126

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