Method for detecting improved sand inter-particle cementation
By determining the particle size and stress-strain curves of improved sand, and combining microscopic testing and theoretical mechanical models, the problem of low efficiency and accuracy in detecting the cementing force of improved sand was solved. This enabled accurate and rapid detection of the cementing force between improved sand particles, ensuring engineering stability.
Patent Information
- Application Number
- CN202411710942.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-27
- Publication Date
- 2025-12-09
- Estimated Expiration
- 2044-11-27
AI Technical Summary
The existing technology for testing the cementation strength of improved sand has low efficiency and accuracy, which leads to problems such as foundation settlement, piping, and sand liquefaction in engineering construction.
By determining the particle size curve and improvement material of the improved sand, the stress-strain curve and shear strength are obtained. The number of particles and average radius are determined by microscopic testing methods, and the cementation force is calculated by combining theoretical mechanical models.
It enables accurate and rapid detection of the bonding force between improved sand particles, improving detection efficiency and accuracy, and ensuring project stability.
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Figure CN119666728B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of geotechnical engineering, and particularly relates to a detection method for improved sand soil inter-particle cementation. BACKGROUND
[0002] The relationship between the macroscopic mechanical properties of soil and the mineral composition and microstructure of soil has been one of the key technical problems in the field of soil mechanics. As a product of the third and fourth geological action, the microstructure of soil is complex and highly heterogeneous, and there are great differences in the microscopic scale of material composition and the macroscopic properties of strength and deformation compared with other materials. In the natural state, sand soil has problems such as low mechanical properties and poor engineering properties due to its loose structure and weak inter-particle adhesion. In the actual process of engineering construction, natural sand soil with weak mechanical stability can easily cause a series of engineering problems such as foundation settlement, piping, sand soil liquefaction, and cause disastrous damage to China's infrastructure construction and social and economic development. In view of the above problems, soil improvement materials need to be introduced to reinforce natural sand soil to meet the requirements of engineering construction and ecological environment.
[0003] In the related art, the detection of the cementation of various materials improved sand soil has the problems of low efficiency and precision. SUMMARY
[0004] The embodiments of the present application provide a detection method for the cementation of improved sand soil inter-particles and an evaluation method, which can solve the problem of low efficiency and precision in the detection of the cementation of various materials improved sand soil.
[0005] In a first aspect, the embodiments of the present application provide a detection method for the cementation of improved sand soil inter-particles, comprising: S1 determining the particle size curve of the improved sand soil and the improvement material; S2 obtaining the stress-strain curve and the shear strength of the improved sand soil; S3 determining the number of particles and the average radius of the improved sand soil by using a micro-test method; and S4 substituting the number of particles of the improved sand soil and the average radius of the improved sand soil into a theoretical mechanics model to determine the cementation of the improved sand soil inter-particles.
[0006] In a possible implementation manner of the first aspect, the generation method of the particle size curve of the improved sand soil in the above step (S1) comprises:
[0007] The sand soil sample is dried, and the drying temperature is a preset temperature;
[0008] The dispersion medium is added to the laser particle size analyzer, and the sand soil sample is added to the laser particle size analyzer for dispersion treatment to measure the particle size distribution of the sand soil sample;
[0009] The particle size curve of the improved sand soil is drawn according to the particle size distribution of the sand soil sample, and the average particle size R1 of the improved sand soil is obtained.
[0010] Optionally, in a further possible implementation form of the first aspect, the method for determining the number of particles and the average radius in step S3 comprises:
[0011] After the improved sandy soil is subjected to drying treatment, crushing treatment and sieving treatment, a slice is prepared;
[0012] The slice is subjected to NMR testing to obtain the effective number N of particles of the improved sandy soil;
[0013] The slice is subjected to SEM testing to obtain the average radius R2 of the improved sandy soil.
[0014] Optionally, in a further possible implementation form of the first aspect, the NMR testing of the slice to obtain the effective number N of particles of the improved sandy soil comprises:
[0015] Obtaining a nuclear magnetic resonance signal of the slice;
[0016] Generating the effective number N of particles of the improved sandy soil according to the nuclear magnetic resonance signal of the slice and the pore diameter of the slice.
[0017] Optionally, in a further possible implementation form of the first aspect, the SEM testing of the slice to obtain the average radius R2 of the improved sandy soil comprises:
[0018] Obtaining surface features, unit cell structures, pore features and connectivity states of the slice, and determining the average radius R2 of the improved sandy soil according to the surface features, the unit cell structures, the pore features and the connectivity states.
[0019] Optionally, in a further possible implementation form of the first aspect, the method for determining the cementation force in step (S4) comprises:
[0020] Calculating macro-mechanical parameters of the improved sandy soil in the mechanical test;
[0021] Substituting the number of particles of the improved sandy soil, the average radius of the improved sandy soil and the macro-mechanical parameters of the improved sandy soil into a theoretical mechanics model to obtain total energy of total work, rolling energy dissipation, sliding energy dissipation and cementation energy dissipation, the total energy of total work being obtained by summing up the rolling energy dissipation, the sliding energy dissipation and the cementation energy dissipation;
[0022] Dividing the cementation energy dissipation by displacement, the number of particles of the improved sandy soil and effective contact area to obtain the cementation force between the particles of the improved sandy soil, the effective area being determined according to the average particle size R1 of the improved sandy soil and the average radius R2 of the improved sandy soil.
[0023] In a second aspect, the embodiments of the present application provide an evaluation method, applied to the improved sand inter-particle cementation force detection method, comprising: N1 generating particles by a particle size curve of the improved sand, establishing a numerical model of the improved sand, and simulating the contact by using a parallel bonding model for the particles; N2 setting a parallel cohesion and a parallel internal friction angle as the model particle micro-mechanical parameters of N1; and N3 obtaining an accuracy M of the inter-particle cementation force of the improved sand according to the inter-particle cementation force of the improved sand and an actual value of the cementation force.
[0024] In a possible implementation manner of the second aspect, the parallel cohesion and the parallel internal friction angle are obtained by comparing the macro-mechanical strength with the simulated strength through a trial-and-error method.
[0025] Optionally, in another possible implementation manner of the second aspect, the accuracy M is obtained by a ratio of an absolute value of a difference between the inter-particle cementation force of the improved sand and the actual value of the cementation force to the actual value of the cementation force.
[0026] Optionally, in another possible implementation manner of the second aspect, when M < 10%, the improved sand inter-particle cementation force detection is evaluated as accurate; when 10%≤M < 20%, the improved sand inter-particle cementation force detection is evaluated as relatively accurate; and when 20%≤M≤100%, the improved sand inter-particle cementation force detection is evaluated as inaccurate.
[0027] In the technical solution of the present application, the particle size curve and the improved material of the improved sand are determined first, then the stress-strain curve and the shear strength of the improved sand are obtained, then the number of particles and the average radius of the improved sand are determined by using a micro-test method, and finally the number of particles of the improved sand and the average radius of the improved sand are substituted into a theoretical mechanics model to determine the inter-particle cementation force of the improved sand. Thus, the improved sand shear mechanics model based on the cementation is established, the mutual relationship between the macro-mechanics and the micro-structure of the improved sand is quantitatively corresponded, and the cementation force of the improved sand of various materials can be accurately and quickly detected. BRIEF DESCRIPTION OF DRAWINGS
[0028] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort.
[0029] Figure 1 is a flowchart of the improved sand inter-particle cementation force detection method provided by an embodiment of the present application;
[0030] Figure 2 is a flowchart of the evaluation method provided by an embodiment of the present application;
[0031] Figure 3 is a flowchart of an evaluation method provided by another embodiment of the present application. DETAILED DESCRIPTION
[0032] In the following description, for purposes of explanation and not limitation, specific details are set forth such as particular architectures, techniques, etc. in order to provide a thorough understanding of the embodiments of the present application. However, it will be apparent to those skilled in the art that the present application can be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known methods, devices, circuits, and
[0033] It is to be understood that the terminology "includes", "has", "holds", "contains" or "comprising", "comprised of", "comprising", or grammatical variants thereof when used in this specification and / or the appended claims, specifies the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.
[0034] It is also to be understood that the terminology "and / or" when used in this specification and / or the appended claims, refers to at least one of the items, or any combination of one or more of the items, associated with the "and / or" term.
[0035] As used in this specification and the appended claims, the term "if" can be interpreted as meaning "when" or "upon" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrase "if determined" or "if detected [the described condition or event]" can be interpreted as meaning "upon determining" or "in response to determining" or "upon detecting [the described condition or event]" or "in response to detecting [the described condition or event]", depending on the context.
[0036] In addition, in the description of the specification and the appended claims, the terms "first", "second", "third", etc. are used only to distinguish descriptions, and cannot be understood as indicating or implying relative importance.
[0037] Reference within the specification of this application to "one embodiment" or "some embodiments" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the application. The appearances of the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in additional embodiments," and so on, in various places in the specification are not necessarily all referring to the same embodiment, unless otherwise specifically specified
[0038] The improved sand soil inter-particle cementation force detection method and evaluation method provided in the application are described in detail below with reference to the accompanying drawings.
[0039] Figure 1 A flowchart of an improved sand soil inter-particle cementation force detection method provided in an embodiment of the application is shown.
[0040] As Figure 1 shown, the improved sand soil inter-particle cementation force detection method includes the following steps:
[0041] Step 101, determine the particle size curve of the improved sand soil and the improvement material.
[0042] Step 102, obtain the stress-strain curve and shear strength of the improved sand soil.
[0043] As a possible implementation, the stress-strain curve and shear strength of the improved sand soil can be obtained by a direct shear test, which is performed according to the direct shear test procedure in the Soil Test Code (JTG3430-2020).
[0044] Step 103, determine the number of particles and the average radius of the improved sand soil using a microscopic testing method.
[0045] Step 104, substitute the number of particles of the improved sand soil and the average radius of the improved sand soil into a theoretical mechanics model to determine the inter-particle cementation force of the improved sand soil.
[0046] Further, in the embodiments of the application, the above step 101 includes:
[0047] Step 1011, dry the sand soil sample, and the drying temperature is a preset temperature.
[0048] Preferably, the above preset temperature can be 110°C.
[0049] At step 1012, the dispersing medium is added into the laser particle size analyzer, and the sandy soil sample is added into the laser particle size analyzer for dispersion treatment to measure the particle size distribution of the sandy soil sample.
[0050] Preferably, the common dispersing medium includes water, anhydrous ethanol and other organic solvents, and the commonly used dispersing medium for the sandy soil is water.
[0051] Preferably, the commonly used dispersion mode for the sandy soil is a stirrer.
[0052] At step 1013, the particle size curve of the improved sandy soil is drawn according to the particle size distribution of the sandy soil sample, and the average particle size R1 of the improved sandy soil is obtained.
[0053] Further, in the embodiment of the present application, the step 103 includes:
[0054] At step 1031, the improved sandy soil is dried, crushed and sieved to form a slice.
[0055] At step 1032, the slice is subjected to NMR testing to obtain the effective number N of particles of the improved sandy soil.
[0056] Preferably, the NMR testing is used to measure the molecular weight of the improved material.
[0057] In the embodiment of the present application, the nuclear magnetic resonance signal of the slice can be obtained first, and then the effective number N of particles of the improved sandy soil is generated according to the nuclear magnetic resonance signal of the slice and the pore size of the slice.
[0058] At step 1033, the slice is subjected to SEM testing to obtain the average radius R2 of the improved sandy soil.
[0059] Preferably, the SEM testing is used to measure the microstructure of the improved material.
[0060] In the embodiment of the present application, the surface features, unit cell structure, pore features and connectivity state of the slice can be obtained, and the average radius R2 of the improved sandy soil is determined according to the surface features, unit cell structure, pore features and connectivity state.
[0061] Further, in the embodiment of the present application, the step 104 includes:
[0062] At step 1041, the macroscopic mechanical parameters of the improved sandy soil in the mechanical test are calculated.
[0063] At step 1042, the particle number of the improved sandy soil, the average radius of the improved sandy soil and the macroscopic mechanical parameters of the improved sandy soil are substituted into the theoretical mechanics model to obtain the total energy of the total work, the rolling energy dissipation, the sliding energy dissipation and the cementation energy dissipation, and the total energy of the total work is obtained by the sum of the rolling energy dissipation, the sliding energy dissipation and the cementation energy dissipation.
[0064] Step 1043, cementation energy consumption is divided by displacement, improved sand particle number and effective contact area, to obtain the cementation force between improved sand particles, and the effective area is determined according to the average particle size R1 of the improved sand and the average radius R2 of the improved sand.
[0065] In an embodiment, the mechanical parameters include k constant, shear angle a, internal friction angle f, a, b and c constants. As a possible way, the k constant and the shear angle a are 2√3 and 30° respectively when the sand particles are assumed to be arranged in a diamond shape, the a, b and c constants are determined by the direct shear test, and the shear mechanical model is derived from the static equilibrium condition and the functional transformation principle, and the functional transformation principle is that the total energy Q of the total work of the external world is equal to the sum of the cementation energy consumption, the rolling energy consumption and the sliding energy consumption of the improved sand particles, wherein the total energy Q of the total work of the external world is calculated by integrating the stress-strain curve, the rolling energy consumption = 7 / 10mV t 2 t V s is the initial speed at the beginning of the test, the sliding energy consumption = f s 2 -V t 2 s+m / 2(V s is the sliding friction on the shear surface, s is the shear displacement, V s is the velocity during shearing, V t is the initial speed at the beginning of the test, the cementation energy consumption is obtained by the total energy Q-rolling energy consumption-sliding energy consumption, and the effective area = k*((R1+R2) / 2)^ 2 .
[0066] The detection method for the cementation force between improved sand particles provided by the embodiments of the present application first determines the particle size curve of the improved sand and the improvement material, then obtains the stress-strain curve and the shear strength of the improved sand, then determines the particle number and the average radius of the improved sand by using the microscopic test method, and finally substitutes the particle number of the improved sand and the average radius of the improved sand into the theoretical mechanics model to determine the cementation force between the improved sand particles. Thus, the shear mechanical model of the improved sand based on the cementation is established, the mutual relationship between the macro mechanics and the micro structure of the improved sand is quantitatively corresponded, and the cementation force of the improved sand of various materials can be accurately and quickly detected.
[0067] Figure 2 A flowchart of an evaluation method provided by another embodiment of the present application is shown.
[0068] As Figure 2 shown, the evaluation method is applied to the detection method for the cementation force between improved sand particles, and includes the following steps:
[0069] Step 201, generating particles through a particle size curve of the improved sand soil, establishing a numerical model of the improved sand soil, and the particles are simulated by using a parallel bond model.
[0070] It should be noted that the numerical model of the improved sand soil is established by generating particles through a particle size curve of the improved sand soil, the numerical model of the improved sand soil is consistent with the sample of the direct shear test, and the particles of the numerical model of the improved sand soil are simulated by using a parallel bond model.
[0071] Step 202, setting the parallel cohesive force and the parallel internal friction angle as the mesoscopic mechanical parameters of the model particles in step 201.
[0072] It should be noted that the mesoscopic parameters of the numerical model of the improved sand soil are the parallel cohesive force and the parallel internal friction angle.
[0073] It should be noted that the parallel cohesive force and the parallel internal friction angle are obtained by comparing the macroscopic mechanical strength and the simulated strength through a trial-and-error method.
[0074] Step 203, obtaining the accuracy M of the cementing force between the particles of the improved sand soil according to the cementing force between the particles of the improved sand soil and the actual value of the cementing force.
[0075] It should be noted that the accuracy M is obtained by the ratio of the absolute value of the difference between the cementing force between the particles of the improved sand soil and the actual value of the cementing force and the actual value of the cementing force.
[0076] In the embodiment of the present application, when M < 10%, the evaluation of the detection of the cementing force between the particles of the improved sand soil is accurate; when 10%≤M < 20%, the evaluation of the detection of the cementing force between the particles of the improved sand soil is relatively accurate, and when 20%≤M≤100%, the evaluation of the detection of the cementing force between the particles of the improved sand soil is inaccurate.
[0077] The evaluation method provided by the present application is applied to the detection method of the cementing force between the particles of the improved sand soil in the above embodiment. First, particles are generated through a particle size curve of the improved sand soil, a numerical model of the improved sand soil is established, and the particles are simulated by using a parallel bond model. Then, the parallel cohesive force and the parallel internal friction angle are set as the mesoscopic mechanical parameters of the model particles in step 201. Finally, the accuracy M of the cementing force between the particles of the improved sand soil is obtained according to the cementing force between the particles of the improved sand soil and the actual value of the cementing force. Thus, the detection of the detection method of the cementing force between the particles of the improved sand soil can be more accurate by using the above evaluation method.
[0078] The evaluation method provided by the present application is further described by an embodiment.
[0079] The evaluation method provided by the present application is further described by an embodiment. Figure 3
[0080] The particle size curve of the improved sand soil is measured by the improved detection method of the inter-particle cementing force of the sand soil in the above embodiment, and the average particle size R1 of the improved sand soil is 0.1 mm.
[0081] The stress-strain curve and the shear strength of the improved sand soil are obtained by the direct shear test, the shear strength is 601.45 kPa, and the integral area of the stress-strain curve is 67.21.
[0082] The improved sand soil is dried, crushed, sieved and sliced, and the NMR and SEM tests are performed on the slices to obtain the particle number N and the average radius R2 of the improved sand soil, which are 4×104 and 0.092 mm respectively.
[0083] The shear mechanical parameters are calculated to determine the k constant, the shear angle α, the internal friction angle φ, and the constants a, b and c, which are 2√3, 30°, 31.58°, 81.06, 263.09 and-43.87 respectively.
[0084] The total energy of the total work, the rolling energy dissipation, the sliding energy dissipation and the cementing energy dissipation are obtained by substituting the model calculation formula, which are 67.21 kJ, 0.0192, 0.2086 kJ and 66.9822 kJ respectively.
[0085] The effective area of the particle is 0.00000396.
[0086] The cementing force is calculated to be 4.8×105 Pa.
[0087] The numerical model is established, and the numerical cementing force is obtained by comparing with the indoor direct shear test, which is 3.9×105 Pa.
[0088] The calculation accuracy M is 18.75%, and the accuracy M is in the range of 10%-20%, which indicates that the evaluation of the detection of the inter-particle cementing force of the sand soil improved by the organic polymer is relatively accurate.
[0089] The above only describes exemplary embodiments of the present application, and the described embodiments are only part of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.
[0090] In the above embodiments, the description of each embodiment has its own focus, and the parts not described or recorded in a certain embodiment can be referred to the related description of other embodiments.
[0091] Those skilled in the art can understand that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be realized in electronic hardware or a combination of computer software and electronic hardware. Whether the functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.
[0092] In the embodiments provided by the present application, it should be understood that the disclosed apparatus / terminal device and method can be implemented in other ways. For example, the division of the described apparatus / terminal device embodiments is merely a logical function division, and there can be another division manner in actual implementation. For example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the displayed or discussed mutual couplings or direct couplings or communication connections between the units can be indirect couplings or communication connections through some interfaces, devices or units, and can be electrical, mechanical or in other forms.
[0093] The units described as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, i.e. can be located in one place, or can be distributed on a plurality of network units. Part or all of the units can be selected according to actual needs to achieve the purpose of the embodiments.
[0094] The above-described embodiments are only used to illustrate the technical solutions of the present application, rather than limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application.
Claims
1. A method for detecting improvement of inter-particle cementation of sandy soil, characterized by, The method comprises the following steps: S1: determining the particle size curve of the improved sand and the improvement material; S2: obtaining the stress-strain curve and the shear strength of the improved sand; S3: determining the particle number and the average radius of the improved sand by using a microscopic testing method; S4: substituting the particle number of the improved sand and the average radius of the improved sand into a theoretical mechanics model to determine the cementation force between the particles of the improved sand; The method for determining the cementation force in the step S4 comprises: calculating the macroscopic mechanical parameters of the improved sand in the mechanical test; substituting the particle number of the improved sand, the average radius of the improved sand and the macroscopic mechanical parameters of the improved sand into the theoretical mechanics model to obtain the total energy of the total external work, the rolling energy consumption, the sliding energy consumption and the cementation energy consumption, wherein the total energy of the total external work is obtained by summing up the rolling energy consumption, the sliding energy consumption and the cementation energy consumption; dividing the cementation energy consumption by the displacement, the particle number of the improved sand and the effective contact area to obtain the cementation force between the particles of the improved sand, wherein the effective area is determined according to the average particle size R1 of the improved sand and the average radius R2 of the improved sand.
2. The method of claim 1, wherein, The method for generating the particle size curve of the improved sand in the step S1 comprises: drying the sand sample, wherein the drying temperature is a preset temperature; adding a dispersion medium into a laser particle size analyzer and adding the sand sample into the laser particle size analyzer for dispersion treatment to measure the particle size distribution of the sand sample; drawing the particle size curve of the improved sand according to the particle size distribution of the sand sample and obtaining the average particle size R1 of the improved sand.
3. The method of claim 1, wherein, The method for determining the particle number and the average radius in the step S3 comprises: preparing a slice after drying, crushing and sieving the improved sand; performing NMR test on the slice to obtain the effective particle number N of the improved sand; performing SEM test on the slice to obtain the average radius R2 of the improved sand.
4. The method of claim 3, wherein, The NMR test on the slice to obtain the effective particle number N of the improved sand comprises: obtaining the nuclear magnetic resonance signal of the slice; generating the effective particle number N of the improved sand according to the nuclear magnetic resonance signal of the slice and the pore size of the slice.
5. The method of claim 3, wherein, The SEM test on the slice to obtain the average radius R2 of the improved sand comprises: obtaining the surface characteristics, unit structure, pore characteristics and connectivity state of the slice and determining the average radius R2 of the improved sand according to the surface characteristics, the unit structure, the pore characteristics and the connectivity state.
6. An evaluation method characterized by, The method for detecting the cementation force between the particles of the improved sand according to the method of claim 1 comprises the following steps: N1: generating particles by the particle size curve of the improved sand, establishing an improved sand numerical model, and simulating the contact by using parallel bonding model for the particles; N2: setting the parallel cohesion and the parallel internal friction angle as the model particle microscopic mechanics parameters of N1; N3 Accuracy M of the inter-particle cementing force of the improved sand soil is obtained according to the inter-particle cementing force of the improved sand soil and the actual value of the inter-particle cementing force.
7. The method of claim 6, wherein, The parallel cohesive force and the parallel internal friction angle are obtained by comparing the macro mechanical strength with the simulation strength through trial and error.
8. The method of claim 6, wherein, The accuracy M is obtained by the ratio of the absolute value of the difference between the inter-particle cementing force of the improved sand soil and the actual value of the inter-particle cementing force to the actual value of the inter-particle cementing force.
9. The method of claim 8, wherein, When M < 10%, the evaluation of the inter-particle cementing force detection of the improved sand soil is accurate; when 10% ≤ M < 20%, the evaluation of the inter-particle cementing force detection of the improved sand soil is relatively accurate; and when 20% ≤ M ≤ 100%, the evaluation of the inter-particle cementing force detection of the improved sand soil is inaccurate.
Citation Information
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