Gravelly soil liquefaction settlement prediction method based on dynamic penetration test

Abstract

The invention belongs to the technical field of geotechnical engineering, and provides a gravelly soil liquefaction settlement prediction method based on a dynamic penetration test, which can make full use of in-situ dynamic penetration test data, comprehensively considers physical characteristics of gravelly soil and uncertainty of liquefaction settlement, and provides a gravelly soil liquefaction settlement prediction method based on a dynamic penetration test. Therefore, the dynamic response characteristics are effectively reflected, and a scientific basis is provided for anti-seismic safety evaluation and design of the foundation. According to the technical scheme, the gravelly soil liquefaction settlement prediction method based on the dynamic penetration test comprises the following steps that S1, a DPT test is conducted on a site, the DPT hammering number is corrected, and a volume strain curve is established, S2, prediction settlement and the probability of exceeding a given settlement value are calculated, and S3, a liquefaction settlement exceeding probability curve is drawn according to different target settlement values.

Description

Technical Field

[0001] This invention relates to a method for predicting liquefaction settlement of gravelly soil based on dynamic penetration testing, which belongs to the technical field of geotechnical engineering. Background Technology

[0002] Earthquake liquefaction is a crucial research issue in earthquake engineering. It refers to the phenomenon where saturated sand or gravelly soil experiences a significant decrease in strength and stiffness due to a rapid increase in pore water pressure under intense earthquake vibrations. Liquefaction often causes uneven settlement, lateral displacement, and even overall instability in buildings and infrastructure, seriously threatening the safety of engineering structures and personnel. Extensive earthquake damage surveys have shown that liquefaction and liquefaction-induced settlement problems also exist in coarse-grained soil layers such as gravelly sand and gravelly silty soil, especially prominent in areas prone to strong earthquakes and in embankment foundations.

[0003] Currently, the prediction of liquefaction and its resulting foundation settlement mainly relies on in-situ testing and empirical methods. Among these, the Standard Penetration Test (SPT) and the Cone Penetration Test (CPT) are the two most widely used in-situ testing methods, and relatively mature empirical formulas for liquefaction discrimination and settlement prediction have been developed. However, for foundation soil layers containing a certain particle size distribution, especially those dominated by gravel, both SPT and CPT have limitations in terms of testing accuracy and applicability. 1. Limitations of SPT: SPT often encounters problems such as probe failure, excessive or unstable blow count in gravelly soils, making it difficult to obtain effective blow count data; due to severe sample disturbance and uneven energy transfer, the test results are difficult to accurately reflect the actual soil liquefaction resistance. 2. Limitations of CPT: CPT often leads to data distortion or even test interruption in coarse particles, gravel interlayers, or pebble layers due to probe obstruction, abnormal fluctuations in friction signals, or sensor overload. At the same time, CPT equipment is highly sensitive to coarse particles and obstacles, is easily damaged, and is difficult to advance in gravel layers, which significantly reduces the continuity and reliability of its tests and greatly limits its application range.

[0004] Dynamic penetration testing (DPT), as an efficient, economical, and easy-to-operate in-situ testing method, is widely used in my country and other earthquake-prone countries. DPT measures the number of blows required for a standard falling hammer to penetrate a certain depth in soil, enabling rapid acquisition of the relative density and mechanical properties of foundation soil. Existing research has shown that DPT test results have a good correlation with the relative density, shear strength, and liquefaction potential of the soil. Therefore, DPT has significant potential for application in the liquefaction evaluation of gravelly soil layers.

[0005] However, current research on liquefaction identification and settlement prediction based on earthquake liquefaction testing (DPT) remains relatively limited. Existing methods mainly focus on liquefaction identification of gravelly soils and liquefaction settlement analysis of sandy soils, while research on settlement prediction caused by liquefaction of gravelly soils is relatively insufficient, even nonexistent, lacking systematic computational models and probabilistic analysis frameworks. Furthermore, foundation settlement caused by earthquake liquefaction exhibits significant uncertainty and regional differences, and existing prediction models often struggle to balance deterministic analysis and probabilistic assessment, thus limiting their applicability in seismic design and risk assessment for engineering projects.

[0006] Therefore, there is an urgent need to propose a method for predicting liquefaction settlement of gravelly soil based on dynamic penetration test (DPT). This method can make full use of in-situ dynamic penetration test data, comprehensively consider the physical properties of gravelly soil and the uncertainty of liquefaction settlement, thereby effectively reflecting its dynamic response characteristics and providing a scientific basis for the seismic safety assessment and design of foundations. Summary of the Invention

[0007] To address one of the aforementioned technical deficiencies, this invention provides a method for predicting liquefaction settlement of gravelly soil based on dynamic penetration tests. This method can fully utilize in-situ dynamic penetration test data, comprehensively consider the physical properties of gravelly soil and the uncertainty of liquefaction settlement, thereby effectively reflecting its dynamic response characteristics and providing a scientific basis for the seismic safety assessment and design of foundations.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: a method for predicting liquefaction settlement of gravelly soil based on dynamic penetration tests, comprising the following steps: S1. Conduct DPT tests on the site, correct the DPT hammer blow count, and establish a volumetric strain curve; S2. Calculate the predicted settlement and the probability of exceeding the given settlement value; S3. Plot the liquefaction settlement exceedance probability curve based on different target settlement values.

[0009] In step S1, DPT testing is performed on the site, the DPT blow count is corrected, and a volumetric strain curve is established. The specific steps are as follows: S11. Determine the thickness H of the soil layer for testing at the site, and divide the soil layer into layers, labeled 1, 2, 3… n DPT testing was conducted to obtain the measured DPT hammer blow count for each soil layer. ; S12, Correction coefficient for overburden pressure C N and the actual measured DPT hammer blow count for each soil layer The product of these can be converted into the corrected DPT hammer blow count for each soil layer. : (1); In the formula, This indicates the corrected DPT hammer blow count for each soil layer; This represents the actual number of DPT hammer blows measured for each soil layer; C N This indicates the overburden pressure correction factor; (2); In the formula, Indicates the effective stress of the overlying material; S13. For a horizontal free site, the vertical strain and volumetric strain ε of the soil caused by an earthquake. v Similarly, in order to measure the volumetric strain ε v - Safety factor F S – Relative density D r The relationship is transformed into a more engineering-practical ε v – F S – Relationships need to be established. D r and The relationship between them: (3); S14, based on volumetric strain ε v - Safety factor F S – Relative density D r Relationship, substitution D r and The relationship between the soil layers is used to calculate the liquefaction volumetric strain ε of each soil layer. v ; Volumetric strain ε v - Safety factor F S – Relative density D r The correspondence is as follows: (4); In the formula, , , , , , ; According to formula 3-4, ε v – F S – D r The correlation is transformed into ε v – FS – The relationship, and thus obtained Volumetric strain ε v With safety factor F S And the corrected DPT hammer strike count A one-to-one correspondence is established, and then the liquefaction volumetric strain ε of each soil layer is calculated. v The original image is approximated by the following equation through curve fitting: (5); In the formula, , , , , .

[0010] The safety factor in step S14 F S The formula is as follows: F S =CRR / CSR (6); In the formula, CSR is the liquefaction stress ratio; CRR is the liquefaction resistance ratio; The specific formula for CSR is as follows: (7); In the formula, CSR 7.5 This is the equivalent periodic stress ratio or liquefaction stress ratio; and These are the total overburden stress and effective overburden stress of the soil at the calculated depth, respectively, in kPa; a max The maximum ground acceleration is given in m / s². 2 ; g The acceleration due to gravity is m / s². 2 ; r d Stress reduction factor; MSF is the magnitude scaling factor; K σ This is the overburden stress correction factor; r d The calculation formula is as follows: (8); In the formula, z represents the depth, in meters (m). MSF is the magnitude. M w The function is calculated using the following formula: (9); K σ The calculation formula is as follows: (10); In the formula, f =0.7; It is reference pressure; The specific formula for CSR is as follows: (11); Calculating CRR requires knowing the liquefaction probability. P L The value of is used to calculate the liquefaction probability using the following formula. P L : (12); In the formula, M w It is the magnitude of the earthquake; It is the inverse function of the cumulative distribution function of the standard normal distribution; It is the effective stress of the overlying layer; It is the reference pressure; GC represents the gravel content of the soil layer.

[0011] The steps in step S2, which involve calculating the predicted settlement and the probability of exceeding a given settlement value, are as follows: S21. For each soil layer at each DPT measuring point, calculate the liquefaction settlement of the entire soil layer using the following formula: (13); In the formula, S p Ground subsidence caused by liquefaction; ε v,i For the first i Soil volumetric strain; Δz i For the first i Soil layer thickness; I D,i This is a liquefaction indicator variable, with a value of 1 for liquefaction and 0 for non-liquefaction. S22, liquefaction indicator variable I D,i Treating it as a random variable, its expected value and variance are related to the liquefaction probability. P L Relatedly, calculate the average settlement of this soil layer. and the variance of the soil layer : The relative frequency of occurrence is denoted as abbreviated as This indicates the liquefaction probability of the soil layer. Its expression is: (14); The relative frequency of occurrence is denoted as abbreviated as This indicates the liquefaction probability of the soil layer as 1- Its expression is: (15); Therefore, the average settlement of this soil layer and the variance of the soil layer It can be determined as follows: (16); (17); Using the assumption that the liquefaction indicator functions of each soil layer are independent, the average settlement of the entire soil layer is predicted. variance of the entire soil layer The following can be calculated by summation: (18); (19); Predicting settlement It is considered to be a log-normal distribution with a mean of The standard deviation is , Equivalent standard normal distribution variable It can be represented as: (20); In the formula, The mean and standard deviation are as follows: (twenty one); (twenty two); coefficient of variation The probability of exceeding a given settlement value s P ( S p > s The following method can be used to calculate: (twenty three).

[0012] In step S3, liquefaction settlement exceedance probability curves are plotted based on different target settlement values. The specific steps are as follows: By analyzing several given settlement values s Repeatedly calculate the exceedance probability and plot the exceedance probability. The relationship curve with a given settlement value s is used to obtain the site-specific probability curve of settlement exceeding the liquefaction limit. This curve shows the probability of exceeding a specific settlement limit and clarifies the probability of exceeding a specific settlement amount.

[0013] The method for predicting liquefaction settlement of gravelly soil based on dynamic penetration test provided by this invention establishes the conversion relationship between volumetric strain, relative density, and DPT corrected blow count. By combining quantitative analysis and probabilistic statistics, it achieves a reasonable assessment of liquefaction settlement of gravelly soil, improves the accuracy and reliability of settlement prediction, and has important significance for the evaluation and design of foundation seismic safety in actual engineering projects. It can provide a scientific basis for seismic reinforcement, project site selection, and construction scheme optimization. Attached Figure Description

[0014] The present invention will now be described in further detail with reference to the accompanying drawings; Figure 1 This is a schematic diagram illustrating the steps of the gravel soil liquefaction settlement prediction method based on dynamic penetration test of the present invention. Figure 2 This is the curve used in this invention to determine the volumetric strain based on the safety factor; Figure 3 These are typical DPT curves and volumetric strain calculation results in embodiments of the present invention; Figure 4 The above figures show the site-specific probabilistic liquefaction settlement exceedance curve and observed settlement curve of the DPT-3 measuring point under the action of the 2016 Muisne-Pednares earthquake in an embodiment of the present invention. Figure 5 This is a diagram showing the predicted settlement points in a liquefied site according to an embodiment of the present invention. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments; based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] like Figure 1 As shown, the present invention provides a method for predicting liquefaction settlement of gravelly soil based on dynamic penetration tests, comprising the following steps: S1. Conduct DPT tests on the site, correct the DPT hammer blow count, and establish a volumetric strain curve; S2. Calculate the predicted settlement and the probability of exceeding the given settlement value; S3. Plot the liquefaction settlement exceedance probability curve based on different target settlement values.

[0017] In step S1, DPT testing is performed on the site, the DPT blow count is corrected, and a volumetric strain curve is established. The specific steps are as follows: S11. Determine the thickness H of the soil layer for testing at the site, and divide the soil layer into layers (usually in 30 cm increments), denoted as 1, 2, 3… n DPT testing was conducted to obtain the measured DPT hammer blow count for each soil layer. ; S12, Correction coefficient for overburden pressure C N and the actual measured DPT hammer blow count for each soil layer The product of these can be converted into the corrected DPT hammer blow count for each soil layer. : (1); In the formula, This indicates the corrected DPT hammer blow count for each soil layer; This represents the actual number of DPT hammer blows measured for each soil layer; C N This indicates the overburden pressure correction factor; (2); In the formula, Indicates the effective stress of the overlying material; S13. For a horizontal free site, the vertical strain and volumetric strain ε of the soil caused by an earthquake. v Similarly, in order to measure the volumetric strain ε v – Relative density D r The relationship is transformed into a more engineering-practical ε v – Relationships need to be established. D r and The relationship between them, based on China's extensive experience in dynamic penetration testing (DPT) (Chinese Design Code 2001), has been given. and D r Correlation: (3); S14, based on volumetric strain ε v - Safety factor F S – Relative density D r Relationship, substitution D r and The relationship between the soil layers is used to calculate the liquefaction volumetric strain ε of each soil layer. v ; Volumetric strain ε v - Safety factor F S – Relative density D r The correspondence is as follows: (4); In the formula, , , , , , ; According to formula 3-4, ε v – F S – D r The correlation is transformed into ε v – F S – The relationship was then obtained, thus yielding the volumetric strain. ε v With safety factor F S And the corrected DPT hammer strike count A one-to-one correspondence is established, and then the liquefaction volumetric strain ε of each soil layer is calculated. v When the site conditions are a horizontal ground, without additional shear stress from buildings and / or without free surfaces, the volumetric strain and shear strain can be estimated using the method proposed by Ishihara and Yoshimine (1992), such as... Figure 2 The dashed lines shown can convert the values ​​in the original graph by Ishihara and Yoshimine (1992) into corresponding values, and through curve fitting, the original graph can be approximated by the following equation: Figure 2 The solid line shown: (5); In the formula, , , , , .

[0018] Safety factor F S The formula is as follows: F S =CRR / CSR (6); In the formula, CSR is the liquefaction stress ratio; CRR is the liquefaction resistance ratio; The specific formula for CSR is as follows: (7); In the formula, CSR 7.5 This is the equivalent periodic stress ratio or liquefaction stress ratio; and These are the total overburden stress and effective overburden stress of the soil at the calculated depth, respectively, in kPa; a max The maximum ground acceleration is given in m / s². 2 ; g The acceleration due to gravity is m / s². 2 ; r d Stress reduction factor; MSF is the magnitude scaling factor; K σ This is the overburden stress correction factor; r d The calculation formula is as follows: (8); In the formula, z represents the depth, in meters (m). MSF is the magnitude. M w The function is calculated using the following formula: (9); K σ The calculation formula is as follows: (10); In the formula, f =0.7; It is reference pressure; The specific formula for CSR is as follows: (11); Calculating CRR requires knowing the liquefaction probability. P L The value of is used to calculate the liquefaction probability using the following formula. P L : (12); In the formula, M w It is the magnitude of the earthquake; It is the inverse function of the cumulative distribution function of the standard normal distribution; It is the effective stress of the overlying layer; It is the reference pressure; GC represents the gravel content of the soil layer.

[0019] The steps in step S2, which involve calculating the predicted settlement and the probability of exceeding a given settlement value, are as follows: S21. For each soil layer at each DPT measuring point, calculate the liquefaction settlement of each soil layer using the following formula: (10); In the formula, S p Ground subsidence caused by liquefaction; ε v,i For the first i Soil volumetric strain; Δz i For the first i Soil layer thickness; I D,i This is a liquefaction indicator variable, with a value of 1 for liquefaction and 0 for non-liquefaction. S22, liquefaction indicator variable I D,i Treating it as a random variable, its expected value and variance are related to the liquefaction probability. P L Relatedly, calculate the average settlement of this soil layer. and the variance of the soil layer : The relative frequency of occurrence is denoted as abbreviated as This indicates the liquefaction probability of the soil layer. Its expression is: (11); The relative frequency of occurrence is denoted as abbreviated as This indicates the liquefaction probability of the soil layer as 1- Its expression is: (12); Therefore, the average settlement of this soil layer and the variance of the soil layer It can be determined as follows: (13); (14); Using the assumption that the liquefaction indicator functions of each soil layer are independent, the average settlement of the entire soil layer is predicted. variance of the entire soil layer The following can be calculated by summation: (15); (16); Predicting settlement It is considered to be a log-normal distribution with a mean of The standard deviation is , Equivalent standard normal distribution variable Represented as: (17); In the formula, The mean and standard deviation are as follows: (18); (19); coefficient of variation The exceedance probability P( exceeding a given settlement value s) S p > s), can be calculated as follows: (20).

[0020] In step S3, liquefaction settlement exceedance probability curves are plotted based on different target settlement values. The specific steps are as follows: By analyzing several given settlement values s Repeatedly calculate the exceedance probability and plot the exceedance probability. The relationship curve between the settlement value s and the given settlement value s is used to obtain the site-specific probability curve of settlement exceeding the liquefaction limit. This curve shows the probability of exceeding a specific settlement limit and clarifies the probability of exceeding a specific settlement amount, providing a decision-making basis for foundation design.

[0021] Example

[0022] Taking the Puerto Manta DPT-3 case study from the April 16, 2016 Ecuador earthquake as an example, the soil profile surrounding the site mainly consists of sandy gravel and gravelly sands, with a thickness of 9-14 m. In this case, liquefaction of the gravelly soil and ground subsidence were clearly observed (Lopez et al., 2018; Rollins et al., 2021). Ground subsidence observed near the DPT-3 measuring point ranged from 15-39 cm (Lopez et al., 2018). The ground and seismic parameters are as follows (Lopez et al., 2018; Rollins et al., 2021): groundwater level GWT = 3.9 m; moment magnitude... M w =7.8; Maximum ground acceleration a max =0.46 g. According to Lopez et al. (2018), the gravel content of the sample in this case reached 80%. The report shows that the critical liquefaction layer depth is 3.9–7.2 m.

[0023] S1. Conduct DPT tests on the site, correct the DPT hammer blow count, and establish a volumetric strain curve; For the S11 and Manta Harbour DPT-3 site tests, the soil layer thickness was 10.5m. The top 10m layer was selected, divided into 10 layers of 100cm each (the bottom 0.5m layer was less than 100cm and the soil was relatively hard, so it was not considered). DPT testing was conducted on each soil layer, and the actual number of DPT hammer blows measured was recorded. The records are 5 times, 3 times, 2 times, 2 times, 2 times, 1 time, 2 times, 3 times, 3 times; S12, Correction coefficient for overburden pressure C N and The product of these can be converted into the corrected DPT hit count. ; (1); In the formula, This indicates the corrected DPT hammer strike count (strokes / 100 cm). This indicates the number of measured DPT hammer blows (per 100 cm) (Rollins et al., 2021). C N This indicates the overburden pressure correction factor; (2); In the formula, Indicates the effective stress of the overlying material; Corrected DPT hammer blow counts for each soil layer The recorded times were 14.9, 12.3, 10.8, 10.3, 13.4, 12.9, 10.9, 15.2, 24.4, and 18.2. S13, In order to reduce the volumetric strain ε v - Safety factor F S – Relative density D r The relationship is transformed into a more engineering-practical ε v – F S – Relationships need to be established. D r and The relationship between them, based on China's extensive experience in dynamic penetration testing (DPT) (Chinese Design Code 2001), has been given. and D r Correlation: (3); S14, based on volumetric strain ε v - Safety factor F S – Relative density D r Relationship, substitution D r and The relationship between the soil layers is used to calculate the liquefaction volumetric strain ε of each soil layer. v ; Volumetric strain ε v - Safety factor F S – Relative density D r The correspondence is as follows: (4); In the formula, , , , , , ; According to formula 3-4, ε v – F S – D r The correlation is transformed into ε v – F S – The relationship was then obtained, thus yielding the volumetric strain. ε v With safety factor F S And the corrected DPT hammer strike count A one-to-one correspondence is established, and then the liquefaction volumetric strain ε of each soil layer is calculated. v The original image is approximated by the following equation through curve fitting: (5); In the formula, , , , , .

[0024] Safety factor F S The formula is as follows: F S =CRR / CSR (6); In the formula, CSR is the liquefaction stress ratio; CRR is the liquefaction resistance ratio; The specific formula for CSR is as follows: (7); In the formula, CSR 7.5 This is the equivalent periodic stress ratio or liquefaction stress ratio; and These are the total overburden stress and effective overburden stress of the soil at the calculated depth, respectively, in kPa; a max The maximum ground acceleration is given in m / s². 2 ; g The acceleration due to gravity is m / s². 2 ; r d Stress reduction factor; MSF is the magnitude scaling factor; K σ This is the overburden stress correction factor; The calculated cyclic stress ratios (CSRs) for each soil layer are: 0.300, 0.298, 0.297, 0.294, 0.316, 0.338, 0.356, 0.369, 0.380, and 0.387. r d The calculation formula is as follows: (8); In the formula, z represents the depth, in meters (m). MSF is the magnitude. M w The function is calculated using the following formula: (9); K σ The calculation formula is as follows: (10); In the formula, f =0.7; It is reference pressure; The specific formula for CRR is as follows: (11); Calculating CRR requires knowing the liquefaction probability. P L The value of is used to calculate the liquefaction probability using the following formula. P L : (12); In the formula, M w It is the magnitude of the earthquake; It is the inverse function of the cumulative distribution function of the standard normal distribution; It is the effective stress of the overlying layer; It is the reference pressure; GC represents the gravel content of the soil layer; Liquefaction probability of each soil layer P L The calculation results are: 0.61, 0.79, 0.92, 0.94, 0.84, 0.91, 0.99, 0.74, 0.56, 0.57; Finally, the volumetric strain ε of each soil layer was calculated. v The calculated results are: 2.6%, 3.9%, 4.5%, 4.6%, 3.7%, 4.0%, 4.5%, 3.3%, 2.3%, 2.2%.

[0025] Following the above procedure, the corrected DPT blow counts for each soil layer at different depths were calculated. Cyclic stress ratio (CSR) and liquefaction probability P L and volumetric strain ε v The result is as follows Figure 3 As shown.

[0026] S2. Calculate the predicted settlement and the probability of exceeding the given settlement value; S21. For each soil layer at each DPT measuring point, calculate the liquefaction settlement of the entire soil layer using the following formula: (10); In the formula, S p Ground subsidence caused by liquefaction; ε v,i For the first i Soil volumetric strain; Δz i For the first i Soil layer thickness; I D,i This is a liquefaction indicator variable, with a value of 1 for liquefaction and 0 for non-liquefaction. It can be noted that the predicted liquefaction probability (the critical layer is almost 100%) is in high agreement with the field observation results, indicating that the proposed liquefaction assessment method is reliable. Since the soil layer below the groundwater level has a high liquefaction probability, considering only the volumetric strain of the critical layer may lead to an underestimation of ground settlement. Therefore, when predicting ground settlement, the entire soil profile below the groundwater level should be considered. S22, liquefaction indicator variable I D,i Treating it as a random variable, its expected value and variance are related to the liquefaction probability. P L Relatedly, calculate the average settlement of this soil layer. and the variance of the soil layer : The relative frequency of occurrence is denoted as abbreviated as This indicates the liquefaction probability of the soil layer. Its expression is: (11); The relative frequency of occurrence is denoted as abbreviated as This indicates the liquefaction probability of the soil layer as 1- Its expression is: (12); Therefore, the average settlement of this soil layer and the variance of the soil layer It can be determined as follows: (13); (14); The average settlement of each soil layer is calculated based on the above formula and steps. The variances for each soil layer are: 0.61, 0.79, 0.92, 0.94, 0.84, 0.91, 0.99, 0.74, 0.56, and 0.57. The values ​​are: 0.24, 0.16, 0.07, 0.06, 0.13, 0.08, 0.01, 0.19, 0.25, 0.24; Using the assumption that the liquefaction indicator functions of each soil layer are independent, the average settlement of the entire soil layer is predicted. variance of the entire soil layer The following can be calculated by summation: (15); (16); For the DPT-3 case, assume the target liquefaction probability P L =50%, the mean and variance of the predicted settlement are as follows: =23.36 cm, =1.42 cm. The settlement predicted by the DPT-3 measuring point is within the observed settlement range (i.e., 15~39 cm), indicating that the proposed settlement estimation method has practical application value.

[0027] Predicting settlement It is considered to be a log-normal distribution with a mean of The standard deviation is , Equivalent standard normal distribution variable Represented as: (17); In the formula, The mean and standard deviation are as follows: (18); (19); coefficient of variation The exceedance probability P( exceeding a given settlement value s) S p > s), can be calculated as follows: (20).

[0028] As mentioned earlier, the predicted settlement follows a log-normal distribution. Its equivalent normal distribution parameters (intermediate parameters) are as follows: =3.149, = 0.061. Then, the probability of exceeding the specified settlement value s can be calculated as follows:

[0029] S3. Draw liquefaction settlement exceedance probability curves based on different target settlement values; By analyzing several given settlement values s Repeatedly calculate the exceedance probability and plot the exceedance probability. The relationship curve with a given settlement value s is used to obtain the site-specific probability curve of settlement exceeding the liquefaction limit. This curve shows the probability of exceeding a specific settlement limit and clarifies the probability of exceeding a specific settlement amount.

[0030] The ground subsidence measured at the nearest observation station to DPT-3 was approximately 33 cm (Lopez et al., 2018), a value consistent with the subsidence predicted by the method of this invention (see [reference needed]). Figure 4 The results are largely consistent with the experimental results. Given the complexity and uncertainty of the physical process of liquefaction settlement, and the spatial variability of underground conditions, existing research generally considers that the estimation of liquefaction settlement can only achieve an accuracy of orders of magnitude (Yazdi and Moss, 2017). However, the prediction results of the method in this case are in high agreement with the measured results, fully verifying the scientific validity and reliability of the proposed method. This method not only has good prediction accuracy but also possesses the advantages of simplicity and economy, providing important guidance for the seismic safety assessment and design of foundations in practical engineering projects.

[0031] In the process of settlement prediction, the method proposed in this invention also considers an important aspect that is often overlooked: validation on non-liquefiable sites (Hayati and Moss, 2011). Specifically, this method selects 12 non-liquefiable cases from four typical earthquakes for validation: the Alaska earthquake, the Wenchuan earthquake, the L'Aquila earthquake, and the Grasmere Lake earthquake. P L = 50%, such as Figure 5 As shown in (a), the verification results indicate that no sedimentation occurred in the predictions for most non-liquefaction cases. Further analysis revealed that the predicted sedimentation amount was related to the selected target liquefaction probability. P L Closely related. When P L =85%, such as Figure 5 As shown in (b), the predicted settlement for all cases is 0. This demonstrates that the method of this invention can be flexibly adjusted according to the importance of the project. P L This value ensures a high degree of consistency with risk-based design principles.

[0032] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting liquefaction settlement of gravelly soil based on dynamic cone penetration tests, characterized in that... Includes the following steps: S1. Conduct DPT tests on the site, correct the DPT hammer blow count, and establish a volumetric strain curve; S2. Calculate the predicted settlement and the probability of exceeding the given settlement value; S3. Plot the liquefaction settlement exceedance probability curve based on different target settlement values.

2. The method for predicting liquefaction settlement of gravelly soil based on dynamic penetration testing according to claim 1, characterized in that, In step S1, DPT testing is performed on the site, the DPT blow count is corrected, and a volumetric strain curve is established. The specific steps are as follows: S11. Determine the thickness H of the soil layer for testing at the site, and divide the soil layer into layers, labeled 1, 2, 3… n DPT testing was conducted to obtain the measured DPT hammer blow count for each soil layer. ; S12, Correction coefficient for overburden pressure C N and the actual measured DPT hammer blow count for each soil layer The product of these can be converted into the corrected DPT hammer blow count for each soil layer. : （1）； In the formula, This indicates the corrected DPT hammer blow count for each soil layer; This represents the actual number of DPT hammer blows measured for each soil layer; C N This indicates the overburden pressure correction factor; （2）； In the formula, Indicates the effective stress of the overlying material; S13. For a horizontal free site, the vertical strain and volumetric strain ε of the soil caused by an earthquake. v Similarly, in order to measure the volumetric strain ε v - Safety factor F S – Relative density D r The relationship is transformed into a more engineering-practical ε v – F S – Relationships need to be established. D r and The relationship between them: （3）； S14, based on volumetric strain ε v - Safety factor F S – Relative density D r Relationship, substitution D r and The relationship between the soil layers is used to calculate the liquefaction volumetric strain ε of each soil layer. v ; Volumetric strain ε v - Safety factor F S – Relative density D r The correspondence is as follows: （4）； In the formula, , , , , , ; According to formula 3-4, ε v – F S – D r The correlation is transformed into ε v – F S – The relationship, and thus obtained Volumetric strain ε v With safety factor F S And the corrected DPT hammer strike count A one-to-one correspondence is established, and then the liquefaction volumetric strain ε of each soil layer is calculated. v The original image is approximated by the following equation through curve fitting: （5）； In the formula, , , , , .

3. The method for predicting liquefaction settlement of gravelly soil based on dynamic penetration testing according to claim 2, characterized in that, The safety factor in step S14 F S The formula is as follows: F S =CRR / CSR (6); In the formula, CSR is the liquefaction stress ratio; CRR is the liquefaction resistance ratio; The specific formula for CSR is as follows: （7）； In the formula, CSR 7.5 This is the equivalent periodic stress ratio or liquefaction stress ratio; and These are the total overburden stress and effective overburden stress of the soil at the calculated depth, respectively, in kPa; a max The maximum ground acceleration is given in m / s². 2 ; g The acceleration due to gravity is m / s². 2 ; r d Stress reduction factor; MSF is the magnitude scaling factor; K σ This is the overburden stress correction factor; r d The calculation formula is as follows: （8）； In the formula, z represents the depth, in meters (m). MSF is the magnitude. M w The function is calculated using the following formula: （9）； K σ The calculation formula is as follows: （10）； In the formula, f =0.7; It is reference pressure; The specific formula for CSR is as follows: （11）； Calculating CRR requires knowing the liquefaction probability. P L The value of is used to calculate the liquefaction probability using the following formula. P L : （12）； In the formula, M w It is the magnitude of the earthquake; It is the inverse function of the cumulative distribution function of the standard normal distribution; It is the effective stress of the overlying layer; It is the reference pressure; GC represents the gravel content of the soil layer.

4. The method for predicting liquefaction settlement of gravelly soil based on dynamic penetration testing according to claim 2, characterized in that, The steps in step S2, which involve calculating the predicted settlement and the probability of exceeding a given settlement value, are as follows: S21. For each soil layer at each DPT measuring point, calculate the liquefaction settlement of the entire soil layer using the following formula: （13）； In the formula, S p Ground subsidence caused by liquefaction; ε v,i For the first i Soil volumetric strain; Δz i For the first i Soil layer thickness; I D,i This is a liquefaction indicator variable, with a value of 1 for liquefaction and 0 for non-liquefaction. S22, liquefaction indicator variable I D,i Treating it as a random variable, its expected value and variance are related to the liquefaction probability. P L Relatedly, calculate the average settlement of this soil layer. and the variance of the soil layer : The relative frequency of occurrence is denoted as abbreviated as This indicates the liquefaction probability of the soil layer. Its expression is: （14）； The relative frequency of occurrence is denoted as abbreviated as This indicates the liquefaction probability of the soil layer as 1- Its expression is: （15）； Therefore, the average settlement of this soil layer and the variance of the soil layer It can be determined as follows: （16）； （17）； Using the assumption that the liquefaction indicator functions of each soil layer are independent, the average settlement of the entire soil layer is predicted. variance of the entire soil layer The following can be calculated by summation: （18）； （19）； Predicting settlement It is considered to be a log-normal distribution with a mean of The standard deviation is , Equivalent standard normal distribution variable It can be represented as: （20）； In the formula, The mean and standard deviation are as follows: （21）； （22）； coefficient of variation The probability of exceeding a given settlement value s P ( S p > s The following method can be used to calculate: （23）。 5. The method for predicting liquefaction settlement of gravelly soil based on dynamic penetration testing according to claim 1, characterized in that, In step S3, liquefaction settlement exceedance probability curves are plotted based on different target settlement values. The specific steps are as follows: By analyzing several given settlement values s Repeatedly calculate the exceedance probability and plot the exceedance probability. The relationship curve with a given settlement value s is used to obtain the site-specific probability curve of settlement exceeding the liquefaction limit. This curve shows the probability of exceeding a specific settlement limit and clarifies the probability of exceeding a specific settlement amount.

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