Estimation of Pressuremeter Modulus and Limit Pressure in Weathered Granite Based on the SPT-N Value and Chemical Weathering Index: A Case Study in South Korea

A pressuremeter test (PMT) is a representative and highly reliable in situ test for assessing the stress–strain behavior of weathered granite. Its application, however, is restricted by its cost and time requirements. Many researchers have also investigated the correlations between the SPT-N value and the pressuremeter modulus (Em) and limit pressure (PL) of soils, but they have mostly focused on sand, silt, and clay and have employed simple regression analysis. In this study, equations for Em and PL were derived for weathered granite through multiple nonlinear regression analyses using a chemical weathering index that quantitatively represents the degree of weathering. Nonlinear multiple regression analyses were conducted by combining the allometric models that produced the optimal correlations between Em, PL, energy corrected SPT-N (SPT-N60), and normalized VR (Vogt’ ratio) with vertical effective stress. The obtained equations for Em and PL had higher R2 values (0.76 and 0.46, respectively) compared with the simple regression equations reported in previous studies. Because local characteristics are important determinants of the engineering properties of geo-materials, the Em and PL equations proposed in this paper are intended for use in geotechnical surveys of weathered granite in South Korea.


Introduction
Weathered granite, including residual soil and highly and completely weathered rocks, is widespread in South Korea and is used as the support base in the construction of major roads, bridges, and tunnels. It is therefore important to assess the geotechnical properties of weathered granite to ensure satisfactory structural performance and safety. Although geotechnical properties are typically assessed by in situ testing, sampling techniques that minimize the disturbance of the weathered granite sample, such as the triple core barrel method, have been in limited use more recently. However, it is challenging to secure sufficient undisturbed samples that are suitable for laboratory testing due to the frequent occurrence of disturbance during the transportation and fabrication of the test specimens. Clayton et al. [1] have recommended that in situ testing should be performed to obtain proper geotechnical properties in the case when it is difficult to retrieve an undisturbed sample.
The representative in situ tests applied to weathered granite are the standard penetration test (SPT) and pressuremeter test (PMT). The SPT, which is conducted simultaneously with a borehole investigation, is most widely used in the geotechnical field due to its convenience and economic feasibility. It is used to estimate geotechnical properties such as friction angle, unconfined compressive strength, and elastic modulus based on accumulated data and may also be used to calculate the bearing capacity of the foundation and assess ground liquefaction [2][3][4]. However, the equations currently used to determine the geotechnical properties should be used withcaution because most empirical equations are proposed based on the SPT-N values measured from soils, and penetration into the highly and completely weathered granite during an SPT is quite subtle. The PMT is used to assess the radial stress-strain behavior of the ground around a borehole and can also be applied for the calculation of the pressuremeter modulus (E m ) and limit pressure (P L ) of the base ground according to the obtained stress-strain curve. The E m is used to calculate the settlement of a shallow foundation and the coefficient of the horizontal subgrade reaction, as well as the strength parameter of the ground, the bearing capacity of a shallow foundation and a pile foundation using the limit pressure. It is applicable to a wide range of ground types, ranging from soils to weak rocks, and particularly to geo-materials in a transition state between rock and soil, such as weathered granite [5]. However, it is more time-consuming and costly than the SPT and thus its use is limited and it often omitted in small-scale projects.
Researchers have used simple regression analyses to investigate the correlation between SPT-N values and the E m and P L interpreted from PMTs to assess the geotechnical properties of grounds with a high degree of reliability, because SPTs are relatively convenient and economical. For example, Chiang and Ho [6] proposed nonlinear relationships between N and E m and between N and P L for weathered granite, including highly weathered granite and residual soil, in Hong Kong. Yagiz et al. [7] proposed linear relationships between N and E m and between N and P L based on the results of a test conducted in sandy silty clay developed at a shallow depth (within 2 m) in Denizli, Turkey. Bozbey and Togrol [8] proposed nonlinear relationships between the same parameters for sandy soil and clayey soil using the results of tests conducted in Istanbul, Turkey, while Cheshomi and Ghodrati [9] did the same for silty sand and silty clay based on SPTs and PMTs conducted in Mashhad, Iran. However, most of these previous studies dealt with soils with SPT-N values of ≤50; none considered weathered granite with an N value of ≥50. SPT is not recommended for hard geo-materials such as hard soil, soft rock, and highly weathered rock because its penetrability is not sufficient [5]. However, conventionally SPT rather than PMT is used in field practice to estimate the geotechnical properties of weathered granite because of time consuming process and high cost of PMT. Therefore, it is important to suggest the correlation between the SPT and PMT results conducted in weathered granite with N value ≥50 (i.e., hard residual soil, completely weathered rock, highly weathered rock).
Meanwhile, many studies have been conducted on the variation of the engineering properties of rocks due to weathering. The feasibility of representing the engineering properties of a rock by a chemical weathering index has also been suggested through a correlation analysis of the index with the engineering properties (unconfined compressive strength, dry density, shear strength, etc.) [10][11][12][13][14]. This index quantitatively describes the degree of weathering based on the changes in the chemical composition of the rock constituent minerals.
In the present study, empirical equations for determining E m and P L based on an SPT-N value and chemical weathering index were derived through a case study of weathered granite, including highly weathered granite and residual soil, in South Korea. The results of SPTs and PMTs conducted at three sites were used, and the equations of E m and P L were derived through the multiple nonlinear regression analysis of the SPT-N value and chemical weathering index, respectively. The values of E m and P L determined by the proposed equations were compared with those obtained in previous studies and by field measurements.

Study Area
The present study was conducted at three sites in the central and western parts of South Korea where weathered granite is commonly found (Figure 1). The study areas were selected based on a review of geotechnical investigation reports for the adjacent areas as roughly identified from a geological map of South Korea provided by the Korea Institute of Geoscience and Mineral Resources. The three sites, identified in this paper as sites A, B, and C, were all within Jurassic granite areas, and weathered granite (i.e., residual soil, highly and completely weathered granite rock) was thickly developed with thicknesses of 14, 25, and 23 m, respectively, according to a borehole investigation ( Figure 2). The samples retrieved by triple core barrel from each test site shows similar condition; the samples were brown, and their rock texture and structures were preserved especially in highly and completely weathered granite ( Figure 3). An SPT and PMT were conducted at each site, and samples were collected for assessment of the chemical weathering indices. The details of the test methods and the obtained data are provided in Sections 3 and 4.
The present study was conducted at three sites in the central and western parts of South Korea where weathered granite is commonly found (Figure 1). The study areas were selected based on a review of geotechnical investigation reports for the adjacent areas as roughly identified from a geological map of South Korea provided by the Korea Institute of Geoscience and Mineral Resources. The three sites, identified in this paper as sites A, B, and C, were all within Jurassic granite areas, and weathered granite (i.e., residual soil, highly and completely weathered granite rock) was thickly developed with thicknesses of 14, 25, and 23 m, respectively, according to a borehole investigation ( Figure 2). The samples retrieved by triple core barrel from each test site shows similar condition; the samples were brown, and their rock texture and structures were preserved especially in highly and completely weathered granite ( Figure 3). An SPT and PMT were conducted at each site, and samples were collected for assessment of the chemical weathering indices. The details of the test methods and the obtained data are provided in Sections 3 and 4.

SPT and PMT
The SPT was conducted in three steps, namely the preliminary blows, main blows 1, and main blows 2, according to ASTM D1586 [15]. The preliminary blows are the number of blows required to penetrate 15 cm in the initial stage of the test. When the two main blows produced a combined penetration of <30 cm after 50 or more blows, the penetration produced by the first 50 blows was measured. If penetration was not achieved after 10 consecutive blows, the SPT was terminated. The SPT results for the weathered granite

SPT and PMT
The SPT was conducted in three steps, namely the preliminary blows, main blows 1, and main blows 2, according to ASTM D1586 [15]. The preliminary blows are the number of blows required to penetrate 15 cm in the initial stage of the test. When the two main blows produced a combined penetration of <30 cm after 50 or more blows, the penetration produced by the first 50 blows was measured. If penetration was not achieved after 10 consecutive blows, the SPT was terminated. The SPT results for the weathered granite

SPT and PMT
The SPT was conducted in three steps, namely the preliminary blows, main blows 1, and main blows 2, according to ASTM D1586 [15]. The preliminary blows are the number of blows required to penetrate 15 cm in the initial stage of the test. When the two main blows produced a combined penetration of <30 cm after 50 or more blows, the penetration produced by the first 50 blows was measured. If penetration was not achieved after Appl. Sci. 2021, 11, 3411 5 of 13 10 consecutive blows, the SPT was terminated. The SPT results for the weathered granite layer revealed a penetration of <30 cm after 50 blows because of the insufficient penetrability of the SPT device. Despite this limitation, the geotechnical properties of weathered granite (especially highly and completely weathered granite rock) are generally evaluated by SPT in practice field. Thus, many studies have used the converted SPT-N values linear extrapolated to the N value representing the number of blows required to penetrate 30 cm [16][17][18]. In the estimation of the geotechnical properties using the N value, an energy correction is necessary in order to obtain reliable results. Accordingly, the converted SPT-N value was corrected to SPT-N 60 , which corresponds to 60% of the energy efficiency for the energy transfer rate of the equipment used in the test.
The PMT was conducted using an Elastometer-2 (OYO Corporation, Japan) in compliance with ASTM D4719 [19]. The test was conducted at the depth intervals of approximately 2 m in the weathered granite layer, and E m and P L were determined from the obtained pressure-radius curve. E m is the modulus of the pseudo-elastic range and represents the deformation characteristic in the initial linear section under the horizontal pressure on the borehole wall. P L represents the pressure at which the ground of the borehole wall reaches the state of destruction and is defined as the pressure that causes a continuous displacement without increasing the loading pressure beyond the initial elastic zone and plastic zone in the pressure-radius curve. In an actual test, however, it is difficult to reach P L , due to the limited capacity of the testing equipment. Thus, in this study, the loading pressure was determined as the P L at which the volume of the probe is twice the initial soil cavity volume (V i ) following the recommendation in ASTM D4719 [19]. The details of the PMT test and the methods for determining E m and P L are available in ASTM D4719.

Geochemical Analysis for Determination of Chemical Weathering Index
A chemical weathering index was calculated based on the weight percentage of the major oxides in the rock formed by weathering through the X-ray fluorescence (XRF) analysis. The index enables the evaluation of the degree of weathering regardless of the physical disturbance of the samples and is therefore appropriate for weathered granite, which easily shatters during sampling. In this study, the XRF analysis was conducted on weathered granite samples collected at the depths of the SPTs and PMTs at the three study sites. The chemical weathering index was calculated by converting the determined weight percentage of the major oxides into the molecular ratio.
Various chemical weathering indices have been proposed [12,[20][21][22][23]. However, in this study, the representative chemical weathering index (Vogt's ratio (VR, Equation (1)) [24]) was used to conduct a nonlinear multiple regression analysis based on the study by Lee [25], in which eight types of chemical weathering indices and geotechnical properties of weathered granite in South Korea were analyzed; the assessment revealed the adequacy of the engineering property and degree of weathering based on VR. VR is the index which is calculated by considering the mobility of alkali and alkaline oxides during the weathering process, with a larger VR corresponding toa more weathered state.
The results of the SPTs and PMTs conducted at the three sites and the VR values of the collected samples determined by the XRF analysis are presented in Table 1.

Test Data
The E m values determined by the PMTs were between 7.8 and 864.2 MPa and generally increased with depth at each test site. The E m at site A dramatically increased and those at site B decreased with depth below 29 m (Figure 4a). This tendency was also found for P L (Figure 4b). The SPT-N 60 determined by linear extrapolation conversion for a penetration of 30 cm corresponded to blows of between 61 and 644 at the three sites. Overall, SPT-N 60 tended to increase with increasing depth at each test site, but those at site B decreased with depth below 29 m ( Figure 5). As shown in Figures 4 and 5, the measured geotechnical properties showed different distribution due to different site conditions. Site A is near the riverside, so that it is rarely affected by the geological forces making fold and fissure. On the other hand, sites B and C are located in mountain areas that experienced complex geological forces (Figure 1).
The VR values, indicating the degree of weathering generally decreased with increasing depth at each test site. Weathering was affected by the vertical effective stress. Therefore, to exclude the effects resulted from the different depth and thickness at which the weathered granite layer was developed, VR was normalized using vertical effective stress and atmospheric pressure (Figure 6b); the vertical effective stress was calculated based on the results of in-situ density logging conducted at each test site. This is consistent with the results suggested in many studiesand the theoretical trend of VR, that is, the increase of VR with greaterweathering [25][26][27][28]. In this study, nonlinear multiple regression was used to estimate E m and P L based on SPT-N 60 and the normalized VR. The details of the analysis and the results are presented in the next section.   The VR values, indicating the degree of weathering generally decreased with increasing depth at each test site. Weathering was affected by the vertical effective stress. Therefore, to exclude the effects resulted from the different depth and thickness at which the weathered granite layer was developed, VR was normalized using vertical effective stress and atmospheric pressure (Figure 6b); the vertical effective stress was calculated based on the results of in-situ density logging conducted at each test site. This is consistent with the results suggested in many studiesand the theoretical trend of VR, that is, the increase of VR with greaterweathering [25][26][27][28]. In this study, nonlinear multiple regression was used to estimate Em and PL based on SPT-N60 and the normalized VR. The details of the analysis and the results are presented in the next section.   The VR values, indicating the degree of weathering generally decreased with increasing depth at each test site. Weathering was affected by the vertical effective stress. Therefore, to exclude the effects resulted from the different depth and thickness at which the weathered granite layer was developed, VR was normalized using vertical effective stress and atmospheric pressure (Figure 6b); the vertical effective stress was calculated based on the results of in-situ density logging conducted at each test site. This is consistent with the results suggested in many studiesand the theoretical trend of VR, that is, the increase of VR with greaterweathering [25][26][27][28]. In this study, nonlinear multiple regression was used to estimate Em and PL based on SPT-N60 and the normalized VR. The details of the analysis and the results are presented in the next section.

Nonlinear Multiple Regression Analysis
To derive the equations for estimating Em and PL based on the chemical weathering index (VR) determined by the XRF analysis of the collected samples and the results of the PMTs and SPTs conducted at the three considered sites, nonlinear multiple regression analysis was performed using the following three steps: 1) Deduction of the relationships between Em and SPT-N60 and between PL and SPT-N60 by simple regression analyses;

Nonlinear Multiple Regression Analysis
To derive the equations for estimating E m and P L based on the chemical weathering index (VR) determined by the XRF analysis of the collected samples and the results of the PMTs and SPTs conducted at the three considered sites, nonlinear multiple regression analysis was performed using the following three steps: (1) Deduction of the relationships between E m and SPT-N 60 and between P L and SPT-N 60 by simple regression analyses; (2) Deduction of the relationships between E m and normalized VR and between P L and normalized VR by simple regression analyses; (3) Nonlinear multiple regression analysis using the relationships deduced in steps (1) and (2) above.
In the implementation of the first step, the relationship between the PMT results (E m or P L ) and SPT-N 60 was derived through a simple regression analysis. The aim of this step was to determine the basic function of the independent variable (i.e., SPT-N 60 ) to be used for the nonlinear multiple regression analysis. Empirical relationships between E m and SPT-N 60 and between P L and SPT-N 60 obtained in related research are presented in Table 2. Based on these several empirical relationships, simple regression analysis using an allometric model and a linear model was employed to derivate each of the equations. E m increased with increasing SPT-N 60 , with both the allometric and linear models revealing relatively high correlations as shown by the coefficient of determination (R 2 ) of 0.71 and 0.71, respectively ( Figure 7). P L exhibited lower correlations in the empirical equations compared with E m (R 2 = 0.44 and 0.43, respectively) ( Figure 8). Table 2. Empirical equations for the relationships of E m and P L with SPT-N 60 .

Empirical Equations
Researchers   In the second step, the procedure of the first step was applied to normalized VR. Em was decreased with increasing normalized VR, with a higher correlation coefficient obtained for the allometric model (R 2 = 0.67) than for the linear model (R 2 = 0.31) (Figure 9). The correlation of PL with normalized VR was also higher for the allometric model compared with the linear model, although the R 2 values (0.33 and 0.18, respectively) were lower than that for the correlation between Em and normalized VR (Figure 10). In the second step, the procedure of the first step was applied to normalized VR. E m was decreased with increasing normalized VR, with a higher correlation coefficient obtained for the allometric model (R 2 = 0.67) than for the linear model (R 2 = 0.31) (Figure 9). The correlation of P L with normalized VR was also higher for the allometric model compared with the linear model, although the R 2 values (0.33 and 0.18, respectively) were lower than that for the correlation between E m and normalized VR ( Figure 10).
Subsequently, the nonlinear multiple regression analysis models of E m and P L were established by combining the allometric model, which produced the better correlations between the PMT results (E m and P L ) and SPT-N 60 and normalized VR. The obtained models are: (a n = const .) and (2)   Subsequently, the nonlinear multiple regression analysis models of Em and PL were established by combining the allometric model, which produced the better correlations between the PMT results (Em and PL) and SPT-N60 and normalized VR. The obtained models are: ) a 5 (a n = const.) and (2) The results derived by nonlinear multiple regression analysis revealed improved correlations compared with those from the equations derived by simple regression analysis. Even though the obtained slight increase in the coefficient of determination was lower than expected, this study is meaningful in that it is demonstrates that improved prediction of the Em and PL values of weathered granite can be obtained by additionally considering the VR, chemical weathering index that represents the physical properties of weathered granite. The equation for Em as a function of SPT-N60 and normalized VR is presented in Equation (4), for which R 2 = 0.76, which is larger than that for the simple regression analysis equation (Figure 7a and Figure 9a). The equation for PL derived by nonlinear multiple The results derived by nonlinear multiple regression analysis revealed improved correlations compared with those from the equations derived by simple regression analysis. Even though the obtained slight increase in the coefficient of determination was lower than expected, this study is meaningful in that it is demonstrates that improved prediction of the E m and P L values of weathered granite can be obtained by additionally considering the VR, chemical weathering index that represents the physical properties of weathered granite. The equation for E m as a function of SPT-N 60 and normalized VR is presented in Equation (4), for which R 2 = 0.76, which is larger than that for the simple regression analysis equation (Figures 7a and 9a). The equation for P L derived by nonlinear multiple regression analysis is presented in Equation (5) and, also has a higher R 2 of 0.46 compared with the corresponding simple regression equation (Figures 8a and 10a): For evaluation, the results obtained by the empirical Equations (4) and (5) derived in this study were compared with the results of equations derived in relevant previous studies presented in Table 2, as shown in Figure 11. The types of soils for the equation presented in Table 2 are different from that used in this study. However, unfortunately, there are very few studies for estimating the relationship between the results of PMT and SPT on weathering granite. Therefore, in this study, the most similar studies performed on sandy material among the existing studies were compared with the Equations (4) and (5). The equations in the previous studies used a single variable, SPT-N 60 , and can thus be only used to estimate E m or P L for a certain SPT-N 60 . However, the equations derived in this study use an additional variable, VR, which is a measure of the degree of weathering and can thus be used to estimate E m and P L from SPT-N 60 . Furthermore, the present empirical equations derived by nonlinear multiple regression can more accurately reproduce the PMT results for South Korean granite compared with the equations suggested by the other studies that are presented in Table 2

Conclusions
In this study, the modulus of deformation Em (pressuremeter modulus) and limit pressure PL of weathered granite in South Korea were assessed based on the SPT-N60 value and chemical weathering index VR. Nonlinear multiple regression analysis was conducted using SPT-N60 and VR as the independent variables, specifically for the values measured at three sites in South Korea. The analysis was used to derive empirical equations for Em and PL, and the predictions of the equations were compared with the equations suggested in the previous relevant studies. The study and its findings can be summarized as follows: 1) The relationships between the PMT and SPT-N60 results were derived by simple regression analyses, which revealed that Em tended to increase with increasing SPT-N60. Relatively high correlations were observed when both an allometric model and linear model were utilized, as represented by R 2 of 0.71. The correlations were lower for PL, as represented by the R 2 values of 0.44 and 0.43 for the two models, respectively, revealing no significant difference. 2) The chemical weathering index that has been rarely considered in previous studies was used to evaluate the PMT results. The normalized VR with vertical effective stress revealed a relatively good correlation with Em (R 2 = 0.67). Therefore, it is useful as a simple method for the estimation of Em of weathered granite in preliminary site characterization. 3) Nonlinear multiple regression analyses were conducted by combining the allometric models that produced improved correlations between Em, PL, SPT-N60, and normalized VR. The obtained equations of Em and PL had better R 2 values (0.76 and 0.46, respectively) than the equations obtained by simple regression in other studies. Even though the obtained slight increase in the coefficient of determination was lower than expected, this study is meaningful in that it is possible to obtain improved prediction of the Em and PL values of weathered granite by additionally considering VR, which is a chemical weathering index that represents the physical properties of weathered granite. 4) Empirical equations suggested in other studies were based on a single variable (i.e., SPT-N60) and can thus be only used to estimate either Em or PL for a particular SPT-N60. However, the empirical equations proposed in this paper utilize an additional variable VR can thus predict the Em and PL by considering both the degree of weathering and SPT-N60. To determine the engineering properties of geo-materials, this study proposes the Em and PL for use in geotechnical surveys of weathered granite in South Korea. Although the equation proposed by Chiang and Ho [6] was based on the analysis of weathered granite in Hong Kong, which is similar to the target stratum of this study, it underestimates E m and P L for the weathered granite of the present study. This is because Chiang and Ho [6] derived the equations using data that contained SPT-N 60 values of ≤130, as opposed to those with SPT-N 60 values of 61-644 that were used in the present study. The equations proposed by Bozbey and Togrol [8] were based on the results of SPTs and PMTs conducted on the medium to very dense sandy soils with SPT-N 60 ≤ 100 and also underestimate the PMT results for the weathered granite examined in the present study. However, Cheshomi and Ghodrati [9] obtained their empirical equations based on data for dense to very dense silty sands (SPT-N 60 < 50), with the predictions of E m for weathered granite comparable to those of the present corresponding equation; however, their predicted P L are higher than those obtained in the presented study. Regarding the similarity for E m , the E m values for the specific samples used by Cheshomi and Ghodrati [9], where SPT-N 60 ≥ 35, were approximately 30% larger than those for the samples used by Bozbey and Togrol [8]. Therefore, a local correlation based on the local rock characteristics is important for predicting the engineering properties of geo-materials. The proposed equations of E m and P L are intended for use in the geotechnical survey of weathered granite in South Korea.

Conclusions
In this study, the modulus of deformation E m (pressuremeter modulus) and limit pressure P L of weathered granite in South Korea were assessed based on the SPT-N 60 value and chemical weathering index VR. Nonlinear multiple regression analysis was conducted using SPT-N 60 and VR as the independent variables, specifically for the values measured at three sites in South Korea. The analysis was used to derive empirical equations for E m and P L , and the predictions of the equations were compared with the equations suggested in the previous relevant studies. The study and its findings can be summarized as follows: (1) The relationships between the PMT and SPT-N 60 results were derived by simple regression analyses, which revealed that E m tended to increase with increasing SPT-N 60 . Relatively high correlations were observed when both an allometric model and linear model were utilized, as represented by R 2 of 0.71. The correlations were lower for P L , as represented by the R 2 values of 0.44 and 0.43 for the two models, respectively, revealing no significant difference. (2) The chemical weathering index that has been rarely considered in previous studies was used to evaluate the PMT results. The normalized VR with vertical effective stress revealed a relatively good correlation with E m (R 2 = 0.67). Therefore, it is useful as a simple method for the estimation of E m of weathered granite in preliminary site characterization. (3) Nonlinear multiple regression analyses were conducted by combining the allometric models that produced improved correlations between E m , P L , SPT-N 60 , and normalized VR. The obtained equations of E m and P L had better R 2 values (0.76 and 0.46, respectively) than the equations obtained by simple regression in other studies. Even though the obtained slight increase in the coefficient of determination was lower than expected, this study is meaningful in that it is possible to obtain improved prediction of the E m and P L values of weathered granite by additionally considering VR, which is a chemical weathering index that represents the physical properties of weathered granite. (4) Empirical equations suggested in other studies were based on a single variable (i.e., SPT-N 60 ) and can thus be only used to estimate either E m or P L for a particular SPT-N 60 . However, the empirical equations proposed in this paper utilize an additional variable VR can thus predict the E m and P L by considering both the degree of weathering and SPT-N 60 . To determine the engineering properties of geo-materials, this study proposes the E m and P L equations for use in geotechnical surveys of weathered granite in South Korea.