Correlation analysis of physical and mechanical parameters of inland ﬂ uvial - lacustrine soft soil based on di ﬀ erent survey techniques

: Based on the collected soil property index test data of more than 2,500 groups of inland ﬂ uvial - lacus - trine soft soil, the correlation of physical and mechanical parameters of this soft soil was systematically analyzed. The results show that the physical indexes of inland ﬂ u - vial - lacustrine soft soil are close to that of marine soft soil, while its mechanical indexes are higher. However, the variation coe ﬃ cient of its mechanical indexes is much larger than that of the physical indexes. In addi - tion, it is found that the cone penetration parameters of this soft soil are signi ﬁ cantly correlated with its physical and mechanical indexes by establishing a series of empirical relationships between the static point resistance and the natural unit weight, the liquidity index, the quick shear cohesion, and vane shear strength. On the basis of the pre - vious research results, the disturbance strength of inland ﬂ uvial - lacustrine soft soil can be converted into in situ strength by deriving the theoretical formula between the vane shear strength and the disturbance degree. The calcu - lation process of the above conversion relation is explained in detail through an engineering case, which indicates that the theoretical formulas have good applicability for inland ﬂ uvial - lacustrine soft soil.


Introduction
Soft soil is a kind of special soil with the widest distribution, the most involvement, and the greatest impact on engineering among all kinds of foundation soils, and its genesis, structures, and forms are often quite different [1][2][3][4][5][6][7][8]. According to the geomorphological characteristics, the distribution areas of soft soils can be divided into coastal plains, lacustrine plains, river alluvial plains, mountain valleys, peat swamps, etc. Among them, there are many genetic types of soft soils in coastal plains, including littoral facies, lagoon facies, drowned-valley facies, and delta facies. The origin of the soft soil in other distribution areas is mainly fluviatile-lacustrine facies and valley facies, and the fluviatile-lacustrine soft soil is mainly concentrated in the inland, so it is called the inland fluvial-lacustrine soft soil [9]. The inland fluviallacustrine soft soil is distributed sporadically and not in pieces, with the characteristics of bedding and texture. Sometimes it is mixed with fine sand layers, and the stratification is uneven, which is a typical layered geological formation. Since the early construction of high-grade highways is mostly concentrated in the economically developed coastal areas, the research on soft soil foundation at home and abroad mainly focuses on the coastal soft soil, while the research on inland fluvial-lacustrine soft soil is seldom carried out. At present, Chinese scholars are focusing on the research of engineering characteristics, foundation deformation calculation, and stability monitoring of inland fluvial-lacustrine soft soil, so as to propose such soft soil foundation treatment schemes with low investment and effective result.
Geotechnical investigation is the important premise and foundation for engineering design and construction, and the correctness and reliability of the survey data are crucial for selecting the appropriate foundation treatment scheme. Compared with the common marine sedimentary soft soil, the inland fluvial-lacustrine soft soil has smaller continuous distribution range, uneven stratification, and the thickness of soft soil layers varies greatly, so the investigation methods of the two types of soft soils are different. However, there is no clear provision for the survey technology of inland fluvial-lacustrine soft soil in the current domestic and foreign standard specifications, but only for the survey technology of the marine soft soil, which makes relevant technicians often have a certain degree of randomness in the survey work of inland fluvial-lacustrine soft soil foundation.
In addition, most of the research on soft soil foundation survey at home and abroad is carried out for marine soft soil, and the content involved mainly focuses on in situ tests, sampling disturbance and laboratory geotechnical tests. In terms of in situ testing, Duan et al. [10] took the marine clay from Lianyungang in Jiangsu Province of China as the research object, the relationships between undrained shear strength (S u ) and seismic piezocone test (SCPTU) parameters at the Lianyungang site were determined by SCPTU, and the results showed that SCPTU tests can be used comprehensively to estimate the S u of Jiangsu marine clay. Konkol et al. [11] revealed a geotechnical characterization of deltaic soft soil deposits in the Vistula Marshlands, northern Poland, and proposed the limited applicability of organic soil classifications based on piezocone penetration test (CPTU) and dilatometer test (DMT). Firuzi et al. [12] conducted correlation analysis on physical and mechanical indexes of alluvial soft soil through different in situ tests, and obtained regression relationships between some parameters. Bombasaro and Kasper [13] conducted multiple groups of CPTU on marine soft soil in the Pearl River Delta region, and the random field model parameters of normalized tip resistance were proposed. As for the research on sampling disturbance, Hu [14] pointed out that the disturbance of soil samples was composed of stress release, artificial disturbance, and environmental disturbance. Schmertmann [15] proposed a quantitative evaluation method, that is, the sampling disturbance index was used to reflect the degree of soil disturbance. Ladd and Lambe [16] found that the undrained shear modulus was very sensitive to soil sample disturbance, and the corresponding formula was also proposed. On the other hand, in view of the research on laboratory soil tests, many scholars conducted the relatively comprehensive analysis on the correlation between physical and mechanical parameters and indexes of soft soil in several coastal areas of China through a large number of laboratory tests, including Jiangsu Province [17][18][19][20], Shanghai [21], Tianjin [22], Zhejiang Province [23], Guangdong Province [24] etc., thus providing a basis for the value of engineering geotechnical parameters in different coastal soft soil areas.
Based on the above literature results, it can be seen that although domestic and foreign scholars have carried out a lot of research on the engineering characteristics of soft soil in coastal areas and the relationship between soil property indexes by using different investigation techniques such as in situ tests, drilling sampling, and laboratory geotechnical tests, there are relatively few studies on the relationship between various soil property indicators obtained by different survey methods for inland fluviallacustrine soft soil due to the obvious regional characteristics of soft soils, which cannot provide reference for the investigation of this kind of soft soil. In addition, the above methods for evaluating soil disturbance degree can only reflect the change in soil void ratio caused by sampling disturbance, but the relationship between the strength and disturbance degree of inland fluvial and lacustrine soft soil has not been established.
In view of this, according to the collected laboratory geotechnical test and in situ test data of more than 2,500 groups of inland fluvial-lacustrine soft soil, the correlation between cone penetration test parameters and soil property indexes of inland fluvial-lacustrine soft soil is first analyzed by the regression analysis method on the basis of statistical analysis of the soil property indexes, and corresponding empirical formulas are obtained in this study. On the other hand, in view of the unavoidable problem of sampling disturbance, the relationship between the strength of inland fluvial-lacustrine soft soil and the disturbance degree is further explored combined with previous research results, and the rationality of the relationship between the two is verified by a real case study. The research results can provide reference for the investigation and design of soft soil ground in the inland fluvial-lacustrine sediments.

Statistical analysis of soil properties of inland fluviallacustrine soft soil
Inland fluvial-lacustrine soft soil in China has sporadic distribution. In order to study the engineering characteristics and regional distribution law of soil property indexes of inland fluvial-lacustrine soft soil in China, in this study, a large number of solid projects were analyzed and more than 2,500 groups of soil properties of inland fluvial-lacustrine soft soil in different regions of China were collected. The statistical results are shown in Tables 1 and 2. In addition, by referring to relevant research results [22][23][24][25][26], the physical and mechanical properties of inland fluviallacustrine soft soil and marine soft soil in different coastal areas were compared. The comparison results are shown in Table 3. From Tables 1-3, it can be seen that the overall characteristics of inland fluvial-lacustrine soft soil are as follows: (1) Compared with other soil, inland fluvial-lacustrine soft soil still has the basic characteristics of higher natural moisture content, higher compressibility, larger void ratio, and lower shear strength.
(2) Compared with the variation coefficient of physical index of inland fluvial-lacustrine soft soil, the variation coefficient of mechanical index is obviously larger, and the effect of the variation in mechanical index of this kind of soft soil must be considered in engineering.

Correlation between cone penetration test parameters and soil property indexes
Considering that the inland fluvial-lacustrine soft soil has rheological property and other undesirable properties, the sampling continuity is poor, and it is difficult to accurately reflect the real stress and strain state of soil by using single drilling sampling in laboratory test. However, the in situ test is a direct field test of the soil in the basic natural state, which can effectively avoid the problem of sampling disturbance. At present, there are many in situ test methods at home and abroad. In order to improve the universality of engineering applications, this study only conducts relevant research on the two most commonly used soft soil in situ testing methods: cone penetration test (CPT) [27,28] and vane shear test (VST) [29,30].
In the investigation of soft soil foundation, the correlation between soil property indexes is mainly reflected by empirical formula. At present, relevant scholars at home and abroad have put forward some practical empirical formulas for the correlation between CPT parameters and soil property indexes of marine soft soil. However, these empirical formulas often have limited range of CPT parameters and are not applicable to inland fluvial-lacustrine soft soil. Therefore, it is necessary to study the correlation between CPT parameters and soil property indexes of inland fluvial-lacustrine soft soil.
Combined with the difficulty of obtaining each index, the cone tip resistance (P s ), natural unit weight (γ), liquidity index (I L ), quick shear cohesion (C q ), and vane shear strength (C u ) are selected as the correlation index of the study.

Correlation analysis of CPT parameters and natural unit weight
Through linear regression analysis of P s and γ of inland flux-lacustrine soft soil, the correlation diagram of two parameters was obtained, as shown in Figure 1. As can be seen from Figure 1, P s increases continuously with the increase in γ for inland fluvial-lacustrine soft soil, and the relationship between them is linearly increasing on the whole. The regression equation between these two parameters is as follows: Among them, the correlation coefficient (R) is 0.742, indicating that the fitting degree of this line is good.
Inland  In addition, the reliability of the regression equation was further tested by R. The confidence of regression equation P = 0.98, that is, the significance level λ = 0.01, and the critical value of correlation coefficient r 0 = 0.181 can be obtained by looking up the table. Since r 0 = 0.181 < R = 0.742, the correlation of the above regression equation is significant.

Correlation analysis of CPT parameters and natural liquidity index
Similarly, through linear regression analysis of P s and I L of inland flux-lacustrine soft soil, the correlation diagram of two parameters was obtained, as shown in Figure 2. As can be seen from Figure 2, P s and I L show a linear decreasing relationship on the whole, that is, P s gradually decreases with the increase in I L . The regression equation between these two parameters is as follows: where R = 0.736, indicating that the fitting degree of this line is good. In addition, the reliability of the regression equation was further tested by R. Since r 0 = 0.181 < R = 0.736, the correlation of the above regression equation is significant.

Correlation analysis of CPT parameters and quick shear cohesion
C q is the basic mechanical index of soil, which reflects the ultimate strength of soil to resist shear failure. Through linear regression analysis of P s and C q of inland fluvial-lacustrine soft soil, the correlation diagram of two parameters was obtained, as shown in Figure 3. As can be seen from Figure 3, P s gradually increases with the increase in C q . The regression equation between these two parameters is as follows: where R = 0.813, indicating that the fitting degree of this line is good. In addition, the reliability of the regression equation was further tested by R. Since r 0 = 0.181 < R = 0.813, the correlation of the above regression equation is significant.

Correlation analysis of CPT parameters and vane shear strength
In order to explore the correlation between strength parameters measured by two common in situ testing methods (CPT and VST) of soft soil, this study carried out linear regression analysis on P s and C u of inland fluvial-lacustrine soft soil to obtain the correlation diagram of these two parameters, as shown in Figure 4. As can be seen from Figure 4, there is a linear increasing relationship between P s and C u on the whole. The regression equation between these two parameters is as follows: where R = 0.851, indicating that the fitting degree of this line is good. In addition, the reliability of the regression equation was further tested by R. Since r 0 = 0.181 < R = 0.851, the correlation of the above regression equation is significant.

Relationship between sampling disturbance and soil strength
In the survey of highway soft soil foundation, sampling disturbance is inevitable, and the strength of soil after disturbance will change with the change in disturbance degree. Although many scholars at home and abroad have proposed some methods to determine the soil disturbance degree, the relationship between the disturbance degree of inland fluvial-lacustrine soft soil and its strength and yield stress has not been studied in detail. Therefore, on the basis of previous research results, this study will further study the relationship between sampling disturbance and strength characteristics of inland fluvial-lacustrine soft soil.

Correlation analysis between disturbance degree and soil strength
In view of the influence of disturbance on soil strength and yield stress, Butterfield [31] found that the double logarithmic coordinates of consolidation pressure (p) and specific volume (v = 1 + e) can better describe the characteristics of soil consolidation compression curve based on a large number of consolidation test results. Hong and Onitsuka [32] further improved the traditional volume compression method by combining Butterfield system, and proposed a simple expression of disturbance degree (D) as follows: where C CLB and C CLR , respectively, represent the slope of the compression curve of the disturbed soil and the remolded soil in the double logarithmic coordinates before yielding ( Figure 5).
On this basis, in order to explore the relationship between yield stress and disturbance degree, Nagaraj and Chung [33] found that the corresponding point of yield stress (lg ′ p y and ln(1 + e y )) was located on the same line in the above double logarithmic coordinate no matter how disturbed the soil sample was ( Figure 6). In addition, as shown in Figure 6, (lg( ′ p yr ) and ln(1 + e r )) is the intersection coordinate of the compression curve of the remolded soil and the extension of the above line, and ′ p yr can be approximated as the equivalent yield stress of the residual strength of the remolded soil. According to Figure 6, if ′ p yr can be determined, the early yield stress of the soil with different disturbance degrees ( ′ p y ) can be obtained. On the other hand, in view of the relationship between soil strength and yield stress, Leroueil et al. [34] analyzed that there was a certain relationship between C u and ′ p y for soft soil, and the ratio was a function of I P given as follows:    For undisturbed soil, ′ p y in the above equation is ′ p c . In this study, combined with the survey data of several inland fluvial-lacustrine soft soil foundations, it is found that for this completely disturbed soft soil (i.e., remolded soil), the relationship between C u and I L is shown in Figure 7, and the corresponding formula is as follows: For the inland fluvial-lacustrine soft soil, ′ p yr can be obtained by substituting equation (8) in equation (7). The corresponding e r can be expressed as follows: As shown in Figure 6, it is assumed that (lg ′ p c , ln(1 + e 0 )), (lg ′ p y , ln(1 + e y )), and (lg ′ p yr , ln(1 + e r )) are the coordinates corresponding to the early yield stress of undisturbed soil, different disturbed soil, and completely disturbed soil, respectively. Combined with the above double logarithmic coordinates, the early yield stress points of soils with different disturbance degrees are all located on the same straight line, the relationship between ′ p y and D for inland fluvial-lacustrine soft soil can be obtained as follows: Since the yield stress of soils with different disturbance degrees in the double logarithmic coordinate is on the same straight line, the M value of soil samples at the same location is equal to the slope of the line of soil yield stress points under any two different disturbance degrees. That is In conclusion, for the inland fluvial-lacustrine soft soil, C u of undisturbed soil can be calculated according to the above series of formulas, which can be used to verify the actual in situ measured values. The specific calculation steps are as follows: (1) The ′ p y and e y of soils with different disturbance degrees in the same location can be measured by consolidation compression test, and the M value can be calculated according to equation (12).
(2) According to C CLB obtained from the consolidation compression curve of disturbed soil in the double logarithmic coordinate, and then substituting the previously obtained M value in equation (11), ′ p c can be obtained.
(3) Substituting the obtained ′ p c in equation (7), C u of undisturbed soil can be calculated.
In addition, combined with the soil physical and mechanical parameters measured in the laboratory tests, C CLR can be calculated by equations (9) and (10). Finally, D can be determined by substituting the obtained C CLB and C CLR in equation (5), so that the corresponding relationship between the disturbance degree of the inland fluvial-lacustrine soft soil and the estimated vane shear strength of the undisturbed soil can be obtained.

Verification and analysis
Taking the soft soil of the Wushao section of , in the inland fluvial and lacustrine soft soil area as an example, the conversion relationship between soil strength, disturbance degree and yield strength proposed above is explained in detail, and the error between the calculated value and the measured value of the vane shear strength is compared. Table 4 shows the physical and mechanical indexes of the soft soil in this section measured through laboratory tests, and Table 5 shows the consolidation compression test results of three groups of soft soils with different disturbance degrees. For consolidation compression test, it is necessary to preload 1 kPa on the sample before the test, so that the parts of the consolidation instrument are closely connected to prevent additional deformation of soil samples. Therefore, it is assumed that the natural void ratio of soil is equal to the initial void ratio at the load of 1 kPa.
According to the test results in Table 4, on the premise that e r is known to be 1.005, ′ p yr can be calculated as 6.748 kPa according to equations (9) and (10), and C CLR = 0.196. In addition, according to the results of consolidation compression test in Table 5, C CLB values of three groups of soil samples with different disturbance degrees can be calculated as 0.028, 0.017, and 0.023, respectively. Substituting the C CLB and C CLR obtained above in equation (5), it can be further calculated that the corresponding disturbance degrees of three groups of soil samples are 14.3, 8.7, and 11.7%, respectively. The disturbance degree calculation results of three groups of soil samples obtained above are summarized, as shown in Table 6.
Based on the above test results and calculation results, ′ p y with different disturbance degrees can be calculated as 14.710, 23.944, and 32.666 kPa, and the corresponding M values are 0.384, 0.253, and 0.187, respectively. Then, according to equation (11), ′ p c of three groups of undisturbed soil in the same location can be calculated as 17.901, 29.641, and 50.215 kPa, respectively. Finally, by substituting the calculated ′ p c value in equation (7), it can be calculated that C u of three groups of undisturbed soil are 15.4, 25.5, and 43.2 kPa, which are compared and analyzed with the actual in situ measurement values at the same site, the comparison results are shown in Table 7.
As can be seen from Table 7, the errors between the field measured value and the theoretical calculated value of three groups of soil samples are relatively small, indicating that the above theoretical formulas have good applicability for inland fluvial-lacustrine soft soil.

Conclusion
(1) Based on the statistical results of soil indexes of more than 2,500 groups of inland fluvial-lacustrine soft soils in different regions of China, it is found that the physical indexes of inland fluvial-lacustrine soft soil are close to those of marine soft soil, while the mechanical indexes of inland fluvial-lacustrine soft soils are slightly better. However, the variation coefficient of mechanical indexes of inland fluvial-lacustrine soft soil is much larger than that of physical indexes, indicating that the influence of mechanical indexes variability of this kind of soft soil should be fully considered in engineering. (2) Combined with a large amount of engineering investigation data, it is found that there are certain differences in the soil index characteristics of inland fluvial-     Among them, the soil indexes in the southern region have great variability and relatively poor properties, while the soil indexes in the central and northern regions are relatively consistent, indicating that the inland fluvial-lacustrine soft soil in the southern region should be treated with stronger foundation measures than other regions. (3) Through the statistical analysis of the correlation between the cone penetration parameters of inland fluvial-lacustrine soft soil and its soil property indexes, it is found that the static point resistance has a linear increasing relationship with the natural unit weight or the quick shear cohesion or the vane shear strength in general, except that the static point resistance has a linear decreasing relationship with the liquidity index. However, there is a significant correlation between the cone penetration parameters of inland fluvial-lacustrine soft soil and soil indexes, and a series of empirical relationships between static point resistance and the natural unit weight, the liquidity index, the quick shear cohesion, and the vane shear strength are established respectively, which has important reference value for calculating other parameters from known parameters. (4) Aiming at the unavoidable problem of sampling disturbance, on the basis of previous research results, the relationship between the vane shear strength, disturbance degree and yield strength of inland fluvial-lacustrine soft soil is further deduced. According to the series of relationship, the disturbance strength of inland fluvial-lacustrine soft soil can be converted into in situ strength. In addition, the calculation process of the above conversion relation is explained in detail through an engineering case, and the calculation results show that the theoretical formulas have good applicability to inland fluvial-lacustrine soft soil.

List of symbols
a v compression coefficient C u vane shear strength C uu consolidated quick shear cohesion C CLA slope of the compression curve of the disturbed soil in the double logarithmic coordinates after yielding C CLB slope of the compression curve of the disturbed soil in the double logarithmic coordinates before yielding C CLR slope of the compression curve of the remolded soil in the double logarithmic coordinates before yielding C q quick shear cohesion D disturbance degree e Natural void ratio e 0 Initial void ratio e r void ratio corresponding to the yield stress of the remolded soil e y void ratio corresponding to the yield stress of the disturbed soil E s compression modulus I L liquidity index I P plasticity index p consolidation pressure ′ p c yield stress of undisturbed soil p 0 ′ overlying effective stress of soil sample ′ p y yield stress of disturbed soil ′ p yr yield stress of remolded soil P confidence P s static point resistance r 0 critical value of the correlation coefficient R correlation coefficient S u undrained shear strength v specific volume w natural moisture content w L liquid limit w P plastic limit ρ natural density γ natural unit weight λ significance level φ q quick shear angle of internal friction φ uu consolidated quick shear angle of internal friction Conflict of interest: The authors declare that there are no conflicts of interest regarding the publication of this article.
Ethical approval: The conducted research is not related to either human or animal use.

Data availability statement:
The data used to support the findings of this study are available from the corresponding author upon request.