The cone penetration test-based simplified liquefaction triggering evaluations are largely based on linking liquefaction manifestations in the field to cone penetration resistance. These relationships are interpreted in such a way that for given penetration resistance, the liquefaction resistance increases as non-plastic fines content (FC) increases. However, several studies have indicated discrepancies in this relationship. Hence, there is a lag in rational scientific understanding of this observation. In this study, an experimental research program was undertaken to investigate the CPT-based liquefaction assessment by considering the effects of drainage conditions on the relationship between CPT resistance and liquefaction resistance. First, clean sand and silty sands having 5, 15, and 35% FC were tested at different relative densities by stress-controlled cyclic direct simple shear (CDSS) tests to investigate cyclic resistance of silty sand with varying amounts of non-plastic fines. Then, a set of tests involving piezocone penetration (CPTu), seismic CPTu (SCPTu), and direct push permeability (DPPT) were undertaken in a large-scale box filled with the same soils used in the CDSS tests. The large-scale test results quantified the effect of drainage conditions (coefficient of consolidation) on cone penetration resistance. Finally, by combining the CDSS and CPTu test results, an alternative CPT-based liquefaction resistance relationship was proposed by considering the effects of drainage conditions.
Research Article
CPT-Based Liquefaction Resistance of Clean and Silty Sands: A Drainage conditions Based Approach
https://doi.org/10.21203/rs.3.rs-1427044/v1
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Liquefaction resistance
cone penetration test
cyclic simple shear test
sand
silt
coefficient of consolidation
relative density
Over the past three decades, researchers have observed that non/low plastic silty sands are commonly involved in liquefaction, and in some cases even silts could liquefy [e.g., 1,2]. Therefore, there have been many laboratory-based studies investigating the liquefaction resistance of silty sands. Many laboratory studies indicated that cyclic liquefaction resistance decreased with increasing FC up to threshold value (btwn. 15% and 40%) [3–10]. Although, the opposite trend (i.e., an increase in cyclic liquefaction resistance with increasing FC) was reported by several other studies [6, 11–13]. Meanwhile, some other studies involve results which denote a temporary increase in the cyclic liquefaction resistance up to a low FC (e.g., 6%), followed by a decrease in liquefaction resistance with further increasing fines content [14–16]. In a recent study, Monkul et al. [16] proposed a new equation on cyclic liquefaction resistance of silty sands, which considers the combined effect of fines content with uniformity coefficient (i.e. gradation). Nevertheless, the problem of fines’ effect on liquefaction is complex, and one of the possible reasons for different observations in the laboratory-based studies mentioned above is the density index parameter (e.g., similar void ratio, inter-granular void ratio, or relative density) used to compare the liquefaction resistances [17–20]. It should be reminded that the fines’ plasticity makes the problem more complicated [21–23]. The mentioned studies above [btwn. 3 to 20] typically investigated the effect of non-plastic fines, except the three [11, 13, 16], which had silts with plasticity index of 3 and 11, respectively.
As summarized by Youd et al. [24], the liquefaction potential of sandy soils can be determined by several in-situ tests, including the standard penetration test (SPT), cone penetration test (CPT), and shear wave velocity (Vs) test. When the commonly used CPT-based liquefaction assessment chart—developed by Robertson and Wride [25]—is considered, the chart is documented in the form of normalized cone penetration resistance (qc1N) versus cyclic resistance ratio (CRR7.5 = τave/σvo’), applicable for an earthquake magnitude of 7.5. In order to account for the variations in the magnitude of an earthquake, (CRR)7.5 requires to be corrected by the scaling factor [24]. In the conventional liquefaction assessment charts, there are three demarcation curves that correspond to three different fines content values of FC ≤ 5%, FC = 15%, and FC = 35%. These demarcation curves were determined by the CPT tests and the field liquefaction observations at different sites, based on the indication of liquefaction (e.g., sand boils, lateral spreading, and bearing capacity loss) during the earthquakes [25]. It has become apparent that liquefaction resistance determined in this manner depends on the grain size distribution characteristics, involving fines content of the soil for a given qc1N. Particularly, the widely used liquefaction assessment chart implies that for the same qc1N the liquefaction resistance increases progressively up, apparently, to a fines content of about 35%, as the curves seem to shift to the left with increasing FC.
Several researchers have studied the effects of fines on liquefaction screening using the cone penetration resistance [e.g., 14, 26–30]. Some studies showed an increase in CRR with increasing FC at a given qc1N [26, 27, 29, 30]. Juang et al. [26] developed a CPT-based empirical equation for CRR using a neural network methodology on CPT data and field liquefaction performance observations during historical earthquakes. Their study resulted in a similar chart with the widely used CPT-based correlations proposed by Robertson and Wride [25]. Huang et al. [27] performed cone penetration chamber tests and cyclic triaxial tests on two different sand types with various FC and relative densities. Their results showed that the CRR-qc1N correlation consistently fell below the accepted correlations.
Moss et al. [29] found significantly different correlations from that of Robertson and Wride’s [25]. There are also some studies that concluded that CRR decreases with the increase of FC at a given qc1N (i.e., the curves seem to shift to the right with increasing FC). For instance, Carraro et al. [14] carried out cyclic triaxial tests and cavity expansion analysis for clean and silty sands at various relative density values, developing a CRR-qc1 relationship. The liquefaction assessment charts that Carraro et al. [14] proposed implies that the higher fines content in sand tends to decrease its liquefaction resistance at a given cone penetration resistance. On the other hand, Kokusho et al. [28] found a single correlation between the CRR and the cone penetration resistance despite the large differences in relative density or FC. These observations show that it is not clear whether the fines reduce the cone penetration resistance or increase the liquefaction resistance. Despite its importance in engineering design, further research is still needed for a rational understanding of the relationship between cone penetration resistance and cyclic resistance of clean and silty sands. Hence, the successful application of CPT-based liquefaction assessment chart methods require detailed insight regarding the effects of non/low plastic fines on the relationship between liquefaction resistance of sands and their CPT resistance.
It needs to be restated that clean and silty sands have different drainage conditions (permeability and coefficient of consolidation) at different relative densities, which influences the cone penetration resistance [31, 32]. Relatively recently, a non-dimensional parameter T (= vd/ch) has been utilized to study the effect of the coefficient of consolidation (ch), the rate of cone penetration (v), and cone diameter (d) on the measured CPT resistance, as well as the excess pore water pressure during penetration of the cone into the soil [33–37]. Two soils having similar CRR may have different FCs, as well as different permeabilities, compressibilities, and coefficients of consolidation. In fact, Robertson and Wride [25] stated that for a given CRR, silty sands have lower CPT resistance than the clean sands in liquefaction charts because of having greater compressibility and smaller permeability (k) than the clean sands.
In order to establish direct correlations between cone penetration resistance and CRR considering the effect of fines and drainage conditions, this study involves systematic laboratory research, in which piezocone penetration (CPTu), seismic CPTu (SCPTu), and direct push permeability (DPPT) tests, and subsequent cyclic direct simple shear (CDSS) tests were carried out on the same soils by changing Dr and FC. The CRR values obtained from CDSS experiments were correlated with qc1N, obtained from several large-scale CPTu tests at the corresponding relative densities. The first part of this paper builds on the results on the effects of relative density and FC on liquefaction resistance, permeability, and consolidation characteristics. The second part implements this understanding to determine how FC and normalized penetration rate (drainage conditions) affect cone penetration resistance and their relationship to liquefaction resistance. Finally, by combining the CDSS and CPTu test results, a liquefaction assessment chart is proposed, where the relationship between CPT resistance and liquefaction resistance is plotted considering the effects of drainage conditions. With such an approach, the influence of fines on liquefaction resistance is also inherently considered in the proposed CPT chart.
Clean sand and non-plastic silt were used in the experimental portion of this study. The base sand was obtained from the Urla district in the city of Izmir. The non-plastic silt was a naturally formed soil from the Babaeski region of Kırklareli. The sand and silt consisted of mainly quaternary sediments which consists of alluvial soils transported by the rivers. Only the minus No 200 portion (< 0.075mm) of the silt, obtained by wet sieving, was used in the experiments. Several sand-silt mixtures were prepared by mixing sand with non-plastic fines (silt) at contents of 5, 15, and 35% by dry weight. Figure 1a shows the grain size distribution curves of clean sand and sand-silt mixtures used in both piezocone penetration tests (CPTu) and cyclic direct simple shear tests. The index properties of clean sand and sand-silt mixtures are listed in Table 1. Based on the unified soil classification scheme [38], the clean sand and the sand-silt mixtures were defined as poorly graded sand (SP) and silty sand (SM), respectively. The microscopic view of silt and sub-angular silica sand particles is shown in Fig. 1b.
The change of maximum (emax) and minimum (emin) void ratios with FC of different silts are plotted in Fig. 2a. As the silt content increases, the emax and emin values of these samples are reduced to about 30 to 35% FC. The limit void ratios for each silty sand sample were obtained by the method proposed by Lade et al. [39], using a 2000 ml calibrated graduated cylinder. Lade et al. [39] explained the experimental procedure, repeatability, and other details of their method, which would not be repeated here. However, some general issues regarding extreme void ratio determination should be reminded here, such as the limitation of most standards for determining emax and emin, which originally intended for sands up to a certain amount of fines content. For example, ASTM procedures were intended for sand with FC up to 15%, while the Japanese Geotechnical Society’s procedures were intended for sand with less than 5% FC [40]. Consequently, the fines content range investigated in this study is technically greater than what is allowed by many standards. Therefore, a non-standard procedure [39] was chosen in this study, which had been successfully used for obtaining the emax and emin of various silty sands in the literature that have quite a wide fines content range [16, 19–21, 41–43].
Figure 2b shows the variation of k with various Dr at different fines content of 0, 5, 15, and 35% for clean and silty sands used in the experiments. For soils having FC = 0% and 5%, the k values were obtained from constant head permeability tests [44]. Additionally, falling head permeability tests [44] were performed for soils having FC = 15 and 35%, at a range of different relative density values. The relationships between k and Dr are shown by the solid trend curves, presented in Fig. 2b, for sand at different FCs between 0% and 35%.
The results show that the permeability of clean and silty sand are not the same, even at the same relative density, which is an expected observation due to the changes in grain and pore size distributions. The permeability of saturated sand containing 5% silt is roughly less than a half order of magnitude smaller than the permeability of clean sand; however, both curves (0% and 5% FC) come close to each other as soils become loose (i.e., Dr≈25%). The permeability of saturated sand containing 15% silt is almost two orders of magnitude smaller than the permeability of clean sand. The significant drop in the k value with an increase of FC towards 15% is mainly because of the reduced pore size within the overall grain matrix. The measured k values of clean sand and 5% are influenced relatively less by the change in relative density within the studied range; although a modest decrease (i.e., less than half an order) can be observed with an increasing Dr. However, the sensitivity of k to Dr is more noticeable at FC = 15% and 35% (i.e., k decreases rapidly as Dr increases towards medium-dense to dense states). Hence, for a given fines content (at FC = 15% or 35%), the k could range within one order of magnitude, depending on the relative density.
3.1 Cyclic Direct Simple Shear Tests (CDSS)
A total of 77 CDSS tests were performed on reconstituted soil samples. The automatic dry funnel deposition method was used to form specimens in cylindrical split molds. More details about automatic dry funnel deposition method such as specially designed aluminum funnel, computer-controlled motor, raising speeds, etc. can be found in [45, 46]. It should be reminded that dry funnel deposition (manual method) has been widely used in various experimental studies on liquefaction [19–21, 39, 47–51]. Deposited simple shear specimens in this study typically had about 20 mm initial height and 64 mm diameter. Teflon-coated rings were stacked around a typical latex membrane to provide lateral confinement during testing. Previous literature has shown that the distribution of silt and sand fractions within the specimen volume is reasonably uniform after being deposited by the dry funnel technique (i.e. segregation of fine and coarse grain fractions is not a concern) [21, 47, 52, 53].
All specimens were consolidated to σ'vc (vertical effective stress) of 100kPa. At the cyclic loading stage, constant volume conditions (equivalent to undrained cyclic loading) of the specimens were maintained by computer control such that the height of specimens were kept constant. This is done by adjusting (i.e. increasing or decreasing) the amount of vertical stress acting on the specimens depending on their volume change tendency. The constant volume CDSS system in this study does not need any pore pressure, because drainage was not controlled. Excess pore-water pressures generated in an equivalent undrained test were predicted from the change of vertical effective stress [53]. Accordingly, an increase in vertical stress (+Δσv) to maintain constant volume conditions matches the negative excess pore pressure change (-Δue) in a truly undrained test (i.e., +Δσv=-Δue). Excess pore-water pressures predicted from a constant volume DSS test are shown to be the same as the pore pressures measured in a truly undrained DSS test [54]
Another important issue for the liquefaction experiments and relevant investigations in the laboratory is the degree of saturation. Finn and Vaid [55] investigated the cyclic liquefaction behavior of Ottawa sand via dry and saturated specimens under constant volume direct simple shear loading and reported an identical response for dry and saturated specimens. This finding was important because it indicates that dry specimens can be used to study the clean sand behavior in undrained conditions. Later, Monkul et al. [56] performed constant volume CDSS tests and compared the liquefaction behavior of specimens in dry and saturated conditions. According to their results, the cyclic liquefaction response of silty sands (i.e. with non-plastic silt only) and clean sands can be determined by using dry specimens under constant volume CDSS loading. Recently, Monkul et al. [57] also tested non-plastic silts in constant volume DSS tests and obtained their monotonic undrained shear strength from dry specimens. There are other studies in which dry specimens were tested in constant volume CDSS tests [58–60]. To benefit the inherent capacity of the constant volume CDSS system explained above and to exclude the demanding saturation process, all the simple shear specimens in this investigation were tested in a dry condition by constant volume CDSS loading.
Shear stresses (τcy) were applied in a uniform manner at four cyclic stress ratios (i.e. CSR = τcy/σ'vc=0.1, 0.12, 0.14, and 0.18) at 0.1 Hz frequency during cyclic loading. When the predicted excess pore water pressure of the samples becomes equal to the initial vertical effective stress of 100kPa liquefaction is considered to occur. Cyclic loading continued until the specimens either liquefied (i.e., ru = Δue/σ'vc=1) or 10% double amplitude (D.A.) shear strain was reached. It should be noted that the influence of the two alternative failure criteria (i.e., 10% D.A. shear strain and ru=1) on the results is not significant, because the average ru value for the specimens at which double amplitude shear strain condition governed was also calculated to be close to 1 (i.e. 0.93). As can be seen in Fig. 3a-b, which show CDSS response for a silty sand specimen, the occurrence of two alternative failure conditions (i.e., ru=1 and 10% D.A. shear strain) is quite close to each other.
3.2 Seismic Cone Penetration and Direct Push Permeability Tests
A group of 13 tests—CPTu, SCPTu, and DPP—were performed on clean and silty sands mentioned before. Summary of the prepared samples and test results are presented in Table 2. Each soil was deposited into a rigid-walled box which would result specimens with a width of 45 cm, a length of 163 cm, and an initial height of 144 cm. For the sample preparation, the dry pluviation method was used, which is equivalent to the method used in the previously explained CDSS tests. For this approach, dry soil is deposited directly through a large funnel into the box to minimize particle segregation of silty sands [62] as well as to be consistent with the fabric of simple shear specimens. Once the dry soil reached a depth of 144 cm, carbon dioxide was evenly introduced into the specimen for about one hour, from the bottom of the box towards the top, in order to remove the air inside the specimen. Then, the water was allowed to flow after the percolation of carbon dioxide. For each sample, the relative density is evaluated in two ways. The first one is based on the dry weight of each sample and the amount of water added to the sample by using relevant phase relationships. With this method, the average Dr was obtained for each sample. The second one is by using the relationship between k and Dr, as demonstrated in Fig. 2b, based on the measured k of specimens by DPPT tests, which will be further explained in the following sections. With this method, Dr values were obtained at specific depths where DPPT tests were conducted. As shown in Table 2, the Dr based on the water content and the relationship between k and Dr are tabulated in columns 7 and 8, respectively. For example, the relative density of sample S1 was determined 21–29% throughout the depth, with an average for the whole deposit close to 26%. For this sample, the average relative density obtained based on the water content was 27% which is in good agreement with the relative density range (and its average) estimated from the relationship between k and Dr. As it is important to obtain relative density at specific depths in the box, the Dr values that are listed at column 8 are used in the further analyses. More details about the sample saturation methodology and preparation process of large samples are detailed in Arik [63].
Figure 4 displays the testing setup and side view of test locations. The probe used in the piezocone penetration test was a classic cone with a tip angle of 60° and a diameter of 35.7 mm. The CPTu tests were conducted with different penetration rates, from 0.8 cm/sec to 1.5 cm/sec. The cone penetration rates, as well as the measured cone penetration resistance (qc) and pore water pressure (u2) values, are tabulated in Table 2. The recorded penetration resistance was normalized as shown below [64]:
Here, σvo' is the effective vertical stress, σvo is the total vertical stress and qc is the measured cone resistance in atm units. c is the stress normalization exponent, which was estimated from Eq. 2, proposed by Olsen [64]. In this study, the c values changed from 0.58 to 0.92 for Dr of 70–21%, respectively.
One of the most important factors affecting the CPTu measurements in the box is the ratio of the diameter of the box to the CPTu probe (Rd=Dc/d). Several researchers [65–67] have studied the effects of boundary conditions on CPTu data. Parkin and Lunne [65] reported that for loose soil, the side boundary effects are negligible. Phillips and Valsangkar [66] and Renzi et al. [67] stated that for dense soil, the side boundary effects are not significant even for Rd = 11. In this study, CPTu tests were performed along one concentric circle that has a diameter of 45 cm. The cone that has a diameter of 3.57 cm gives a Rd value of 13. In view of the above, the boundary conditions of the box can satisfactorily model the in-situ free field conditions when the Rd values revealed in the literature are examined.
Following the CPTu tests, seismic CPTu tests (SCPTu) were performed, based on ASTM D5778-12 [68] standards. As shown in Fig. 4, the SCPTu was performed 0.8 m apart from the CPTu testing hole. The S-plate was placed on the soil sample surface 1 m apart from the SCPTu hole. The horizontal shear waves were generated by hitting the S-plate laterally with a sledgehammer. The S-waves were then transmitted through the soil and reached the seismometer at the seismic rod. The measured Vs values are listed in Table 2 (column 5) and these results were used to derive the coefficient of volume compressibility of the soils (mv) as shown in Eq. 3 below:
Here, ρ is the density of the soil, and ν is the Poisson’s ratio. Precise ν measurement is very difficult due to the bedding errors and system compliance in the laboratory [69, 70]. Therefore, the results of Suwal and Kuwano [71] were used to evaluate the ν of silty sands in fully saturated conditions. Poisson’s ratio values for each FC are given in Table 2.
Following the SCPTu test, permeability was obtained by DPPT at the same depth intervals the SCPTu tests were completed. Figure 4 shows the DPPT testing location. As shown in Fig. 5, a complete DPPT testing tool used in the laboratory contains a cylinder water tank with valve attachment points for water and compressed nitrogen gas, a probe with a 60° tip angle and a 3.57 cm diameter, and a perforated screen with a slit size of 0.3 mm and a length of 45 mm. During the DPPT, the water was first filled inside the cylinder tank specifically designed for the DPPT setup, and then it was rapidly pressurized via compressed nitrogen gas. The flow speed of the water from the perforated screen was then measured as water discharged into the soil over a measured time and pressure. The applied excess head (Δh) and the measured volumetric flow (Q) were used to find the permeability of each sample at distinct depths, as shown below [72]:
$$\text{k}=\frac{\text{Q}}{4{\pi }.{\Delta }\text{h}. {\text{a}}_{\text{s}}}$$
4
where, as represents the spherical injection region radius, which was 1.44 cm in this study. During the tests, drainage is only allowed from the top of the soil samples.
4.1 Effect of Fines and Relative Density on Excess Pore Pressure and CPT Resistance
CPTu test data were used to demonstrate the relationship between relative density and normalized penetration resistance, as well as the relationship between relative density and excess pore water pressure for sand having different FCs. Figure 6a shows the relationship between excess pore water pressure ratio and Dr for the same soils (i.e. FC between 0% and 35%) based on CPTu tests. It is clear that at each fines content, the excess pore water pressure ratio decreases with an increase in Dr. However, at a given relative density, no clear relationship existed between the excess pore water pressure ratio and FC, as the trend curves cross each other. The low confinement stress is clearly contributing to the observed behavior and resulted in enhanced dilation.
Figure 6b illustrates the effect of FC and Dr on the normalized cone penetration resistance data which corresponds with four different FCs. It is clear that at a specified relative density, the qc1N decreased, with an increase in FC from 0 to 35%. For each FC, the CPT resistance increased with an increase in relative density, where the general trend of increase was represented by solid trend curves having exponential functions, seen in Fig. 6b. A change in the relative density of clean sand (FC = 0%) from 20–40% (within loose state) and from 40 to 60% (within medium dense state) increased the qc1N by a factor of about 2.1. For silty sand having 5% and 15% silt, the increase in normalized CPT resistance is almost similar to the increase in clean sand. For silty sand having 35% silt, with an increase in relative density, the normalized cone tip resistance increased more subtly as compared with a lower percentage of silt. A change in relative density of silty sand (containing 35% fines) from 50–75% (medium dense to dense state) increased the normalized CPT resistance by a factor of 1.8.
The relationships between CPT resistance and Dr of clean sand and silty sand having 15% and 35%, determined in this study, are also compared in Fig. 7a with the dashed curves given by Cubrinovski [73]. As shown in the figure, there is a similar trend between qc1N and Dr at FC of 0% and 15%. However, for 35% FC, at a given relative density, the qc1N values developed by Cubrinovski [73] are slightly higher than the ones developed in this study.
4.2 Effect of Fines and Relative Density on CRR
As mentioned before, CDSS tests in this study were performed through a wide range of relative density values on various clean and silty sand specimens, which had different FCs (0%, 5%, 15%, and 35%). The liquefaction resistance of clean and silty sand specimens were compared with (CRR)N=20. According to Ishihara [48], 20 uniform loading cycles could be used to determine the liquefaction resistance of laboratory specimens, based on the typical number of significant cycles in many past earthquakes. Hence, in this study, (CRR)N=20 is considered as the cyclic stress ratio required to cause liquefaction of specimens in 20 uniform cycles.
For determining the (CRR)N=20 of different silty sands, the number of cycles to liquefaction (NL) versus CSR data were plotted on a semi-logarithmic graph for different relative density values. Then, corresponding (CRR)N=20 values were determined at NL=20 for different soil samples. Figure 7b shows the change of liquefaction resistance with relative density and FC. As expected, (CRR)N=20 increases alongside Dr for all samples—as seen in Fig. 7b—and there is a linear relationship between (CRR)N=20 and Dr for the studied range. In several previous studies, such linear relationships have also been observed for other soils [18, 74, 75].
The influence of FC on the (CRR)N=20 of silica sand seems to be complicated. Still, based on Fig. 7b, one can make general observations. Adding 5% silt to the base sand increased its cyclic strength compared to the clean sand (FC = 0%) at a given relative density; however, the level of influence decreased as the soil became looser (i.e., Dr decreased). Further addition of fines from 5–15% and from 15–35% had systematically decreased (CRR)N=20 at a given Dr (trend lines shifted downwards). One can also observe that the clean sand curve is crossed by the 15% silty sand curve around Dr of 45%, which adds complexity to the FC’s effect on liquefaction resistance. Similar crossings of (CRR)N=20 curves for different silty sands could be seen in literature [5, 18], as well as discussed in detail by Tutuncu et al. [75].
4.3 Effect of Fines on CPT Resistance - CRR Correlation
Two relationships were obtained from the laboratory tests conducted with the sand-silt mixtures. The first relationship described briefly before, is between (CRR)N=20 and Dr for clean and silty sands having different FC (Fig. 7b). A correction factor (0.9) proposed by Seed et al. [76] was applied to the results of the CDSS tests to account for the multi-directional shaking during an earthquake (i.e. N = 20 relates to the Mw8.0). Moreover, to obtain Mw7.5, a magnitude scaling factor of 0.83 was applied to the results of the CDSS tests. The second relationship is between qc1N and Dr for the same clean and silty sands having various FC values obtained from CPTu and DPPT tests (Fig. 6b). These two relationships, via common Dr values, were combined to obtain the (CRR)7.5 versus qc1N for various ranges of FCs, as shown in Fig. 8. For relative density less than 70%, the measured qc1N values range from 10 to 125, and the proposed solid curves for each FC fall below a (CRR)7.5 of 0.23. At high qc1N values, the measured data were relatively limited. However, it should be emphasized that the studied qc1N range in this study (< 150) is one of the most critical regions in the CPT-based assessment charts due to the high potential of liquefaction, yet the previous research investigating the liquefaction behavior through this region was also quite limited.
Figure 8 shows that the data points for qc1N less than about 25 were bundled together for sands in this study regardless of the FC. As FC increases from 0–5%, there is an obvious increase in (CRR)7.5 at a given qc1N value over 25. With further increase in FC from 5–15% had relatively increased CRR7.5 at a given qc1N. For the sand with 35% FC, a sharp increase is observed in CRR7.5 with increasing qc1N, however, the qc1N data is limited (< 30). As displayed in the figure CRR7.5 increases relatively more rapidly with qc1N. Moreover, the available experimental data incorporating both controlled in-situ and laboratory tests at this region is extremely limited in the literature.
The findings above indicate that the simplified liquefaction methods should be used with caution. Successful usage of these charts at different drainage conditions could also be considered for better representation of the liquefaction assessments. During the penetration of a cone into saturated sand or silty sand, the penetration causes loads and shear strains on the soil around the cone. The shear strains and the excess pore water pressures around the cone are highly non-uniform. Therefore, depending on the rate of penetration (v), the diameter of the penetrating object (d), and consolidation characteristics of the soil (ch), dissipation of excess pore pressures and consolidation may vary around the cone. For a more accurate assessment of the liquefaction resistance based on the CPT test, there is a clear need for a CRR–qc1N correlation based on ch of the soil, cone penetration rate, and diameter of the cone during penetration. Relatively recently, ch, v, and d were combined to introduce a non-dimensional penetration rate (T), as follows [33, 34]:
The ch of the silty sands plays a primary role in pore water pressure dissipation during cone penetration. Therefore, first, a closer investigation is needed to assess the effect of FC and relative density on ch. At different FCs, Fig. 9 shows the variation of ch with various Dr. The ch of the prepared samples in the box was calculated by Eq. 6 given below:
where, γw is the unit weight of water, and mv (Eq. 3) and k (Eq. 4) were derived from the SCPTu test and DPPT test data, respectively. Therefore, the ch data given in the figure are calculated at depths where SCPTu and DPPT tests were performed. In the figure, the Dr values were obtained by combing the permeability measured by DPPT at each test, as well as the k versus Dr at each FC indicated in Fig. 2b.
As shown in Fig. 9, because of the reduction in permeability when increasing the silt content, the magnitude of ch also decreases by about two orders of magnitude when the silt content increases to 15%, compared to the ch of the clean sand. Moreover, the ch of silty sand with 5% fines is practically not different from that of the clean sand. However, as seen in the figure, the ch of silty sands with 15% and 35% fines is considerably different from clean sand, when compared at the same Dr. The ch of silty sand with 15% and 35% fines are much smaller than the ch of clean sand. The difference of ch between clean sand and silty sands would lead to the variation of dissipation time of induced excess pore water pressure generated as the cone penetrates through the soil. This is quite important because it would result from different drainage conditions in clean and silty sands having different FC and such differences in drainage conditions should be expected to play an important role in the measured cone resistances.
5.1 Effect of Normalized Penetration Rate on Excess Pore Pressure and CPT Resistance
It is expected that the excess pore water pressure and cone penetration resistance differ in soils due to the variations in permeability and non-soil-property-related parameters, such as v and d. In the experiments, the diameter of the cone (35.7 mm) was constant. Hence, T is controlled by the ch (varied from 1 cm2/sec to 103 cm2/sec), and v (varied from 0.8 cm/sec ~ 1.5 cm/sec). Several researchers used T to examine the effect of penetration rates on clean sand and sand with different silt contents [77–79]. The maximum penetration velocity applied in their CPT tests was not large enough to trigger the transformation from drained to partially-drained, or even to undrained conditions. Hence, to have a wide range of T values to trigger transformation from drained to partially-drained, or even to undrained conditions, authors slightly changed the penetration velocity which is close to the penetration rate applied in standard CPT tests (2 cm/sec).
The above given experimental results are presented in Figs. 10a-b in terms of Δu/σvo' versus T and qc1N versus T at different relative densities of the clean and silty sands. In each figure, the data points are obtained for three distinct ranges of relative densities (20% < Dr ≤ 30%, 45% ≤ Dr < 60%, and 60% ≤ Dr < 70%). The corresponding green shaded area in the figure represents the relative density range from 20–30%. The gray area signifies the relative density between 45% and 60%, and the pinkish shaded area represents the relative density from 60 to 70%. Other relevant information of the data points plotted in Figs. 10a-b (such as fines contents, penetration depths, etc.) could be seen in Table 2 based on Dr and T values of the points.
Figure 10a shows the relation between Δu/σvo' behind the cone tip and T for the clean and silty sands with different relative densities. The Δu/σvo' remains very small for all soils when T < 0.01, which could be assumed as a drained condition. At T > 0.01, Δu/σvo' increases at Dr ≤ 30%, while Δu/σvo' decreases at Dr ≥ 60%. Such trends are in accordance with the basic principles of volume change behavior of soils. For instance, for dense states (i.e. Dr ≥ 60%), as T increases, a considerable amount of negative Δu/σvo' develops, which indicates the dilative behavior of the dense soil under cone penetration. Meanwhile, there is a transition behavior from increasing Δu/σvo' to decreasing Δu/σvo' between 45–60% relative density.
The change in T and Dr also effects the cone penetration resistance. The observations from Fig. 10b imply that at a given relative density, the qc1N of a larger T would be smaller than that of a smaller T. A reduction of qc1N is seen in the soil with an increase in T, which can be attributed to the difference in FC (leading to different k and ch) and penetration velocity. Regarding the fines content effect, as mentioned before ch decreases with increasing FC at a given Dr (Fig. 9). Hence, for the same d and v, the T increases with increasing FC (Eq. 5) at a given Dr. Therefore, the effect of FC was inherently reflected in Fig. 10b. Due to the change in the coefficient of the consolidation and penetration rate, the change of the normalized penetration rate was investigated from about T = 0.001 to about T = 5. For each relative density, normalized penetration resistance values are high at low T values (from 0.001 to 0.01). This can cause high effective stress around the cone tip due to the shorter dissipation time of pore water pressure, representing a drained condition. The increase of T from 0.01 to about 5 caused normalized penetration resistance to decrease significantly, representing the partially drained condition. The increase of T from 5 changed normalized penetration resistance in minimal values, representing an almost-undrained condition. A higher T value can cause lower effective stress around the cone tip due to the longer dissipation time of pore water pressure.
The findings of this study align with the related research conducted by several researchers [37, 80–82]. For example, Ecemis [37] found the limiting value of T for drained and undrained conditions between 0.01 and 6, respectively. In the same line, based on the studies of Schneider et al. [80], the partially drained condition was at intermediate T values of about 0.03 to 10. Doan and Lehane [82] suggested partially-drained penetration at 0.01 to 7. Similar experimental observations were also reported in clayey soil by Jaeger et al. [81], in which the limiting valued T for drained and undrained conditions was 0.01 and 20, respectively.
The effect of permeability, the penetration rate, and the diameter of the cone on qc1N and pore water pressure (Δu/σvo') at different Dr values agrees favorably with one another once they are normalized to the same T value. So, it can be inferred that T would be a more reasonable parameter than the fines content of the soils to quantify the degree of consolidation during cone penetration.
5.2 Effect of the Normalized Penetration Rate on CPT Resistance – CRR Correlations
Two relationships were combined to obtain the (CRR)7.5 versus qc1N for different ranges of T values. The first relationship is between (CRR)7.5 and T at different relative density ranges. (CRR)7.5 and T relationship is obtained by combining, (CRR)N=20-Dr (Fig. 7b) and ch-Dr (Fig. 9) for clean and silty sands having different FC. The second relationship is between qc1N and T (Fig. 10b) at different relative density ranges.
Figure 11a shows the (CRR)7.5 versus qc1N for two distinct ranges of normalized penetration rates. These results are grouped for two sets of T values (a) 0.001 < T < 0.01 and (b) 0.5 < T < 5. The corresponding upper and lower limit values of the T values are represented by the curves. The T values less than 0.01 correspond to a drained condition, whereas the T values more than 5 correspond to an undrained condition as explained in Fig. 10b before. Accordingly, one should expect a transition from drained condition to undrained condition for T values between 0.01 to 5. Figure 11a clearly shows that, as T increases (which is attributed to a decrease in k and ch and an increase in v) from 0.001 to 5, the liquefaction resistance of soils significantly increases when compared at the same qc1N. Similar to the qc1N-(CRR)7.5 variation with FC, the data points corresponding to different T ranges are bundled together for qc1N values smaller than 30 (i.e. the boundary curves became somewhat unclear/cross each other).
Figure 11b depicts the relationship, along with the field-based relationship, for (CRR)7.5 versus qc1N and FC, corresponding to nearly clean sand (FC < 5%), silty sands at nearly 15% silt content, and 35% silt content as recommended by Robertson and Wride [25]. As mentioned earlier, these curves are widely used in practice for the evaluation of liquefaction resistance based on CPT resistance with FCs from 0–35%. Additionally, a clean sand curve that was proposed by Krage and DeJong [83] was plotted in the figure. It is interesting to observe in Fig. 11b that the T boundary line less than 0.01 follow the curves of Robertson and Wride [25] and Krage and DeJong [83] in a reasonably close manner for FC ≤ 5% and clean sand, respectively. Hence, the proposed curves are consistent with the observed data shown in the figure, as FC less than 5% and clean sand represent the drained condition [84]. The Robertson and Wride [25] curves for 15% and 35% silt content also tends to be in good agreement with the results of this study and falls on the boundary line corresponding to T = 0.5 and T = 5, respectively. The increase of T from 0.01 to about 5 represents the partially drained condition. Consequently, the proposed curves representing different T values are consistent with field observations shown in the figure, as T more than 5 represents the almost-undrained condition.
The results clearly show that for a more accurate assessment of the liquefaction resistance based on the CPT test, the CRR–qc1N correlations based on the coefficient of consolidation of the soil, cone penetration rate, and diameter of the cone during penetration are needed. It should also be reminded that such an approach also inherently considers the effect of FC on the liquefaction resistance of sands.
Based on an extensive experimental program, which involves several different types of experiments including cyclic direct simple shear tests, constant and falling head permeability tests, piezocone penetration tests, seismic CPTu tests, and direct push permeability tests, a normalized penetration rate-dependent liquefaction screening chart was proposed. This chart considers the effects of consolidation characteristics and the penetration rates on cone penetration resistance on clean and non/low plastic silty sands. The following results were determined:
-
Soil having different permeability and coefficient of consolidation experience different drainage conditions, and this can cause different penetration resistance and excess pore water pressure around the cone tip. Cone resistance is sensitive to penetration rate and cone diameter, as well as k and ch. In this study, normalized cone penetration resistance is correlated with relative density and a non-dimensional parameter T. It is found that the effect of permeability, the penetration rate, and the diameter of the cone on qc1N and excess pore water pressure ratio (Δu/σvo') at different Dr agrees favorably with one another once they are normalized to the same T value. Therefore, T can be used to demarcate the drained, partially-drained, and undrained conditions throughout cone penetration-based liquefaction assessments. From the experimental tests performed in this study, it was determined that the limit T value from drained to partially-drained conditions was 0.01 and partially-drained to undrained conditions around 5 during the advancement of the cone penetrometer. So, it can be inferred that T which is influenced by the coefficient of consolidation during penetration would be a more reasonable parameter than the FC of the soils to be utilized in liquefaction assessment of silty sands.
-
At very high T values (low coefficient of consolidation) silty sand contributes to a slow rate of dissipation of excess pore pressures in the soil during cone penetration, leading to smaller effective stress at the tip of a cone (nearly undrained response) when compared with the behavior of silty sand having lower T values (higher coefficient of consolidation) through a wide range of relative densities investigated in this study (i.e. 20% < Dr ≤ 70%) (Figs. 10a-b). This is due to the fact that the ch of the soil decreased along with an increase in FC up to 35% (Fig. 9), indicating that employing T would also inherently involve the FC influence on liquefaction resistance.
-
The CRR-qc1N relationship determined from the laboratory was proposed for ranges of T values (Fig. 11a). It has been observed that field liquefaction resistance increased as T increased (which is attributed to a decrease in k and ch and an increase in the penetration rate) from 0.001 to 5, for each qc1N value. Although the T-dependent qc1N-CRR relationship depicts the same trend as observed in the field-based liquefaction screening procedures, additional studies are required to verify and refine this trend, using penetration tests in large-scale soil models.
- The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.
- The authors have no relevant financial or non-financial interests to disclose.
- All authors contributed to the study conception and design. All authors read and approved the final manuscript.”
- The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
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Tables 1 and 2 are available in the Supplementary Files Section.
- Table1.xlsx
Table 1. Index properties of the clean and silty sands used in the experimental program.
- Table2.xlsx
Table 2. Summary of the CPTu, SCPTu and DPPT tests using sand-silt mix of 0%, 5%, 15%, and 35% fines content.