Method and system for determining equivalent rheological parameters of grouting slurry based on pressure inversion

Abstract

The application discloses a method and system for determining equivalent rheological parameters of grouting slurry based on pressure inversion, which comprises the following steps: constructing an engineering scale single-pipe flow test system, setting at least two test pipes with different inner diameters and different average flow rate conditions, synchronously collecting volume flow data of the grouting slurry and pressure data at different axial positions in the test pipes, calculating equivalent pressure drops along the pipes under corresponding conditions, establishing flow rate-pressure drop calculation relations corresponding to multiple candidate rheological models, inverting rheological parameters corresponding to each candidate rheological model, substituting the inverted parameters into the corresponding flow rate-pressure drop calculation relations to evaluate errors, and determining an equivalent rheological model of the grouting slurry under engineering scale full-pipe flow conditions and equivalent rheological parameters of the grouting slurry. The method can obtain equivalent rheological parameters reflecting flow rate-pressure response characteristics of the grouting slurry under engineering scale full-pipe flow conditions, and can be used for numerical simulation and engineering calculation of grouting projects.

Description

Technical Field

[0001] This invention relates to the fields of grouting engineering and fluid rheology testing technology, specifically to a method and system for determining the equivalent rheological parameters of grouting slurry based on the inversion of single-pipe friction pressure at an engineering scale. Background Technology

[0002] Grouting is widely used in geotechnical engineering, underground engineering, and tunnel engineering. The rheological properties of the grout directly affect its flow range, pressure distribution, and diffusion pattern in pipes, fractures, and fracture networks, and are important input parameters in numerical simulation and engineering calculations of grouting projects.

[0003] Currently, the rheological parameters of grouting slurries are typically obtained through laboratory testing methods such as rotational rheometers. These methods are limited by sample volume, shear rate range, and boundary conditions, and their testing conditions differ from the pressure-driven flow state of the slurry in engineering-scale pipes or fractures. For low-viscosity slurries or shear-thinning non-Newtonian slurries, the parameters obtained from laboratory tests may not adequately characterize the actual flow-pressure response under engineering-scale flow conditions.

[0004] Furthermore, existing methods for obtaining rheological parameters typically rely on pre-defined rheological models, which assume the grout follows a certain constitutive relation and then fit parameters based on test results. When the grout exhibits complex flow characteristics under different shear conditions, a single pre-defined model may be insufficient to accurately describe its engineering-scale pipe flow behavior. Therefore, it is necessary to propose an equivalent rheological parameter determination method based on engineering-scale single-pipe flow tests and friction pressure inversion to obtain an equivalent rheological model and parameters more suitable for grouting engineering calculations and numerical simulations. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing laboratory rheological testing methods in terms of sample size, shear conditions, and engineering applicability, and to provide a method and system for determining the equivalent rheological parameters of grouting slurry based on engineering-scale single-pipe friction pressure inversion.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: Firstly, a method for determining the equivalent rheological parameters of grouting slurry based on pressure inversion is provided, comprising the following steps: Construct an engineering-scale single-pipe flow test system, including at least a test pipe with interchangeable inner diameter; Set up at least two test pipes with different inner diameters, and set up at least three different average flow velocity conditions under the inner diameter conditions of each test pipe, so that the grouting slurry forms a steady full-pipe flow in the test pipe. After each working condition reaches a steady state, the volumetric flow rate data of the grouting slurry and the pressure data at different axial positions in the test pipe are collected simultaneously. Based on the fitting relationship between the pressure data and the corresponding axial position, the pressure gradient along the unit length is obtained, and the equivalent pressure drop along the corresponding working condition is calculated. The obtained volumetric flow rate data, the pressure gradient per unit length or the equivalent pressure drop along the pipe and the geometric parameters of the test pipe are used as a joint inversion dataset. Based on the theoretical relationship between flow rate and pressure drop under steady-state flow conditions in a circular pipe, the flow rate and pressure drop calculation relationship corresponding to multiple candidate rheological models is established. The rheological parameters corresponding to each candidate rheological model are inverted to obtain the inversion parameters, and the inversion parameters are substituted back into the corresponding flow-pressure drop calculation relationship for error evaluation. Based on the error evaluation results, and combined with the applicability of the candidate rheological model and the physical rationality of the inversion parameters, the equivalent rheological model and its equivalent rheological parameters of the grouting slurry under the full-pipe flow condition on an engineering scale are determined.

[0007] Furthermore, the test pipe is a straight, replaceable pipe, and different test pipes have the same effective test length and different inner diameters; the inner diameter of the test pipe includes two or more of 15mm, 20mm, 25mm and 30mm.

[0008] Furthermore, the average flow rate condition is achieved by adjusting the volumetric flow rate of the grouting slurry, and the different average flow rate conditions include at least three of 0.3 m / s, 0.5 m / s, 0.75 m / s and 1.0 m / s.

[0009] Furthermore, each set of operating conditions (test conditions) determined by the inner diameter of the test pipe and the average flow velocity was repeated multiple times, and the average value of the steady-state interval data was used as the representative data of the test condition.

[0010] Preferably, each set of test conditions is repeated at least three times.

[0011] Furthermore, the pressure gradient along the unit length is obtained by linearly fitting the pressure values ​​at at least three pressure measuring points with their corresponding axial positions. The equivalent pressure drop along the unit length is calculated based on the pressure gradient along the unit length and the effective measuring segment length, where the effective measuring segment length is the axial distance between the first and last pressure measuring points participating in the linear fitting.

[0012] Furthermore, the candidate rheological model includes two or more of the following: Newtonian fluid model, power-law fluid model, Bingham fluid model, and Herschel-Balclay fluid model; the rheological parameters include one or more of the following: dynamic viscosity corresponding to the Newtonian fluid model, consistency coefficient and flow index corresponding to the power-law fluid model, yield stress and plastic viscosity corresponding to the Bingham fluid model, and yield stress, consistency coefficient, and flow index corresponding to the Herschel-Balclay fluid model.

[0013] Furthermore, the physical rationality of the inversion parameters includes: dynamic viscosity greater than zero, consistency coefficient greater than zero, flow index greater than zero, plastic viscosity greater than zero, and yield stress not less than zero.

[0014] The error evaluation uses one or more of the following as evaluation indicators: average relative error, average absolute percentage error, root mean square error, average absolute error, and coefficient of determination between theoretically calculated values ​​and experimentally measured values.

[0015] In some implementations, the determined equivalent rheological model and its equivalent rheological parameters are used to construct the shear rate-shear stress relationship and the shear rate-apparent viscosity relationship of the grout under full-pipe flow conditions on an engineering scale.

[0016] In some implementations, the determined equivalent rheological model and its equivalent rheological parameters are used as grout constitutive input parameters in numerical simulation analysis or engineering calculations of grouting projects to predict the flow range, pressure distribution, or diffusion behavior of the grout.

[0017] Secondly, a system for determining the equivalent rheological parameters of grouting slurry based on the inversion of single-pipe friction pressure at an engineering scale is provided. This system is used to realize the method for determining the equivalent rheological parameters of grouting slurry based on the inversion of single-pipe friction pressure at an engineering scale as described above. The system includes: a slurry storage container, a grouting pump, a flow regulating device, a flow measuring device, a test pipe with replaceable inner diameter, multiple pressure measuring devices, a data acquisition device, and a data processing device. The slurry storage container is connected to the grouting pump, which is used to deliver the grout to be tested to the test pipeline; The flow regulating device is installed on the grout delivery path and is used to regulate the volume flow rate of the grout entering the test pipe; The flow measurement device is installed at the inlet end of the test pipe and is used to measure the volumetric flow rate of the grout entering the test pipe. The test pipeline is a straight, replaceable pipeline, used to create full-pipe flow conditions under different pipe diameter constraints. The plurality of pressure measuring devices are arranged at intervals along the axial direction of the test pipe to measure pressure data at different axial positions. The data acquisition device is connected to the flow measurement device and multiple pressure measurement devices respectively, and is used to synchronously acquire volumetric flow rate data and pressure data; The data processing device is connected to the data acquisition device and is used to calculate the pressure gradient or equivalent pressure drop per unit length based on the volumetric flow rate data, pressure data, and test pipeline geometric parameters, and to perform parameter inversion and error evaluation of candidate rheological models in order to determine the equivalent rheological model and its equivalent rheological parameters.

[0018] Furthermore, the data processing device is also configured to establish the flow-pressure drop calculation relationship corresponding to multiple candidate rheological models based on the theoretical relationship of flow-pressure drop under steady-state flow conditions in a circular pipe, and determine the equivalent rheological model and its equivalent rheological parameters based on the error evaluation results, the applicable conditions of the candidate rheological models, and the physical rationality of the inversion parameters.

[0019] Preferably, the flow measurement device is an electromagnetic flow meter, and the nominal diameter of the electromagnetic flow meter is adapted to the inner diameter of the test pipe.

[0020] The plurality of pressure measuring devices are a plurality of pressure sensors, which are arranged at intervals along the axial direction of the test pipe and installed in pressure measuring mounting grooves on the wall of the test pipe.

[0021] Preferably, the number of pressure sensors is no less than three.

[0022] The data acquisition device is a paperless recorder used to synchronously acquire, display, and store volumetric flow rate data and pressure data according to a preset sampling frequency. The data processing device is a computer configured to calculate the pressure gradient per unit length or the equivalent pressure drop per unit length based on the linear fitting relationship between the pressure values ​​at at least three pressure measuring points and their corresponding axial positions.

[0023] The test pipeline includes multiple straight pipes with different inner diameters and the same effective test length, and the multiple straight pipes can be detachably connected to the flow measurement device through flange connections.

[0024] The flow regulating device is a flow regulating valve, which is installed on the slurry delivery path between the grouting pump and the test pipeline.

[0025] Compared with the prior art, the beneficial effects of this invention are: 1. This method for determining the equivalent rheological parameters of grouting slurry based on engineering-scale single-pipe friction pressure inversion can obtain equivalent rheological parameters reflecting the flow-pressure response characteristics of grouting slurry under engineering-scale full-pipe flow conditions, and can be used for numerical simulation and engineering calculation of grouting projects; it can solve the shortcomings of existing laboratory rheological testing methods in terms of sample size, shear conditions, and engineering applicability; 2. This method obtains the unit length friction pressure gradient or equivalent friction pressure drop by fitting the pressure data at multiple pressure measuring points with the corresponding axial positions, avoiding reliance on pressure difference at a single measuring point and improving the stability of friction resistance characterization; 3. By obtaining experimental data through combinations of multiple pipe diameters and multiple average flow velocity conditions, it covers different pipe diameter constraints and different shear conditions, which is beneficial for... 4. Improve the applicability of equivalent rheological parameters under engineering-scale flow conditions; 5. Determine the equivalent rheological model by parameter inversion and error evaluation of multiple candidate rheological models, combined with the applicability of candidate rheological models and the physical rationality of inversion parameters, avoiding model selection bias caused by a single preset rheological model; 6. The equivalent rheological model and equivalent rheological parameters obtained by this invention can be used as slurry constitutive input parameters in numerical simulation analysis or engineering calculations of grouting projects, for predicting slurry flow range, pressure distribution or diffusion behavior; 7. The system of this invention adopts a straight pipe test pipeline with replaceable inner diameter, and is equipped with a flow measurement device, multiple pressure measurement devices, a data acquisition device and a data processing device, which can realize the acquisition of flow-pressure data and parameter inversion under multiple pipe diameters and multiple flow velocity conditions within the same test framework. Attached Figure Description

[0026] Figure 1 This is a top view schematic diagram of a grouting slurry equivalent rheological parameter determination system based on engineering-scale single-pipe friction pressure inversion according to the present invention. Figure 2 This is a front view of a grouting slurry equivalent rheological parameter determination system based on engineering-scale single-pipe friction pressure inversion according to the present invention. Figure 3 This is a schematic diagram of the pressure distribution and pressure drop data along the pipe under different pipe diameters and different average flow velocities according to the present invention. Figure 4 This is a schematic diagram of the shear rate-shear stress relationship obtained by inversion based on multi-diameter and multi-average flow velocity test data. Figure 5 This is a schematic diagram of the shear rate-apparent viscosity relationship obtained by inversion based on test data of multiple pipe diameters and multiple average flow velocities.

[0027] In the diagram: 1. Test pipe; 2. Electromagnetic flow meter; 3. Pressure sensor; 4. Paperless recorder; 5. Computer; 6. Grouting pump; 7. Grout storage container; 8. Flow regulating valve; 9. Flange connector; 10. Bolt. Detailed Implementation

[0028] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present invention, and 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.

[0029] In the description of this invention, it should be noted that the terms "middle," "upper," "lower," "left," "right," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0030] Example 1: A method for determining the equivalent rheological parameters of grouting slurry based on pressure inversion along a single pipe at an engineering scale is provided, comprising the following steps: constructing an engineering-scale single-pipe flow test system, the engineering-scale single-pipe flow test system including a straight pipe test pipe with interchangeable inner diameter, a flow measurement device, multiple pressure measurement devices arranged at intervals along the axial direction of the test pipe, and a data acquisition device; setting up at least two test pipes with different inner diameters, and setting at least three different average flow velocity conditions under each test pipe inner diameter condition, so that the grouting slurry forms a steady-state full-pipe flow in the test pipe; after each condition reaches steady state, simultaneously collecting the volumetric flow rate data of the grouting slurry and the pressure data at different axial positions in the test pipe; based on the fitting relationship between the pressure data and the corresponding axial position... The pressure gradient per unit length was obtained, and the equivalent pressure drop per unit length under the corresponding working conditions was calculated. Using volumetric flow rate data, pressure gradient per unit length or equivalent pressure drop per unit length, and geometric parameters of the test pipes obtained under different test pipe inner diameters and average flow velocities as a joint inversion dataset, and based on the theoretical relationship between flow rate and pressure drop under steady-state flow conditions in circular pipes, the flow rate-pressure drop calculation relationships corresponding to multiple candidate rheological models were established. The rheological parameters corresponding to each candidate rheological model were inverted, and the inverted parameters were substituted back into the corresponding flow rate-pressure drop calculation relationships for error evaluation. Based on the error evaluation results, and combined with the applicable conditions of the candidate rheological models and the physical rationality of the inversion parameters, the equivalent rheological model and its equivalent rheological parameters of the grouting slurry under full-pipe flow conditions at the engineering scale were determined.

[0031] More specifically, the method includes the following steps: Step 1: Assemble the test system. Select straight test pipes with different inner diameters and install them in the test system. In one embodiment, the inner diameter of the test pipe includes 15mm, 20mm, 25mm, and 30mm. For test pipes with different inner diameters, configure flow measurement devices that match their pipe diameters, and install multiple pressure measurement devices in the pressure measurement mounting grooves on the test pipe wall. Connect the flow measurement devices and pressure measurement devices to the data acquisition device, and connect the data acquisition device to the data processing device.

[0032] Step 2: Grout preparation and test system filling. Prepare grout according to the predetermined ratio and stir it. Inject the grout into the test pipe and its matching flow measurement device to fill and vent the test system, so that the test pipe forms a continuous full-pipe flow state.

[0033] Step 3: Set different average flow velocity conditions in test pipes with different inner diameters; the average flow velocity conditions are achieved by adjusting the volumetric flow rate of the grout entering the test pipes. In one embodiment, the average flow velocity conditions include at least three of 0.3 m / s, 0.5 m / s, 0.75 m / s, and 1.0 m / s.

[0034] Step 4: Steady-state data acquisition. After the steady-state full-pipe flow is achieved in each test condition, the volumetric flow rate data of the grouting slurry and the pressure data at multiple axial positions are collected simultaneously through the data acquisition device. For each test condition determined by the inner diameter of the test pipe and the average flow velocity, the test is repeated multiple times, and the data within the steady-state range is selected as the valid test data.

[0035] Step 5: Data processing. Statistically process the steady-state volumetric flow rate and pressure data obtained under each test condition. Use the average value of the measured values ​​within the steady-state range as the representative data of the test condition to obtain volumetric flow rate data, friction pressure distribution data and corresponding average flow velocity data under different test pipe inner diameters and different average flow velocities.

[0036] Step 6: Calculate the pressure gradient along the test path. Based on the relationship between the pressure values ​​at at least three pressure measuring points and their corresponding axial positions, perform linear fitting to obtain the pressure gradient along the test path per unit length under each test condition. Calculate the equivalent pressure drop along the test path under the corresponding test condition based on the pressure gradient along the test path per unit length and the effective measuring segment length. The effective measuring segment length is the axial distance between the first and last pressure measuring points participating in the linear fitting.

[0037] Step 7: Joint Inversion of Candidate Rheological Model Parameters. Based on the theoretical relationship between flow rate and pressure drop under steady-state flow conditions in a circular pipe, the flow rate and pressure drop calculation relationships corresponding to multiple candidate rheological models are established. Volumetric flow rate data, pressure gradient per unit length or equivalent pressure drop, and geometric parameters of the test pipe obtained under different test pipe inner diameters and average flow velocity conditions are used as the joint inversion dataset to invert the rheological parameters corresponding to each candidate rheological model.

[0038] Step 8: Error evaluation and equivalent model determination. Substitute the rheological parameters corresponding to each candidate rheological model obtained by inversion back into the corresponding flow-pressure drop calculation relationship to calculate the theoretical volumetric flow rate or theoretical pressure drop, and evaluate the error with the experimentally measured volumetric flow rate or measured pressure drop. Based on the error evaluation results, and combined with the applicable conditions of the candidate rheological models and the physical rationality of the inversion parameters, determine the equivalent rheological model and its equivalent rheological parameters of the grouting slurry under the full-pipe flow condition on an engineering scale.

[0039] Step 9: Construction and Engineering Application of Equivalent Rheological Relationships. Based on the determined equivalent rheological model and its equivalent rheological parameters, the shear rate-shear stress relationship and the shear rate-apparent viscosity relationship of the grouting slurry are constructed. The equivalent rheological model and its equivalent rheological parameters can be used as constitutive input parameters for the slurry in numerical simulation analysis or engineering calculations of grouting projects.

[0040] This method for determining the equivalent rheological parameters of grouting slurry based on the inversion of pressure along the pipe at the engineering scale can obtain equivalent rheological parameters that reflect the flow-pressure response characteristics of grouting slurry under full-pipe flow conditions at the engineering scale. It can be used for numerical simulation and engineering calculation of grouting projects. It can solve the shortcomings of existing laboratory rheological testing methods in terms of sample size, shear conditions and engineering applicability.

[0041] This method obtains the pressure gradient or equivalent pressure drop per unit length by fitting the pressure data at multiple pressure measurement points with the corresponding axial positions, avoiding reliance on pressure difference at a single measurement point and improving the stability of friction resistance characterization. By acquiring experimental data through combinations of multiple pipe diameters and average flow velocities, covering different pipe diameter constraints and shear conditions, it is beneficial to improve the applicability of equivalent rheological parameters under engineering-scale flow conditions. The equivalent rheological model is determined by parameter inversion and error evaluation of multiple candidate rheological models, combined with the applicability conditions of the candidate rheological models and the physical rationality of the inversion parameters, avoiding model selection bias caused by a single pre-set rheological model.

[0042] Furthermore, the candidate rheological model includes two or more of the following: Newtonian fluid model, power-law fluid model, Bingham fluid model, and Herschel-Balclay fluid model; the rheological parameters include one or more of the following: dynamic viscosity corresponding to the Newtonian fluid model, consistency coefficient and flow index corresponding to the power-law fluid model, yield stress and plastic viscosity corresponding to the Bingham fluid model, and yield stress, consistency coefficient, and flow index corresponding to the Herschel-Balclay fluid model.

[0043] Furthermore, the physical rationality of the inversion parameters includes: dynamic viscosity greater than zero, consistency coefficient greater than zero, flow index greater than zero, plastic viscosity greater than zero, and yield stress not less than zero.

[0044] The error evaluation uses one or more of the following as evaluation indicators: average relative error, average absolute percentage error, root mean square error, average absolute error, and coefficient of determination between theoretically calculated values ​​and experimentally measured values.

[0045] Example 2: A system for determining the equivalent rheological parameters of grouting slurry based on the inversion of friction pressure along a single pipe at an engineering scale is provided to realize the method for determining the equivalent rheological parameters of grouting slurry based on the inversion of friction pressure along a single pipe at an engineering scale as described in Example 1.

[0046] Combination Figure 1 and Figure 2 As shown, the grouting slurry equivalent rheological parameter measurement system includes: slurry storage container 7, grouting pump 6, flow regulating device, flow measuring device, test pipe with replaceable inner diameter 1, multiple pressure measuring devices, data acquisition device and data processing device. The slurry storage container 7 is connected to the grouting pump 6, which is used to transport the grout to be tested to the test pipeline 1. The flow regulating device is installed on the slurry delivery path and is used to regulate the volume flow rate of the grout entering the test pipe 1; The flow measurement device is installed at the inlet end of the test pipe 1 and is used to measure the volumetric flow rate of the grout entering the test pipe 1. The test pipe 1 is a straight replaceable pipe, used to form full-pipe flow conditions under different pipe diameter constraints. The plurality of pressure measuring devices are arranged at intervals along the axial direction of the test pipe to measure pressure data at different axial positions. The data acquisition device is connected to the flow measurement device and multiple pressure measurement devices respectively, and is used to synchronously acquire volumetric flow rate data and pressure data; The data processing device is connected to the data acquisition device and is used to calculate the pressure gradient or equivalent pressure drop per unit length based on the volumetric flow rate data, pressure data, and test pipeline geometric parameters, and to perform parameter inversion and error evaluation of candidate rheological models in order to determine the equivalent rheological model and its equivalent rheological parameters.

[0047] The grouting slurry equivalent rheological parameter determination system of the present invention adopts a straight pipe test pipe with replaceable inner diameter, and is equipped with a flow measurement device, multiple pressure measurement devices, a data acquisition device and a data processing device. It can realize the acquisition of flow-pressure data and parameter inversion under multiple pipe diameters and multiple flow velocity conditions within the same test framework.

[0048] Furthermore, the data processing device is also configured to establish the flow-pressure drop calculation relationship corresponding to multiple candidate rheological models based on the theoretical relationship of flow-pressure drop under steady-state flow conditions in a circular pipe, and determine the equivalent rheological model and its equivalent rheological parameters based on the error evaluation results, the applicable conditions of the candidate rheological models, and the physical rationality of the inversion parameters.

[0049] Preferably, the flow measurement device is an electromagnetic flow meter 2, and the nominal diameter of the electromagnetic flow meter 2 is adapted to the inner diameter of the test pipe.

[0050] The plurality of pressure measuring devices are a plurality of pressure sensors 3, which are arranged at intervals along the axial direction of the test pipe 1 and installed in pressure measuring mounting grooves on the pipe wall of the test pipe 1.

[0051] Preferably, the number of pressure sensors 3 is not less than three.

[0052] The data acquisition device is a paperless recorder 4, used to synchronously acquire, display, and store volumetric flow rate data and pressure data according to a preset sampling frequency. The data processing device is a computer 5, which is configured to calculate the pressure gradient or equivalent pressure drop per unit length based on the linear fitting relationship between the pressure values ​​at at least three pressure measuring points and the corresponding axial positions.

[0053] The test pipeline 1 includes multiple straight pipes with different inner diameters and the same effective test length. The multiple straight pipes can be detachably connected to the flow measurement device through flange connections.

[0054] The flow regulating device is a flow regulating valve 8, which is located on the slurry delivery path between the grouting pump and the test pipeline.

[0055] In this embodiment, the grout equivalent rheological parameter measurement system specifically includes a test pipe 1, an electromagnetic flowmeter 2, a pressure sensor 3, a paperless recorder 4, a computer 5, a grouting pump 6, a grout storage container 7, a flow regulating valve 8, a flange connector 9, and bolts 10.

[0056] The components include: a slurry storage container 7 for storing the grout to be tested; a grouting pump 6 for delivering the slurry to the test pipeline 1; a flow regulating valve 8 for regulating the volumetric flow rate of the slurry entering the test pipeline 1; an electromagnetic flowmeter 2 installed at the inlet end of the test pipeline 1 for measuring the volumetric flow rate of the slurry; pressure sensors 3 arranged at intervals along the axial direction of the test pipeline 1 for measuring pressure data at different axial positions; a paperless recorder 4 for synchronously collecting and storing volumetric flow rate data and pressure data; a computer 5 for data processing, parameter inversion, and error evaluation; and flange connectors 9 and bolts 10 for connecting and fixing the components.

[0057] Test pipe 1 is a straight, replaceable pipe, with its inlet end connected to the electromagnetic flowmeter 2 via flange connector 9. In this embodiment, the overall length of test pipe 1 is 1.6m, and its inner diameters are 15mm, 20mm, 25mm, and 30mm. Test pipes 1 with different inner diameters have the same effective test length to form full-pipe flow conditions under different pipe diameter constraints. Multiple pressure measurement mounting slots are provided axially on the pipe wall of test pipe 1 for mounting pressure sensors 3.

[0058] Before the test, the grout was prepared according to the predetermined ratio and stirred. Then, the grout was injected into the test pipe 1 and its matching electromagnetic flowmeter 2 to fill and vent the test system, so that the test pipe 1 formed a continuous full-pipe flow state.

[0059] During the test, multiple average flow velocity conditions were set in test pipes 1 with different inner diameters by adjusting the flow regulating valve 8. In this embodiment, the average flow velocity conditions include at least three of the following: 0.3 m / s, 0.5 m / s, 0.75 m / s, and 1.0 m / s.

[0060] After the steady-state full-pipe flow was achieved under each test condition, the electromagnetic flowmeter 2 collected the slurry volumetric flow rate data, and multiple pressure sensors 3 simultaneously collected pressure data at different axial positions within the test pipe 1. All measurement signals were simultaneously recorded by the paperless recorder 4 and transmitted to the computer 5 for processing. For each test condition determined by the inner diameter of the test pipe and the average flow velocity, the test was repeated multiple times, and the average value of the measurement data within the steady-state range was taken as the representative data for that condition. Figure 3The diagram illustrates the pressure distribution and pressure drop data along the pipe under different pipe diameters and average flow velocities. Based on the steady-state volumetric flow rate and pressure data obtained under the above multi-diameter and multi-average flow velocity conditions, the equivalent rheological parameters of the grouting slurry under full-pipe flow conditions on an engineering scale are inverted.

[0061] During data processing, based on pressure data measured by multiple pressure sensors 3, a linear fit is performed on the relationship between the pressure value and the corresponding axial position within the steady-state range to obtain the pressure gradient along the unit length; then, based on the pressure gradient along the unit length and the effective measurement segment length... Calculate the equivalent pressure drop along the friction line The effective measurement segment length This refers to the axial distance between the first and last pressure measurement points participating in the linear fitting.

[0062] Under steady-state laminar flow conditions, the wall shear stress of flow inside a circular pipe. With equivalent pressure drop along the process The following relationship must be satisfied: , in, For wall shear stress, To test the inner radius of pipe 1, To effectively measure segment length, For effective segment length measurement The equivalent pressure drop along the flow path.

[0063] Based on the above relationships and the theoretical relationship of flow rate-pressure drop under steady-state flow conditions in a circular pipe, the flow rate-pressure drop calculation relationships corresponding to multiple candidate rheological models are introduced, and the volumetric flow rate data and equivalent friction pressure drop are combined. The test pipeline geometry parameters are used as joint inversion data for rheological parameter inversion. The candidate rheological models include two or more of the following: Newtonian fluid model, power-law fluid model, Bingham fluid model, and Herschel-Balclay fluid model.

[0064] To illustrate the parameter inversion process, a power-law fluid model is used as one implementation method. For a power-law fluid model, the relationship between shear stress and shear rate can be expressed as: , in, For shear stress, Shear rate, This is the consistency coefficient. This is the liquidity index.

[0065] Based on the steady-state laminar flow conditions in a circular pipe, the volumetric flow rate of a power-law fluid. With equivalent pressure drop along the process The relationship can be represented as: , in, For volumetric flow rate, To test the inner radius of pipe 1, To effectively measure segment length, For effective segment length measurement The equivalent pressure drop along the pipe. For the Newtonian fluid model, Bingham fluid model, and Herschel-Barclay fluid model, the parameters can be inverted using their respective flow-pressure drop relationships under steady-state laminar flow conditions in a circular pipe.

[0066] During the parameter inversion process, multiple sets of volumetric flow rate-pressure drop data obtained under multiple pipe diameter and multiple average flow velocity conditions are substituted into the flow rate-pressure drop calculation relationship corresponding to each candidate rheological model to invert the rheological parameters corresponding to each candidate rheological model.

[0067] Furthermore, the rheological parameters obtained from the inversion are substituted back into the corresponding flow-pressure drop calculation relationship to calculate the theoretical volumetric flow rate or theoretical pressure drop along the flow path, and the error is evaluated by comparing it with the experimentally measured volumetric flow rate or measured pressure drop along the flow path. The error evaluation is characterized by one or more of the following: relative error, average relative error, average absolute percentage error, root mean square error, average absolute error, and coefficient of determination.

[0068] Based on the error evaluation results, and combined with the applicability of the candidate rheological model and the physical rationality of the inversion parameters, the equivalent rheological model and its equivalent rheological parameters of the grouting slurry under the full-pipe flow condition on an engineering scale are determined.

[0069] In one implementation, when a power-law fluid model is determined to be an equivalent rheological model after parameter inversion, error evaluation, model applicability judgment, and parameter physical rationality judgment, the consistency coefficient obtained from the inversion is used. and liquidity index This is used as the equivalent rheological parameter for grouting slurry under full-pipe flow conditions on an engineering scale. This embodiment is only used to illustrate the process of determining the equivalent rheological model of the present invention, and does not limit the equivalent rheological model determined by the present invention to a power-law fluid model; when other candidate rheological models are determined as the equivalent rheological model, the model parameters obtained by their corresponding inversion are used as the equivalent rheological parameters.

[0070] Figure 4 This diagram illustrates the shear rate-shear stress relationship of grouting fluid obtained from inversion of test data with multiple pipe diameters and multiple average flow velocities. Figure 5A schematic diagram of the shear rate-apparent viscosity relationship of grouting slurry obtained by inversion from test data of multiple pipe diameters and multiple average flow velocities is shown. The shear rate-shear stress relationship and the shear rate-apparent viscosity relationship are used to characterize the equivalent rheological behavior of grouting slurry under full-pipe flow conditions on an engineering scale, and can be used as the constitutive input of slurry in numerical simulation analysis or engineering calculations of grouting projects.

[0071] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for determining the equivalent rheological parameters of grouting slurry based on pressure inversion, characterized in that, Includes the following steps: Construct an engineering-scale single-pipe flow test system, including at least a test pipe with interchangeable inner diameter; Set up at least two test pipes with different inner diameters, and set up at least three different average flow velocity conditions under the inner diameter conditions of each test pipe, so that the grouting slurry forms a steady full-pipe flow in the test pipe. After each working condition reaches a steady state, the volumetric flow rate data of the grouting slurry and the pressure data at different axial positions in the test pipe are collected simultaneously. Based on the fitting relationship between the pressure data and the corresponding axial position, the pressure gradient along the unit length is obtained, and the equivalent pressure drop along the corresponding working condition is calculated. The obtained volumetric flow rate data, the pressure gradient per unit length or the equivalent pressure drop along the pipe and the geometric parameters of the test pipe are used as a joint inversion dataset. Based on the theoretical relationship between flow rate and pressure drop under steady-state flow conditions in a circular pipe, the flow rate and pressure drop calculation relationship corresponding to multiple candidate rheological models is established. The rheological parameters corresponding to each candidate rheological model are inverted to obtain the inversion parameters, and the inversion parameters are substituted back into the corresponding flow-pressure drop calculation relationship for error evaluation. Based on the error evaluation results, and combined with the applicability of the candidate rheological model and the physical rationality of the inversion parameters, the equivalent rheological model and its equivalent rheological parameters of the grouting slurry under the full-pipe flow condition on an engineering scale are determined.

2. The method for determining the equivalent rheological parameters of grouting slurry based on pressure inversion according to claim 1, characterized in that, The test pipe is a straight, replaceable pipe, and different test pipes have the same effective test length and different inner diameters; the inner diameter of the test pipe includes two or more of 15mm, 20mm, 25mm and 30mm.

3. The method for determining the equivalent rheological parameters of grouting slurry based on pressure inversion according to claim 1, characterized in that, The average flow rate condition is achieved by adjusting the volumetric flow rate of the grouting slurry. Different average flow rate conditions include at least three of the following: 0.3 m / s, 0.5 m / s, 0.75 m / s, and 1.0 m / s.

4. The method for determining the equivalent rheological parameters of grouting slurry based on pressure inversion according to claim 1, characterized in that, The pressure gradient along the unit length is obtained by linearly fitting the pressure values ​​at at least three pressure measuring points with their corresponding axial positions. The equivalent pressure drop along the unit length is calculated based on the pressure gradient along the unit length and the effective measuring segment length, where the effective measuring segment length is the axial distance between the first and last pressure measuring points participating in the linear fitting.

5. The method for determining the equivalent rheological parameters of grouting slurry based on pressure inversion according to claim 1, characterized in that, The candidate rheological models include two or more of the following: Newtonian fluid model, power-law fluid model, Bingham fluid model, and Herschel-Balclay fluid model; the rheological parameters include one or more of the following: dynamic viscosity corresponding to the Newtonian fluid model, consistency coefficient and flow index corresponding to the power-law fluid model, yield stress and plastic viscosity corresponding to the Bingham fluid model, and yield stress, consistency coefficient, and flow index corresponding to the Herschel-Balclay fluid model.

6. The method for determining the equivalent rheological parameters of grouting slurry based on pressure inversion according to claim 1, characterized in that, The physical rationality of the inversion parameters includes: dynamic viscosity greater than zero, consistency coefficient greater than zero, flow index greater than zero, plastic viscosity greater than zero, and yield stress not less than zero.

7. The method for determining the equivalent rheological parameters of grouting slurry based on pressure inversion according to claim 1, characterized in that, The determined equivalent rheological model and its equivalent rheological parameters are used to construct the shear rate-shear stress relationship and the shear rate-apparent viscosity relationship of the grout under full-pipe flow conditions on an engineering scale.

8. The method for determining the equivalent rheological parameters of grouting slurry based on pressure inversion according to claim 1, characterized in that, The determined equivalent rheological model and its equivalent rheological parameters are used as the constitutive input parameters of the grout in numerical simulation analysis or engineering calculations of grouting projects, and are used to predict the flow range, pressure distribution or diffusion behavior of the grout.

9. A system for determining the equivalent rheological parameters of grouting slurry based on pressure inversion, used to implement the method for determining the equivalent rheological parameters of grouting slurry based on pressure inversion as described in any one of claims 1 to 8, characterized in that, The system includes: slurry storage container, grouting pump, flow regulating device, flow measuring device, test pipe with interchangeable inner diameter, multiple pressure measuring devices, data acquisition device and data processing device; The slurry storage container is connected to the grouting pump, which is used to deliver the grout to be tested to the test pipeline; The flow regulating device is installed on the grout delivery path and is used to regulate the volume flow rate of the grout entering the test pipe; The flow measurement device is installed at the inlet end of the test pipe and is used to measure the volumetric flow rate of the grout entering the test pipe. The test pipeline is a straight, replaceable pipeline, used to create full-pipe flow conditions under different pipe diameter constraints. The plurality of pressure measuring devices are arranged at intervals along the axial direction of the test pipe to measure pressure data at different axial positions. The data acquisition device is connected to the flow measurement device and multiple pressure measurement devices respectively, and is used to synchronously acquire volumetric flow rate data and pressure data; The data processing device is connected to the data acquisition device and is used to calculate the pressure gradient or equivalent pressure drop per unit length based on the volumetric flow rate data, pressure data, and test pipeline geometric parameters, and to perform parameter inversion and error evaluation of candidate rheological models in order to determine the equivalent rheological model and its equivalent rheological parameters.

10. The system for determining equivalent rheological parameters of grouting slurry based on pressure inversion according to claim 9, characterized in that, The data processing device is also configured to establish the flow-pressure drop calculation relationship corresponding to multiple candidate rheological models based on the theoretical relationship of flow-pressure drop under steady-state flow conditions in a circular pipe, and determine the equivalent rheological model and its equivalent rheological parameters based on the error evaluation results, the applicable conditions of the candidate rheological models, and the physical rationality of the inversion parameters.

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