CN113312860A - Method for assembling rock rheological element - Google Patents
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Abstract
The invention discloses an assembling method of a rock rheological element, which comprises the following steps: obtaining a rheological strain-time curve of the uniaxial compression rock under the condition of multistage stress loading; realizing series connection and parallel connection of the rock rheological elements by adopting a genetic expression algorithm, and deducing a rheological constitutive equation assembled by the rheological elements; determining a determination coefficient of a rheological constitutive equation through fitting; and determining a rock rheological constitutive model which can reflect the experimental data most through iterative calculation. The invention can overcome the artificial subjectivity in the traditional rheological constitutive model assembling process, realize the automatic assembling of rheological elements and obtain the rock rheological constitutive model which can reflect the experimental data most.
Description
Technical Field
The invention relates to a method for assembling a rock rheological element.
Background
The rheological behavior of the rock is an important mechanical behavior of the rock, and has a great influence on the long-term stability of geotechnical engineering. The rheological behavior of the rock is quantitatively described, at present, various rheological elements (elastic elements, viscous elements and plastic elements) are generally assembled with one another to establish a rheological constitutive model of the rock, the change trend of the rheological elements is analyzed according to a strain-time curve obtained by an indoor experiment, and then the assembly form of the rheological elements is determined, so that the assembly process of the rheological elements has large artificial subjectivity, the acquisition of the rheological constitutive model depends on the subjectivity of testers to a great extent, and the assembly process of the rheological elements is not objective.
Disclosure of Invention
In order to solve the technical problems, the invention provides an assembling method of a rock rheological element, which is simple in algorithm and strong in objectivity.
The technical scheme for solving the problems is as follows: a method of assembling a rock rheological element comprising the steps of:
the method comprises the following steps: obtaining a rheological strain-time curve of the uniaxial compression rock under the condition of multistage stress loading;
step two: realizing series connection and parallel connection of the rock rheological elements by adopting a genetic expression algorithm, and deducing a rheological constitutive equation assembled by the rheological elements;
step three: determining a determination coefficient of a rheological constitutive equation through fitting;
step four: and determining a rock rheological constitutive model which can reflect the experimental data most through iterative calculation.
In the first step, a uniaxial rock compression experiment is carried out on the cylindrical rock sample by adopting a testing machine under different stress levels, and a strain time curve of the rock under different stress levels is obtained.
The assembling method of the rock rheological element comprises the following specific steps:
the gene genetic expression algorithm is adopted to realize the hybridization and variation operation of the gene sequence consisting of the element combination mode and the rheological element, and the determination coefficient is used for determining whether the gene sequence is eliminated according to the corresponding fitting data of the rheological constitutive model corresponding to each gene sequence, wherein the element combination mode comprises parallel connection and series connection, and the rheological element comprises an elastic element, a viscous element and a plastic element;
the gene sequence in the gene genetic expression algorithm comprises an operation gene and a terminal gene, wherein the terminal gene is not connected with any gene, and the operation gene is connected with a corresponding number of operation genes or terminal genes according to specific operands; in the assembly process of the rheological element, namely the elastic element H, the viscous element N and the plastic element Y are regarded as terminal genes, two assembly modes of the rheological element are connected in series + and in parallel// are regarded as operation genes, and the connection number of the two operation genes is 2; according to the gene sequence and the corresponding operand of the gene, the gene sequence is converted into a tree form from top to bottom and from left to right, and the gene sequence of the rheological constitutive model is as follows:
+H||Y N (1)
converting the gene sequence into a gene sequence tree and further converting to obtain a rheological constitutive equation:
where ε (t) is an expression relating strain to time, t is time, σ0For constant stress, k is the elastic element coefficient, η is the viscous element coefficient, σsIs the plastic element coefficient.
The assembling method of the rock rheological element comprises the following three specific processes:
fitting the strain-time curve by adopting the formula (2) to obtain a determination coefficient R of a rheological constitutive equation under different stress levels2Wherein the determination coefficient calculation formula is as follows:
wherein N represents the number of strain-time curve data at the stress level, εiRepresents the experimentally obtained strain,. epsilonmeanRepresents the average value of the strain under the stress level condition; ε (t)i) Representing the strain calculated by a fitting formula;
respectively calculating the determination coefficients of the rheological constitutive equation under different stress levels,
selecting the minimum value of all the determination coefficients as the determination coefficients of the rheological constitutive equation:
and the determined coefficient is the corresponding fitness of the gene sequence.
The assembling method of the rock rheological element comprises the following specific steps:
step 1: determining relevant hyper-parameters of a genetic expression algorithm of a gene: the number of the population pop _ size, the total iteration number of the system total _ iter, the initial iteration number count, the length h of the front end of the gene sequence, the number of the genes which can be connected most at the front end, the tail length t of the gene sequence, and the probability P of gene sequence exchangecProbability of Gene sequence Gene mutation PmGroup elimination ratio Pe(ii) a The length of the tail of the gene sequence is determined according to the following formula:
t＝h(n-1)+1 (5)
the total length of the gene sequence is the sum of the length of the front end of the gene sequence and the length of the tail of the gene sequence, and the total length of the gene sequence is hn + 1.
Step 2: randomly generating pop _ size gene sequences, each gene sequence being hn +1 in length;
and step 3: obtaining a rheological constitutive equation corresponding to the gene sequence according to the gene sequence, calculating a fitting coefficient of the rheological constitutive equation, and taking a minimum determination coefficient under each stress level condition as a fitness value of the gene sequence; arranging the gene sequences from top to bottom according to the fitness value, and eliminating the ranked number in the population, wherein the specifically eliminated gene sequences are pop _ size × Pe(ii) a Then randomly generating pop _ size × PeThe gene sequences enable the number of the population to be pop _ size to be kept unchanged, and the optimal gene sequences and fitness values are stored; continuously updating the optimal gene sequence and the fitness value according to the fitness value in the iterative process;
and 4, step 4: and (3) population crossing: two adjacent genes in the populationRandomly selecting a point as a cross position, and randomly generating a random number of 0 to 1 if the random number of 0 to 1 is less than or equal to PcThen adjacent gene sequences are interleaved to form two new gene sequences as follows:
when the randomly selected cross point is the fourth gene of the gene sequence, then at this time two gene sequences in equation (6) are swapped to form a new gene sequence:
and 5: genetic variation: carrying out mutation operation on all genes in the gene sequence; first, a random number is randomly generated, when the random number is less than or equal to PmThen, mutation operation is performed as follows:
////N N N Y H N H N (8)
when the 6 th gene Y of the gene sequence is mutated into H:
////N N N H H N H N (9)
in the process of mutation operation, if the gene needing mutation is at the front end of the gene sequence, the gene is mutated into an operation gene or a terminal gene, and if the gene needing mutation is at the tail end of the gene sequence, the gene can be mutated into the terminal gene only;
step 6: judging the number of times of population iteration count as count +1, and entering step 3 if the number of times of population iteration count is less than or equal to total _ iter; otherwise, entering step 7;
and 7: and finishing the calculation.
The invention has the beneficial effects that: firstly, acquiring a rheological strain-time curve of uniaxial compression rock under a multistage stress loading condition; then, realizing series connection and parallel connection of the rock rheological elements by adopting a genetic expression algorithm, and deducing a rheological constitutive equation assembled by the rheological elements; determining a determination coefficient of a rheological constitutive equation through fitting; finally, determining a rock rheological constitutive model capable of reflecting experimental data most through iterative calculation; the invention can overcome the artificial subjectivity in the traditional rheological constitutive model assembling process, realize the automatic assembling of rheological elements and obtain the rock rheological constitutive model which can reflect the experimental data most.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a mudstone strain-time graph obtained by a laboratory experiment.
FIG. 3 is a schematic diagram of a gene sequence tree.
Fig. 4 is a schematic diagram of a rheological constitutive model.
FIG. 5 is a schematic diagram of a mudstone rheological gene sequence tree.
FIG. 6 is a schematic diagram of a mudstone rheological constitutive model.
Detailed Description
The invention is further described below with reference to the figures and examples.
As shown in fig. 1, a method of assembling a rock rheological element includes the steps of:
the method comprises the following steps: and acquiring a rheological strain-time curve of the uniaxial compression rock under the condition of multistage stress loading.
A testing machine is adopted to carry out uniaxial rock compression experiments on cylindrical rock samples under different stress level conditions, and strain time curves of the rocks under different stress level conditions are obtained.
Step two: and realizing series connection and parallel connection of the rock rheological elements by adopting a genetic expression algorithm, and deducing a rheological constitutive equation assembled by the rheological elements. The second specific process comprises the following steps:
the gene genetic expression algorithm is adopted to realize the hybridization and variation operation of the gene sequence consisting of the element combination mode and the rheological element, and the coefficient is determined to determine whether the gene sequence is eliminated according to the corresponding fitting data of the rheological constitutive equation corresponding to each gene sequence, wherein the element combination mode comprises parallel connection and series connection, and the rheological element comprises an elastic element, a viscous element and a plastic element;
the gene sequence in the gene genetic expression algorithm comprises an operation gene and a terminal gene, wherein the terminal gene is not connected with any gene, and the operation gene is connected with a corresponding number of operation genes or terminal genes according to specific operands; in the assembly process of the rheological element, namely the elastic element H, the viscous element N and the plastic element Y are regarded as terminal genes, two assembly modes of the rheological element are connected in series + and in parallel// are regarded as operation genes, and the connection number of the two operation genes is 2; according to the gene sequence and the corresponding operand of the gene, the gene sequence is converted into a tree form from top to bottom and from left to right, and the gene sequence of the rheological constitutive model is as follows:
+H||Y N (1)
converting the gene sequence into a gene sequence tree and further converting to obtain a rheological constitutive equation:
step three: determining coefficients of rheological constitutive equations through fitting. The third concrete process is as follows:
fitting the strain-time curve by adopting the formula (2) to obtain a determination coefficient R of a rheological constitutive equation under different stress levels2Wherein the determination coefficient calculation formula is as follows:
wherein N represents the number of strain-time curve data at the stress level, εiRepresents the experimentally obtained strain,. epsilonmeanRepresents the average value of the strain under the stress level condition; ε (t)i) Representing the strain calculated by a fitting formula;
respectively calculating the determination coefficients of the rheological constitutive equation under different stress levels,
selecting the minimum value of all the determination coefficients as the determination coefficients of the rheological constitutive model:
and the determined coefficient is the corresponding fitness of the gene sequence.
Step four: and determining a rock rheological constitutive model which can reflect the experimental data most through iterative calculation.
The fourth specific process of the step is as follows:
step 1: determining relevant hyper-parameters of a genetic expression algorithm of a gene: the number of the population pop _ size, the total iteration number of the system total _ iter, the initial iteration number count, the length h of the front end of the gene sequence, the number of the genes which can be connected most at the front end, the tail length t of the gene sequence, and the probability P of gene sequence exchangecProbability of Gene sequence Gene mutation PmGroup elimination ratio Pe(ii) a The length of the tail of the gene sequence is determined according to the following formula:
t＝h(n-1)+1 (5)
the total length of the gene sequence is the sum of the length of the front end of the gene sequence and the length of the tail of the gene sequence, and the total length of the gene sequence is hn + 1.
Step 2: randomly generating pop _ size gene sequences, each gene sequence being hn +1 in length;
and step 3: obtaining a rheological constitutive equation corresponding to the gene sequence according to the gene sequence, calculating a fitting coefficient of the rheological constitutive equation, and taking a minimum determination coefficient under each stress level condition as a fitness value of the gene sequence; arranging the gene sequences from top to bottom according to the fitness value, and eliminating the ranked number in the population, wherein the specifically eliminated gene sequences are pop _ size × Pe(ii) a Then randomly generating pop _ size × PeThe gene sequences enable the number of the population to be pop _ size to be kept unchanged, and the optimal gene sequences and fitness values are stored; continuously updating the optimal gene sequence according to fitness value in iterative process anda fitness value;
and 4, step 4: and (3) population crossing: randomly selecting a point of two adjacent gene sequences in the population as a cross position, and randomly generating a random number from 0 to 1 if the random number from 0 to 1 is less than or equal to PcThen adjacent gene sequences are interleaved to form two new gene sequences as follows:
when the randomly selected cross point is the fourth gene of the gene sequence, then at this time two gene sequences in equation (6) are swapped to form a new gene sequence:
and 5: genetic variation: carrying out mutation operation on all genes in the gene sequence; first, a random number is randomly generated, when the random number is less than or equal to PmThen, mutation operation is performed as follows:
////N N N Y H N H N (8)
when the 6 th gene Y of the gene sequence is mutated into H:
////N N N H H N H N (9)
in the process of mutation operation, if the gene needing mutation is at the front end of the gene sequence, the gene is mutated into an operation gene or a terminal gene, and if the gene needing mutation is at the tail end of the gene sequence, the gene can be mutated into the terminal gene only;
step 6: judging the number of times of population iteration count as count +1, and entering step 3 if the number of times of population iteration count is less than or equal to total _ iter; otherwise, entering step 7;
and 7: and finishing the calculation.
Examples
As shown in fig. 2: carrying out constant stress (21MPa, 26MPa, 31MPa and 36MPa) loading experiments on the mudstone under the conditions of four stress levels, wherein each stress level is loaded for 20 hours in total, then entering the stress loading of the next stage, and obtaining a strain-time curve of the mudstone by recording strain-time data in the experimental process.
After strain-time test data are obtained, gene genetic expression algorithm is adopted to realize the operation of hybridization and variation of gene sequences consisting of element combination modes (parallel connection and series connection) and rheological elements (elastic elements, viscous elements and plastic elements), and a coefficient is determined according to the corresponding fitting data of a rheological constitutive equation corresponding to each gene sequence to determine whether the gene sequence is eliminated. The gene sequence in the gene genetic expression algorithm mainly comprises an operation gene and a terminal gene, the terminal gene is not connected with any gene, and the operation gene can be connected with a corresponding number of operation genes or terminal genes according to specific operands. In the assembly process of the rheological element, the rheological element (elastic element (H), viscous element (N) and plastic element (Y)) is regarded as a terminal gene, and two assembly modes (series (+) and parallel (/ /)) of the rheological element are regarded as operation genes, and the number of links of the two operation genes is 2. According to the gene sequence and the corresponding operand of the gene, the gene sequence can be converted into a tree form from top to bottom and from left to right. If the gene sequence of the rheological constitutive model is as follows:
+H||Y N
according to the above principle, the gene sequence can be converted into a tree form (FIG. 3), and the gene sequence tree is further converted to obtain a rheological constitutive model, as shown in FIG. 4.
According to the rheological constitutive model, a rheological constitutive equation can be obtained as follows:
then, fitting is carried out by adopting the above formula to correspond to a strain-time curve to obtain a determination coefficient R of a rheological constitutive equation under the conditions of different stress levels2Wherein the determination coefficient calculation formula is as follows:
wherein n represents the number of strain-time curve data at the stress level, εiRepresents the experimentally obtained strain,. epsilonmeanRepresents the average value of the strain under the stress level condition; ε (t)i) The resulting strain is calculated by a fitting formula.
Respectively calculating rheological constitutive equation determining coefficients under different stress levels,
selecting the minimum value of all the determination coefficients as the determination coefficient of the rheological constitutive model:
and the determined coefficient is the corresponding fitness of the gene sequence.
According to the method, the corresponding fitness of the gene sequence can be quickly obtained according to the rheological gene sequence, the optimal rheological gene sequence is obtained through continuous iteration, and the corresponding rheological gene sequence is the gene sequence which is required to be obtained.
The method comprises the following specific steps:
step 1: determining relevant hyper-parameters of a genetic expression algorithm of a gene: the number of the population pop _ size is 400, the total iteration number of the system, total _ iter is 20000, the initial iteration number count is 0, the length h of the front end of the gene sequence is 15, the number of the genes which can be connected most at the front end is n 30, the length t of the tail of the gene sequence is 436, and the probability P of gene sequence exchange isc0.6, probability of gene sequence gene mutation PmIs 0.01, the population elimination rate PeIs 0.1. The length of the tail gene sequence can be determined according to the following formula:
t＝h(n-1)+1
the total length of the gene sequence is the sum of the length of the head gene sequence and the length of the tail gene sequence, and the total length of the gene sequence is 451.
Step 2: 400 gene sequences were randomly generated, each gene sequence having a length of 451.
And step 3: and (3) calculating the fitness value of each gene sequence in the population, arranging the gene sequences from top to bottom according to the fitness values, and eliminating the number of the ranked gene sequences in the population, wherein the specific number of the eliminated gene sequences is 40. Then, 40 gene sequences were randomly generated so that the number of the population was 400, and remained unchanged. And storing the optimal gene sequence and fitness value. And continuously updating the optimal gene sequence and the fitness value according to the fitness value in the iterative process.
And 4, step 4: and (4) crossing the population, and randomly selecting a point of two adjacent gene sequences in the population as a crossing position. And randomly generating a random number of 0 to 1, and if the number is less than or equal to 0.6, performing a crossover operation on adjacent gene sequences to form two new gene sequences as follows:
when the randomly selected cross point is the fourth gene, then a new gene sequence is formed after the two gene sequences in the above formula are exchanged:
and 5: and (5) carrying out gene mutation. All genes in the gene sequence are subjected to mutation operation. Firstly, a random number is randomly generated, and when the random number is less than or equal to 0.01, mutation operation is carried out, as follows:
////N N N Y H N H N
when the 6 th gene of the gene sequence is mutated from Y to H, the gene sequence is changed into:
////N N N H H N H N
in the process of mutation operation, it should be noted that if the gene to be mutated is at the front end of the gene sequence, the gene can be mutated into an operation gene or a terminal gene, and if the gene to be mutated is at the tail end of the gene sequence, the gene can be mutated into the terminal gene only.
Step 6: judging the number of times of population iteration count as count +1, and entering step 3 if the number of times of population iteration count is less than or equal to 20000; otherwise, step 7.
And 7: and finishing the calculation.
According to the process, after iteration is carried out for 20000 times, the optimal gene sequence in all settlement results is preferably selected, and the gene sequence of the mudstone rheological constitutive model is obtained through trial calculation as follows:
the corresponding rheological constitutive model tree is shown in fig. 4. And corresponding rheological constitutive models are obtained. The corresponding rheological constitutive model formula is as follows:
where ε (t) is an expression relating strain to time, t is time, σ0For constant stress, k1Coefficient of first elastic element, k2Is the coefficient of the second elastic element, eta1Is the coefficient of the first viscous element, η2Is the coefficient of the second viscous element.
The corresponding correlation coefficients were obtained as in table 1.
TABLE 1 fitting parameters
| Stress level (MPa) | k1(MPa) | η1(MPa·h) | k2(MPa) | η2(MPa·h) | R2 |
| 21MPa | 34711.05 | 1100846.61 | 99293.74 | 155980.92 | 0.93 |
| 26MPa | 13047.79 | 123918901.65 | 90361.39 | 375980.95 | 0.98 |
| 31MPa | 9953.07 | 3908880.31 | 188253.59 | 225143.76 | 0.94 |
| 36MPa | 5328.21 | 1029447.11 | 40585.21 | 98900.92 | 0.99 |
Compared with the traditional method for determining the empirical formula of the uniaxial compressive strength of the rock, the method provided by the invention can fully utilize all experimental data, has no artificial subjectivity in the process of determining the empirical formula, and is suitable for the field of testing the uniaxial compressive strength of the rock.
Claims (5)
1. A method of assembling a rock rheological element comprising the steps of:
the method comprises the following steps: obtaining a rheological strain-time curve of the uniaxial compression rock under the condition of multistage stress loading;
step two: realizing series connection and parallel connection of the rock rheological elements by adopting a genetic expression algorithm, and deducing a rheological constitutive equation assembled by the rheological elements;
step three: determining a determination coefficient of a rheological constitutive equation through fitting;
step four: and determining a rock rheological constitutive model which can reflect the experimental data most through iterative calculation.
2. The method for assembling a rock rheological element according to claim 1, wherein in the first step, a uniaxial rock compression test under different stress level conditions is performed on a cylindrical rock sample by using a testing machine, and a strain time curve of the rock under different stress level conditions is obtained.
3. The method for assembling a rock rheological element according to claim 1, characterized in that the step two specific process is as follows:
the gene genetic expression algorithm is adopted to realize the hybridization and variation operation of the gene sequence consisting of the element combination mode and the rheological element, and the determination coefficient is used for determining whether the gene sequence is eliminated according to the corresponding fitting data of the rheological constitutive model corresponding to each gene sequence, wherein the element combination mode comprises parallel connection and series connection, and the rheological element comprises an elastic element, a viscous element and a plastic element;
the gene sequence in the gene genetic expression algorithm comprises an operation gene and a terminal gene, wherein the terminal gene is not connected with any gene, and the operation gene is connected with a corresponding number of operation genes or terminal genes according to specific operands; in the assembly process of the rheological element, namely the elastic element H, the viscous element N and the plastic element Y are regarded as terminal genes, two assembly modes of the rheological element are connected in series + and in parallel// are regarded as operation genes, and the connection number of the two operation genes is 2; according to the gene sequence and the corresponding operand of the gene, the gene sequence is converted into a tree form from top to bottom and from left to right, and the gene sequence of the rheological constitutive model is as follows:
+H||Y N (1)
converting the gene sequence into a gene sequence tree and further converting to obtain a rheological constitutive equation:
where ε (t) is an expression relating strain to time, t is time, σ0For constant stress, k is the elastic element coefficient, η is the viscous element coefficient, σsIs the plastic element coefficient.
4. The method for assembling a rock rheological element according to claim 3, characterized in that the step three specific processes are as follows:
fitting the strain-time curve by adopting the formula (2) to obtain a determination coefficient R of a rheological constitutive equation under different stress levels2Wherein the determination coefficient calculation formula is as follows:
wherein N represents the number of strain-time curve data at the stress level, εiRepresents the experimentally obtained strain,. epsilonmeanRepresents the average value of the strain under the stress level condition; ε (t)i) Representing the strain calculated by a fitting formula;
respectively calculating the determination coefficients of the rheological constitutive equation under different stress levels,
selecting the minimum value of all the determination coefficients as the determination coefficients of the rheological constitutive equation:
and the determined coefficient is the corresponding fitness of the gene sequence.
5. The method for assembling a rock rheological element according to claim 4, characterized in that the step four specific processes are as follows:
step 1: determining relevant hyper-parameters of a genetic expression algorithm of a gene: the number of the population pop _ size, the total iteration number of the system total _ iter, the initial iteration number count, the length h of the front end of the gene sequence, the number of the genes which can be connected most at the front end, the tail length t of the gene sequence, and the probability P of gene sequence exchangecProbability of Gene sequence Gene mutation PmGroup elimination ratio Pe(ii) a The length of the tail of the gene sequence is determined according to the following formula:
t＝h(n-1)+1 (5)
the total length of the gene sequence is the sum of the length of the front end of the gene sequence and the length of the tail of the gene sequence, and the total length of the gene sequence is hn + 1.
Step 2: randomly generating pop _ size gene sequences, each gene sequence being hn +1 in length;
and step 3: obtaining a rheological constitutive equation corresponding to the gene sequence according to the gene sequence, calculating a fitting coefficient of the rheological constitutive equation, and taking the minimum determination coefficient under each stress level condition as the gene sequenceA fitness value of; arranging the gene sequences from top to bottom according to the fitness value, and eliminating the ranked number in the population, wherein the specifically eliminated gene sequences are pop _ size × Pe(ii) a Then randomly generating pop _ size × PeThe gene sequences enable the number of the population to be pop _ size to be kept unchanged, and the optimal gene sequences and fitness values are stored; continuously updating the optimal gene sequence and the fitness value according to the fitness value in the iterative process;
and 4, step 4: and (3) population crossing: randomly selecting a point of two adjacent gene sequences in the population as a cross position, and randomly generating a random number from 0 to 1 if the random number from 0 to 1 is less than or equal to PcThen adjacent gene sequences are interleaved to form two new gene sequences as follows:
when the randomly selected cross point is the fourth gene of the gene sequence, then at this time two gene sequences in equation (6) are swapped to form a new gene sequence:
and 5: genetic variation: carrying out mutation operation on all genes in the gene sequence; first, a random number is randomly generated, when the random number is less than or equal to PmThen, mutation operation is performed as follows:
// // N N N Y H N H N (8)
when the 6 th gene Y of the gene sequence is mutated into H:
// // N N N H H N H N (9)
in the process of mutation operation, if the gene needing mutation is at the front end of the gene sequence, the gene is mutated into an operation gene or a terminal gene, and if the gene needing mutation is at the tail end of the gene sequence, the gene can be mutated into the terminal gene only;
step 6: judging the number of times of population iteration count as count +1, and entering step 3 if the number of times of population iteration count is less than or equal to total _ iter; otherwise, entering step 7;
and 7: and finishing the calculation.
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| QUNFEI ZHAO等: "Metabolic coupling of two small-molecule thiols programs the biosynthesis of lincomycin A", 《NATURE》 * |
| 赵延林等: "直剪作用下不共面断续节理岩桥破断试验与数值研究", 《土木建筑与环境工程》 * |
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| CN113312860B (en) | 2022-05-03 |
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