CN113076577B - High-speed railway foundation shear wave velocity calculation method, device, equipment and readable storage medium - Google Patents
High-speed railway foundation shear wave velocity calculation method, device, equipment and readable storage medium Download PDFInfo
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Abstract
The invention relates to the technical field of shear wave velocity calculation, in particular to a method, a device and equipment for calculating the shear wave velocity of a high-speed railway foundation and a readable storage medium. The method comprises the following steps: acquiring first data and second data; calculating a first frequency function corresponding to the second data; calculating a first damping ratio of the roadbed at the position of the second acceleration sensor; calculating a first shear modulus of the position of the second acceleration sensor; and calculating the first shear wave speed of the roadbed at the position of the second acceleration sensor according to the first shear modulus. According to the invention, the sensors are arranged in the roadbed in a layered and overlapped mode, vibration wave information is collected in real time, the damping ratio of the soil body is calculated in real time, then the dynamic shear mode ratio of the thin-layer filler is sequentially calculated in real time by utilizing dynamic parameters and a dynamic model of the damping ratio, and then the shear wave speed of the thin-layer filler is calculated in real time according to the dynamic shear modulus without the limitation of detection interval distance and time.
Description
Technical Field
The invention relates to the technical field of shear wave velocity calculation, in particular to a method, a device and equipment for calculating the shear wave velocity of a high-speed railway foundation and a readable storage medium.
Background
The lower structure in the railway construction process is divided into a tunnel, a bridge and a roadbed section, wherein the roadbed section has more important structural stability due to the fact that main composition structures of the roadbed section are fillers such as broken stones, soil and mortar and the like and have heterogeneity, shear wave speeds are important guiding factors for railway roadbed engineering seismic design, and different shear wave speeds not only influence the type classification of soil, but also influence the determination of the thickness of a railway foundation covering layer, so that the shear wave speed determination of a roadbed soil body is particularly important.
Disclosure of Invention
The invention aims to provide a method, a device, equipment and a readable storage medium for calculating the shear wave velocity of a high-speed railway foundation, so as to improve the problems. In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
in one aspect, an embodiment of the present application provides a method for calculating a shear wave velocity of a high-speed railway subgrade, where the method includes:
acquiring first data and second data, wherein the first data comprises first acceleration time-course data acquired by a first acceleration sensor arranged on a variable-frequency vibration exciter; the second data comprises second acceleration time-course data collected by a second acceleration sensor arranged in a roadbed right below the variable-frequency vibration exciter;
calculating a first frequency function corresponding to the second data according to the first data and the second data;
calculating a first damping ratio of the roadbed at the position of the second acceleration sensor according to the first frequency function;
calculating a first shear modulus of the position of the second acceleration sensor according to the first damping ratio;
and calculating the first shear wave speed of the roadbed at the position of the second acceleration sensor according to the first shear modulus.
Optionally, after the calculating the shear wave speed of the position where the second acceleration sensor is located according to the shear modulus, the method further includes:
acquiring third data, wherein the third data comprises third acceleration time-course data acquired by a third acceleration sensor arranged in a roadbed right below the second acceleration sensor;
calculating a second frequency function corresponding to the third data according to the first data and the third data;
calculating a second damping ratio of the roadbed at the position of the second acceleration sensor according to the second frequency function;
calculating a second shear modulus of the position of the second acceleration sensor according to the second damping ratio;
and calculating a second shear wave speed of the roadbed at the position of the third acceleration sensor according to the first shear modulus, the second shear modulus and the first shear wave speed.
When a plurality of third acceleration sensors are arranged right below the second acceleration sensor, the method is repeated, and the shear wave speed of the roadbed at the position where each third acceleration sensor is located can be obtained.
Optionally, after the acquiring the first data and the second data, the method further includes:
sequentially eliminating trend terms of the first data and the second data through a formula (1), wherein the formula (1) is as follows:
yk＝xk-(a0-a1k-...-amk) (1)
in the formula (1), ykTo eliminate the data after trend terms, xkFor the kth acceleration data, xk can be regarded as xk＝a0+a1k+a2k2+...+amkm，a0、a1And am0, 1, 2, a, m, the 0 th, 1 st and mth order components, respectively;
sequentially filtering the data after eliminating the trend term through a formula (2), wherein the formula (2) is as follows:
in equation (2), T is the period, T is the time, and ω (T) is the frequency.
Optionally, the calculating a first frequency function corresponding to the second data according to the first data and the second data includes:
calculating the first frequency function by equation (3), equation (3) being:
in formula (3), h (k) is the first frequency function; sxy(k) Cross-power spectral density function s for the first data as excitation signal and the second data as response signalxy(k) From equation (4) sxx(k) Is the self-rate spectral density function, s, of the second dataxx(k) The following is obtained from equation (5):
equation (4) is:
equation (5) is:
in equations (4) and (5), xi (k) and Yi (k) are Fourier transforms of the ith data segment of one or two random vibration signals, Xi *(k) Is Xi(k) Complex conjugate of (A), Yi *(k) Is Yi(k) M is the average degree.
Optionally, after calculating a first frequency function corresponding to the second data according to the first data and the second data, the method further includes:
smoothing the first frequency function sequentially through formulas (6) to (10) to obtain smoothed data:
in the formulae (6) to (10), A-2、A-1、A0、A1And A2Representing data in 5 consecutive first frequency functions, respectively.
Optionally, the calculating a first damping ratio of the roadbed where the second acceleration sensor is located according to the first frequency function includes:
fitting the first frequency function by equation (11) and calculating the value of each coefficient to be determined when its modulus is minimum, equation (11) being:
in formula (11), h (jw) is an imaginary component of the first frequency function; a is0、a1、…、a2NTo be a coefficient of undetermination, b0、b1、…、b2NAnd (3) fitting each point according to a formula (11) for undetermined coefficients, and then performing linear processing on an error function to calculate each undetermined coefficient so as to obtain the first damping ratio.
Optionally, the calculating a first shear modulus of the position where the second acceleration sensor is located according to the first damping ratio includes:
the shear strain of the soil is calculated by the formula (12), wherein the formula (12) is as follows:
in the formula (12), k1-k6Respectively are fitting parameters influenced by soil body properties, lambda is a first damping ratio, and gamma is shearing strain;
calculating the first shear modulus according to a formula (13), wherein the formula (13) is as follows:
in the formula (13), GmaxIs the maximum shear modulus, γγFor reference shear strain, gamma for shear strain, as obtained from soil testing, G1Is the first shear modulus.
Optionally, the calculating a first shear wave speed of the roadbed where the second acceleration sensor is located according to the first shear modulus includes:
calculating a first shear wave velocity of the subgrade by equation (14), equation (14) being:
in the formula (14), ρ is the density of the soil body of the roadbed, v1 is the first shear wave velocity, G1Is the first shear modulus.
Optionally, said calculating a second shear wave velocity of the subgrade on which the third acceleration sensor is located according to the first shear modulus, the second shear modulus and the first shear wave velocity comprises:
calculating the difference between the second shear modulus and the first shear modulus by using a formula (15), wherein the formula (15) is as follows:
△G＝G2-G1 (15)
in the formula (15), Δ G is the difference between the second shear modulus and the first shear modulus, G1Is as followsShear modulus, G2A second shear modulus;
and calculating a second shear wave speed of the roadbed by using the formula (16) and the formula (17), wherein the formula (16) and the formula (17) are as follows:
△V＝V2-V1 (17)
in the formula (16), V2At a second shear wave velocity, v1Is the first shear wave velocity, Δ V is the difference between the second shear wave velocity and the first shear wave velocity, Δ G is the difference between the second shear modulus and the first shear modulus, G1For the first shear modulus, A, B is an empirical value after considering soil parameters, and is obtained by a physical mechanical test of soil, wherein the value of A is 3.89, and the value of B is 8.69.
In another aspect, an embodiment of the present application provides an apparatus for calculating a shear wave velocity of a high-speed railway subgrade, where the apparatus includes:
the first acquisition module is used for acquiring first data and second data, wherein the first data comprises first acceleration time-course data acquired by a first acceleration sensor arranged on a variable-frequency vibration exciter; the second data comprises second acceleration time-course data collected by a second acceleration sensor arranged in a roadbed right below the variable-frequency vibration exciter;
the first calculating module is used for calculating a first frequency function corresponding to the second data according to the first data and the second data;
the second calculation module is used for calculating a first damping ratio of the roadbed at the position where the second acceleration sensor is located according to the first frequency function;
the third calculation module is used for calculating a first shear modulus of the position of the second acceleration sensor according to the first damping ratio;
and the fourth calculation module is used for calculating the first shear wave speed of the roadbed at the position where the second acceleration sensor is located according to the first shear modulus.
Optionally, the apparatus further comprises:
the second acquisition module is used for acquiring third data, wherein the third data comprises third acceleration time-course data acquired by a third acceleration sensor arranged in a roadbed right below the second acceleration sensor;
a fifth calculating module, configured to calculate, according to the first data and the third data, a second frequency function corresponding to the third data;
the sixth calculating module is used for calculating a second damping ratio of the roadbed at the position where the second acceleration sensor is located according to the second frequency function;
the seventh calculation module is used for calculating a second shear modulus of the position where the second acceleration sensor is located according to the second damping ratio;
and the eighth calculation module is used for calculating the second shear wave speed of the roadbed at the position where the third acceleration sensor is located according to the first shear modulus, the second shear modulus and the first shear wave speed.
In a third aspect, an embodiment of the present application provides a high-speed railway-based shear wave velocity calculation apparatus, including:
a memory for storing a computer program;
a processor for implementing the steps of the above method when executing the computer program.
In a fourth aspect, the present application provides a readable storage medium, on which a computer program is stored, and the computer program, when executed by a processor, implements the steps of the above method.
The invention has the beneficial effects that:
according to the invention, the sensors are arranged in the roadbed in a layered and overlapped mode, vibration wave information is collected in real time, the damping ratio of the soil body is calculated in real time, then the dynamic shear mode ratio of the thin-layer filler is sequentially calculated in real time by utilizing dynamic parameters and a dynamic model of the damping ratio, and then the shear wave speed of the thin-layer filler is calculated in real time according to the dynamic shear modulus, so that the method is not limited by the detection interval distance and time, and the measurement accuracy is higher.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of the embodiments of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIG. 1 is a schematic structural diagram of a method for calculating shear wave velocity of a high-speed railway foundation according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a high-speed railway-based shear wave velocity calculation apparatus according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of a high-speed railway-based shear wave velocity calculation apparatus according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures. Meanwhile, in the description of the present invention, the terms "first", "second", and the like are used only for distinguishing the description, and are not to be construed as indicating or implying relative importance.
The lower structure in the railway construction process is divided into a tunnel, a bridge and a roadbed section, wherein the roadbed section has more important structural stability due to the fact that main composition structures of the roadbed section are fillers such as broken stones, soil and mortar and the like and have heterogeneity, shear wave speeds are important guiding factors for railway roadbed engineering seismic design, and different shear wave speeds not only influence the type classification of soil, but also influence the determination of the thickness of a railway foundation covering layer, so that the shear wave speed determination of a roadbed soil body is particularly important. The existing method for measuring the shear wave velocity is still a test direct measurement method, mainly comprises the steps of burying an instrument after drilling and applying an excitation signal for measurement, belongs to direct measurement, but has obvious defects in direct measurement and is embodied in the following steps:
1. at present, the shear wave velocity of a soil layer on the surface layer (the thickness is within 30 cm) cannot be accurately tested by a conventional shear wave velocity test, the thickness of a thin layer compacted by a high-speed railway roadbed is about 30cm, and the conventional test method cannot be applied.
2. The excitation signal is difficult to control, the existing method is usually a manual hammering method, the emission consistency of the signal every time is difficult to ensure, the excitation signal possibly has wave scattering, reflection and refraction effects for soil bodies, the excitation signal possibly has the wave effect due to hard soil bodies in a roadbed and can generate novel derivative surface waves such as love waves, Rayleigh waves and the like, so the tested wave speed is actually the comprehensive average wave speed formed by overlapping a plurality of waveforms, the method has no real-time property, and the requirement of compaction timeliness of the high-speed railway roadbed cannot be met.
3. The detection of the traditional excitation method usually needs to be spaced by 20m or more, the range represented by the test result is too large, the error is difficult to control, and the detection is extremely inconvenient.
4. The traditional method needs drilling, and secondary damage to the stratum with the compaction quality meeting the requirements of the original high-speed railway foundation is easily caused.
Example 1
As shown in fig. 1, the present embodiment provides a high-speed railway-based shear wave velocity calculation method, which includes step S101, step S102, step S103, step S104, and step S105.
S101, acquiring first data and second data, wherein the first data comprises first acceleration time-course data acquired by a first acceleration sensor arranged on a variable-frequency vibration exciter; the second data comprise second acceleration time-course data collected by a second acceleration sensor arranged in a roadbed right below the variable-frequency vibration exciter;
the actual engineering thickness, economic effect and effectiveness of the roadbed filling are considered. Lay a plurality of acceleration sensor groups in the road bed, the second acceleration sensor sets up in the acceleration sensor group, and including the second acceleration sensor and at least one third acceleration sensor of even setting in every acceleration sensor group, the second acceleration sensor sets up on the top layer of road bed, the third acceleration sensor sets up in the road bed under the second acceleration sensor. When the number of the third acceleration sensors is two or more, the first distance is equal to the second distance, the first distance is the distance between the second acceleration sensor and the third acceleration sensor closest to the second acceleration sensor, and the second distance is the distance between the third acceleration sensors. And the signals acquired by each acceleration sensor in the acceleration sensor group are transmitted to the signal acquisition instrument.
The acceleration sensor group can be arranged in any net shape, and is temporarily arranged along the length direction of the roadbed by 5 m/group and the width direction by 2 m/group. The engineering thickness of the roadbed filling is about 30 cm.
The layout method of each acceleration sensor in the acceleration sensor group comprises the following steps:
when each layer of filler is laid, firstly carrying out virtual laying, detecting the laying thickness, then digging holes, installing and fixing an acceleration sensor, correcting the direction of the sensor, and recording the serial number of the sensor; the virtual paving is to pile the soil body on the surface layer, but not to compact, so that the sensor can be embedded into the soil body.
A variable-frequency vibration exciter is arranged right above the second acceleration sensor, the acquisition frequency of each acceleration sensor in the acceleration sensor group is set to be at least 1000Hz, the measuring range is more than 8g, the parameter setting between the signal acquisition instrument and the acceleration sensor is connected and debugged, and the normality of the acceleration sensor is judged by oscillography;
when the first data and the second data are obtained, a variable frequency vibrator is used for carrying out vibration waves with the frequency of 0-100Hz and the gradual change along with time on the top layer of the roadbed filling, and the loading time is not less than 60 s.
S102, calculating a first frequency function corresponding to the second data according to the first data and the second data;
s103, calculating a first damping ratio of the roadbed at the position where the second acceleration sensor is located according to the first frequency function;
s104, calculating a first shear modulus of the position of the second acceleration sensor according to the first damping ratio;
and S105, calculating a first shear wave speed of the roadbed at the position where the second acceleration sensor is located according to the first shear modulus.
Through steps S101 to S105, the shear wave velocity of the roadbed surface layer can be tested.
In a specific embodiment of the present disclosure, the method may further include step S106, step S107, step S108, step S109, and step S110.
S106, third data are obtained, wherein the third data comprise third acceleration time-course data collected by a third acceleration sensor arranged in a roadbed right below the second acceleration sensor;
s107, calculating a second frequency function corresponding to the third data according to the first data and the third data;
s108, calculating a second damping ratio of the roadbed at the position where the second acceleration sensor is located according to the second frequency function;
step S109, calculating a second shear modulus of the position of the second acceleration sensor according to the second damping ratio;
and S110, calculating a second shear wave speed of the roadbed at the position of the third acceleration sensor according to the first shear modulus, the second shear modulus and the first shear wave speed.
In a specific embodiment of the present disclosure, after the step S110, a step S111 may be further included.
And S111, when two or more third acceleration sensors are arranged under the second acceleration sensor, repeating the method, and obtaining the shear wave velocity of the roadbed at the position of each third acceleration sensor. That is, the shear wave velocity of each layer in the subgrade can be measured.
When the roadbed shear wave speed of the position of which acceleration sensor group is required to be tested is required, a variable frequency vibration exciter is arranged right above the acceleration sensor group, and the test is carried out according to the steps from the step S101 to the step S111.
In a specific embodiment of the present disclosure, after the step S101, steps S1011 and S1012 may be further included.
Step S1011, eliminating trend terms of the first data and the second data sequentially through a formula (1), wherein the formula (1) is as follows:
yk＝xk-(a0-a1k-...-amk) (1)
in the formula (1), ykTo eliminate the data after trend terms, xkFor the kth acceleration data, xk can be regarded as xk＝a0+a1k+a2k2+...+amkm，a0、a1And am0, 1, 2,.., m, the 0 th, 1 st and mth order components, respectively;
step S1012, filtering the data after the trend term is eliminated through a formula (2), wherein the formula (2) is as follows:
in equation (2), T is the period, T is the time, and ω (T) is the frequency.
In a specific embodiment of the present disclosure, the step S102 may further include a step S1021.
Step S1021, calculating the first frequency function through a formula (3), wherein the formula (3) is as follows:
in formula (3), h (k) is the first frequency function; sxy(k) Cross-power spectral density function s for the first data as excitation signal and the second data as response signalxy(k) From equation (4) sxx(k) Is the self-rate spectral density function, s, of the second dataxx(k) The following equation (5) yields:
equation (4) is:
equation (5) is:
in equations (4) and (5), xi (k) and Yi (k) are Fourier transforms of the ith data segment of one or two random vibration signals, Xi *(k) Is Xi(k) Complex conjugate of (A), Yi *(k) Is Yi(k) M is the average degree.
In a specific embodiment of the present disclosure, between step S102 and step S103, step S1022 may be further included.
Step S1022, smoothing the first frequency function sequentially through a formula (6) to a formula (10) to obtain smoothed data:
in the formulae (6) to (10), A-2、A-1、A0、A1And A2Representing data in 5 consecutive first frequency functions, respectively.
In a specific embodiment of the present disclosure, step S1031 may be further included in step S103.
Step S1031, fitting the first frequency function through a formula (11), and calculating the value of each coefficient to be determined when the modulus is minimum, wherein the formula (11) is as follows:
in formula (11), h (jw) is an imaginary component of the first frequency function; a is0、a1、…、a2NTo be a coefficient of undetermination, b0、b1、…、b2NFor undetermined coefficients, each point is pressedAfter fitting is performed on the equation (11), the error function linear processing is performed, and then each coefficient to be determined can be calculated, so that the first damping ratio is obtained.
In a specific embodiment of the present disclosure, the step S104 may further include a step S1041 and a step S1042.
Step S1041, calculating to obtain the shearing strain of the soil through a formula (12), wherein the formula (12) is as follows:
in the formula (12), k1-k6Respectively, the fitting parameters are influenced by soil body properties, lambda is a first damping ratio, and gamma is shear strain.
The fitting parameters can be corrected according to the soil body properties, specifically, the fitting parameters can be obtained by experiments, or can be filled according to existing research reference values, and the values of the fitting parameters are shown in a fitting parameter comparison table.
Step S1042, calculating according to a formula (13) to obtain the first shear modulus, wherein the formula (13) is as follows:
in the formula (13), GmaxIs the maximum shear modulus, γγFor reference shear strain, gamma for shear strain, obtained from soil testing, G1Is the first shear modulus.
In a specific embodiment of the present disclosure, step S1051 may be further included in step S105.
Step S1051, calculating a first shear wave velocity of the roadbed through a formula (14), wherein the formula (14) is as follows:
in the formula (14), ρ is the density of the soil body of the roadbed, v1 is the first shear wave velocity, G1Is the first shear modulus.
In a specific embodiment of the present disclosure, the step S110 may further include a step S1101 and a step S1102.
Step S1101, calculating a difference value between the second shear modulus and the first shear modulus through a formula (15), wherein the formula (15) is as follows:
△G＝G2-G1 (15)
in the formula (15), Δ G is the difference between the second shear modulus and the first shear modulus, G1Is the first shear modulus, G2A second shear modulus;
step S1102, calculating to obtain a second shear wave velocity of the roadbed according to a formula (16) and a formula (17), wherein the formula (16) and the formula (17) are as follows:
△V＝V2-V1 (17)
in the formula (16), V2At a second shear wave velocity, v1Is the first shear wave velocity, Δ V is the difference between the second shear wave velocity and the first shear wave velocity, Δ G is the difference between the second shear modulus and the first shear modulus, G1For the first shear modulus, A, B is an empirical value after considering soil parameters, and is obtained by a physical mechanical test of soil, wherein the value of A is 3.89, and the value of B is 8.69.
Example 2
As shown in fig. 2, the present embodiment provides an apparatus for calculating a shear wave velocity of a high-speed railway subgrade, which includes a first obtaining module 701, a first calculating module 702, a second calculating module 703, a third calculating module 704, and a fourth calculating module 705.
The first acquisition module 701 is used for acquiring first data and second data, wherein the first data comprises first acceleration time-course data acquired by a first acceleration sensor arranged on a variable-frequency vibration exciter; the second data comprises second acceleration time-course data collected by a second acceleration sensor arranged in a roadbed right below the variable-frequency vibration exciter;
a first calculating module 702, configured to calculate a first frequency function corresponding to the second data according to the first data and the second data;
a second calculating module 703, configured to calculate, according to the first frequency function, a first damping ratio of the roadbed where the second acceleration sensor is located;
a third calculating module 704, configured to calculate a first shear modulus of a position where the second acceleration sensor is located according to the first damping ratio;
a fourth calculating module 705, configured to calculate, according to the first shear modulus, a first shear wave speed of the roadbed where the second acceleration sensor is located.
In a specific embodiment of the present disclosure, the apparatus may further include a second obtaining module 706, a fifth calculating module 707, a sixth calculating module 708, a seventh calculating module 709, and an eighth calculating module 710.
A second obtaining module 706, configured to obtain third data, where the third data includes third acceleration time-course data acquired by a third acceleration sensor arranged in a roadbed right below the second acceleration sensor;
a fifth calculating module 707, configured to calculate, according to the first data and the third data, a second frequency function corresponding to the third data;
a sixth calculating module 708, configured to calculate, according to the second frequency function, a second damping ratio of the roadbed where the second acceleration sensor is located;
a seventh calculating module 709, configured to calculate a second shear modulus of a position where the second acceleration sensor is located according to the second damping ratio;
an eighth calculating module 710, configured to calculate a second shear wave speed of the roadbed where the third acceleration sensor is located according to the first shear modulus, the second shear modulus, and the first shear wave speed.
In a specific embodiment of the present disclosure, the first calculation module 702 may be further configured to perform step S1011, step S1012, step S1021, and step S1022.
In a specific embodiment of the present disclosure, the second calculating module 703 may be further configured to execute step S1031.
In a specific embodiment of the present disclosure, the third calculation module 704 may be further configured to perform step S1041 and step S1042.
In a specific embodiment of the present disclosure, the fourth calculating module 705 can be further configured to execute step S1051.
In a specific embodiment of the present disclosure, the eighth calculating module 710 may be further configured to perform step S1101 and step S1102.
It should be noted that, regarding the apparatus in the above embodiment, the specific manner in which each module performs the operation has been described in detail in the embodiment related to the method, and will not be elaborated herein.
Example 3
Corresponding to the above method embodiment, the embodiment of the present disclosure further provides a high-speed railway-based shear wave velocity calculation device, and a high-speed railway-based shear wave velocity calculation device described below and a high-speed railway-based shear wave velocity calculation method described above may be referred to correspondingly.
FIG. 3 is a block diagram illustrating a high rail speed rail-based shear wave velocity calculation apparatus 800, according to an example embodiment. As shown in fig. 3, the high-speed rail-based shear wave velocity calculation apparatus 800 may include: a processor 801 and a memory 802. The high-railbased shear wave velocity computing apparatus 800 may also include one or more of a multimedia component 803, an input/output (I/O) interface 804, and a communications component 805.
The processor 801 is configured to control the overall operation of the high-speed railway-based shear wave velocity calculation apparatus 800, so as to complete all or part of the steps of the high-speed railway-based shear wave velocity calculation method. The memory 802 is used to store various types of data to support operation at the high-rail-based shear-wave velocity computing device 800, which may include, for example, instructions for any application or method operating on the high-rail-based shear-wave velocity computing device 800, as well as application-related data, such as contact data, transceived messages, pictures, audio, video, and so forth. The Memory 802 may be implemented by any type of volatile or non-volatile Memory device or combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic Memory, flash Memory, magnetic disk or optical disk. The multimedia components 803 may include screen and audio components. Wherein the screen may be, for example, a touch screen and the audio component is used for outputting and/or inputting audio signals. For example, the audio component may include a microphone for receiving an external audio signal. The received audio signal may further be stored in the memory 802 or transmitted through the communication component 805. The audio assembly also includes at least one speaker for outputting audio signals. An input/output (I/O) interface 804 provides an interface between the processor 801 and other interface modules, such as a keyboard, mouse, buttons, and the like. These buttons may be virtual buttons or physical buttons. The communication component 805 is used for wired or wireless communication between the high-speed rail-based shear wave velocity calculation apparatus 800 and other apparatuses. Wireless Communication, such as Wi-Fi, bluetooth, Near Field Communication (NFC), 2G, 3G, or 4G, or a combination of one or more of them, so that the corresponding Communication component 805 may include: Wi-Fi module, bluetooth module, NFC module.
In an exemplary embodiment, the high rail speed shear wave calculation Device 800 may be implemented by one or more Application Specific Integrated Circuits (ASICs), Digital Signal Processors (DSPs), Digital Signal Processing Devices (DSPDs), Programmable Logic Devices (PLDs), Field Programmable Gate Arrays (FPGAs), controllers, microcontrollers, microprocessors or other electronic components for performing the above-described high rail speed shear wave calculation method.
In another exemplary embodiment, a computer readable storage medium comprising program instructions which, when executed by a processor, implement the steps of the high-speed rail-based shear wave velocity calculation method described above is also provided. For example, the computer readable storage medium may be the memory 802 described above that includes program instructions executable by the processor 801 of the high-speed rail-based shear-wave velocity calculation apparatus 800 to perform the high-speed rail-based shear-wave velocity calculation method described above.
Example 4
Corresponding to the above method embodiment, the embodiment of the present disclosure further provides a readable storage medium, and a readable storage medium described below and a high-speed railway subgrade shear wave speed calculation method described above may be correspondingly referenced to each other.
A readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the high-speed rail-based shear wave velocity calculation method of the above-described method embodiments.
The readable storage medium may be a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and various other readable storage media capable of storing program codes.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. A high-speed railway subgrade shear wave velocity calculation method is characterized by comprising the following steps:
acquiring first data and second data, wherein the first data comprises first acceleration time-course data acquired by a first acceleration sensor arranged on a variable-frequency vibration exciter; the second data comprises second acceleration time-course data collected by a second acceleration sensor arranged in a roadbed right below the variable-frequency vibration exciter;
calculating a first frequency function corresponding to the second data according to the first data and the second data;
calculating a first damping ratio of the roadbed at the position of the second acceleration sensor according to the first frequency function;
calculating a first shear modulus of the position of the second acceleration sensor according to the first damping ratio;
calculating a first shear wave speed of the roadbed at the position where the second acceleration sensor is located according to the first shear modulus;
the calculating a first damping ratio of the roadbed at the position of the second acceleration sensor according to the first frequency function comprises:
fitting the first frequency function by equation (11) and calculating the value of each coefficient to be determined when its modulus is minimum, equation (11) being:
in formula (11), h (jw) is an imaginary component of the first frequency function; a is0、a1、…、a2NTo be a coefficient of undetermination, b0、b1、…、b2NFitting each point according to a formula (11) for undetermined coefficients, and performing linear processing on an error function to calculate each undetermined coefficient so as to obtain the first damping ratio;
the calculating a first shear modulus of the position of the second acceleration sensor according to the first damping ratio includes:
the shear strain of the soil is calculated by the formula (12), wherein the formula (12) is as follows:
in the formula (12), k1-k6Respectively are fitting parameters influenced by soil body properties, lambda is a first damping ratio, and gamma is shearing strain;
calculating the first shear modulus according to a formula (13), wherein the formula (13) is as follows:
in the formula (13), GmaxIs the maximum shear modulus, γγFor reference shear strain, gamma for shear strain, obtained from soil testing, G1Is the first shear modulus.
2. The method according to claim 1, wherein after calculating the first shear wave velocity of the roadbed where the second acceleration sensor is located according to the first shear modulus, the method further comprises:
acquiring third data, wherein the third data comprises third acceleration time-course data acquired by a third acceleration sensor arranged in a roadbed right below the second acceleration sensor;
calculating a second frequency function corresponding to the third data according to the first data and the third data;
calculating a second damping ratio of the roadbed at the position of the second acceleration sensor according to the second frequency function;
calculating a second shear modulus of the position of the second acceleration sensor according to the second damping ratio;
and calculating a second shear wave speed of the roadbed at the position of the third acceleration sensor according to the first shear modulus, the second shear modulus and the first shear wave speed.
3. The method for calculating the shear wave velocity of the high-speed railway subgrade according to the claim 1, wherein the calculating the first frequency function corresponding to the second data according to the first data and the second data comprises:
calculating the first frequency function by equation (3), equation (3) being:
in formula (3), h (k) is the first frequency function; sxy(k) Cross-power spectral density function s for the first data as excitation signal and the second data as response signalxy(k) From equation (4) sxx(k) Is the self-rate spectral density function, s, of the second dataxx(k) The following is obtained from equation (5):
equation (4) is:
equation (5) is:
in equations (4) and (5), xi (k) and Yi (k) are Fourier transforms of the ith data segment of one or two random vibration signals, Xi *(k) Is Xi(k) Complex conjugate of (A), Yi *(k) Is Yi(k) M is the average degree.
4. The method for calculating the shear wave velocity of the high-speed railway subgrade according to the claim 3, wherein after the calculating the first frequency function corresponding to the second data according to the first data and the second data, the method further comprises:
smoothing the first frequency function sequentially through formulas (6) to (10) to obtain smoothed data:
in the formulae (6) to (10), A-2、A-1、A0、A1And A2Representing data in 5 consecutive first frequency functions, respectively.
5. The method according to claim 1, wherein the calculating a first shear wave velocity of the roadbed where the second acceleration sensor is located according to the first shear modulus comprises:
calculating a first shear wave velocity of the subgrade by equation (14), equation (14) being:
in the formula (14), ρ is the density of the soil body of the roadbed, v1 is the first shear wave velocity, G1Is the first shear modulus.
6. The method according to claim 2, wherein calculating the second shear-wave velocity of the roadbed where the third acceleration sensor is located according to the first shear modulus, the second shear modulus and the first shear-wave velocity comprises:
calculating the difference between the second shear modulus and the first shear modulus by using a formula (15), wherein the formula (15) is as follows:
△G＝G2-G1 (15)
in the formula (15), Δ G is the difference between the second shear modulus and the first shear modulus, G1Is the first shear modulus, G2A second shear modulus;
and calculating a second shear wave speed of the roadbed by using the formula (16) and the formula (17), wherein the formula (16) and the formula (17) are as follows:
△V＝V2-V1 (17)
in the formula (16), V2At a second shear wave velocity, v1Is the first shear wave velocity, Δ V is the difference between the second shear wave velocity and the first shear wave velocity, Δ G is the difference between the second shear modulus and the first shear modulus, G1For the first shear modulus, A, B is an empirical value after considering soil parameters, and is obtained by a physical mechanical test of soil, wherein the value of A is 3.89, and the value of B is 8.69.
7. A high-speed rail bed shear wave velocity calculation apparatus, comprising:
the first acquisition module is used for acquiring first data and second data, wherein the first data comprises first acceleration time-course data acquired by a first acceleration sensor arranged on a variable-frequency vibration exciter; the second data comprises second acceleration time-course data collected by a second acceleration sensor arranged in a roadbed right below the variable-frequency vibration exciter;
the first calculating module is used for calculating a first frequency function corresponding to the second data according to the first data and the second data;
the second calculation module is used for calculating a first damping ratio of the roadbed at the position where the second acceleration sensor is located according to the first frequency function;
the third calculation module is used for calculating a first shear modulus of the position of the second acceleration sensor according to the first damping ratio;
the fourth calculation module is used for calculating the first shear wave speed of the roadbed at the position where the second acceleration sensor is located according to the first shear modulus;
the calculating a first damping ratio of the roadbed at the position of the second acceleration sensor according to the first frequency function comprises:
fitting the first frequency function by equation (11) and calculating the value of each coefficient to be determined when its modulus is minimum, equation (11) being:
in formula (11), h (jw) is an imaginary component of the first frequency function; a is0、a1、…、a2NTo be a coefficient of undetermination, b0、b1、…、b2NFitting each point according to a formula (11) for undetermined coefficients, and performing linear processing on an error function to calculate each undetermined coefficient so as to obtain the first damping ratio;
the calculating a first shear modulus of the position of the second acceleration sensor according to the first damping ratio includes:
the shear strain of the soil is calculated by the formula (12), wherein the formula (12) is as follows:
in the formula (12), k1-k6Respectively are fitting parameters influenced by soil body properties, lambda is a first damping ratio, and gamma is shear strain;
calculating the first shear modulus according to a formula (13), wherein the formula (13) is as follows:
in the formula (13), GmaxIs the maximum shear modulus, γγFor reference shear strain, gamma for shear strain, obtained from soil testing, G1Is the first shear modulus.
8. A high-speed rail bed shear wave velocity calculation apparatus, comprising:
a memory for storing a computer program;
a processor for implementing the steps of the method according to any one of claims 1 to 6 when executing the computer program.
9. A computer-readable storage medium characterized by: the computer-readable storage medium has stored thereon a computer program which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 6.
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