阅读说明：本技术 一种采煤沉陷地表点下沉过程动态预测方法 (Dynamic prediction method for coal mining subsidence earth surface point subsidence process ) 是由 胡青峰 刘文锴 崔希民 王新静 李春意 李志伟 郭广礼 查剑锋 杨泽发 李怀展 于 2021-06-18 设计创作，主要内容包括：本发明公开一种能够精准描述采煤沉陷地表点下沉过程的动态预测方法。该采煤沉陷地表点下沉过程动态预测方法能够同时表达地表点下沉、下沉速度及其加速度的特征,并构建所述采煤地表点下沉过程动态预测时间函数。本发明解决了以下技术问题：目前地表开采沉陷动态发育过程的复杂性和难以准确描述性,以及现有函数模型并不能同时正确表达地表沉陷过程及其速度和加速度的特征,且没有给出相应的模型参数有效求取方法的现状。(The invention discloses a dynamic prediction method capable of accurately describing a coal mining subsidence earth surface point subsidence process. The dynamic prediction method for the coal mining subsidence earth surface point subsidence process can simultaneously express the characteristics of the subsidence, the subsidence speed and the acceleration of the earth surface point, and construct the dynamic prediction time function for the coal mining subsidence earth surface point subsidence process. The invention solves the following technical problems: the complexity and the difficulty of accurate description of the current dynamic development process of surface mining subsidence, the current function model cannot simultaneously and correctly express the characteristics of the surface subsidence process and the speed and the acceleration of the surface subsidence process, and the current situation of a corresponding model parameter effective solving method is not provided.)

1. A dynamic prediction method for a coal mining subsidence earth surface point subsidence process is characterized by comprising the following steps: the dynamic prediction method for the coal mining subsidence earth surface point subsidence process can simultaneously express the characteristics of the subsidence, the subsidence speed and the acceleration of the earth surface point, and construct a dynamic prediction time function of the coal mining earth surface point subsidence process;

the specific method comprises the following steps:

a. constructing a dynamic prediction time function of the coal mining surface point sinking process, as shown in a formula (2),

b. solving a first derivative of t by the formula (2) to obtain a formula (3), wherein the formula (3) effectively expresses the sinking speed characteristic of the mining earth surface point;

c. solving a second derivative of the t by the formula (2) to obtain a formula (4), wherein the formula (4) effectively expresses the sinking acceleration characteristic of the mining surface point;

d. a dynamic prediction function of a coal mining subsidence surface point subsidence process is shown as a formula (1),

wherein W (x, y) is the maximum subsidence value of the coal mining subsidence earth surface point with the coordinate of (x, y); q is the surface subsidence coefficient; m is the coal seam mining thickness; alpha is the coal bed inclination angle; r is the main influence radius of the surface mining subsidence prediction probability integration method; d is the goaf area; eta and zeta are the length and width of the goaf respectively; t is the time elapsed for mining the surface point; c and n are time factor influence coefficients related to mechanical properties of the overburden stratum, c mainly describes dynamic characteristics of a coal mining subsidence surface point sinking process, and n mainly describes time characteristics of mining surface point appearance lagging underground mining.

2. The method for dynamically predicting the subsidence process of the coal mining subsidence surface point according to claim 1, wherein: the method for solving the time factor influence coefficient c related to the mechanical property of the overburden stratum is as follows:

degenerating equation (2), i.e., if n is 1, equation (2) degenerates to the classical Knothe time function (equation (5)), and the parameter c is determined from equation (6);

Φ(t)＝1-e^-ct (5)

wherein H₀And in the average mining depth, tan beta is a main influence angle tangent value of the surface mining subsidence prediction probability integration method, v is a working face advancing speed, and r is a main influence radius of the surface mining subsidence prediction probability integration method.

3. The method for dynamically predicting the subsidence process of the coal mining subsidence surface point according to claim 1, wherein: the method for solving the time factor influence coefficient n related to the mechanical property of the overburden stratum is as follows:

when the size of the underground goaf reaches 3/8H₀The surface begins to sink, and the surface begins to sink is marked by the surface sinking of 10mm, so the following formula holds:

wherein, W₀Is the maximum subsidence value of the earth's surface, W₀M is the coal seam mining thickness, q is the surface subsidence coefficient, a is the coal seam dip angle, v is the working face advancing speed, H₀Mean depth of cut.

Technical Field

The invention belongs to the technical field of mining subsidence research, and particularly relates to a dynamic prediction method for a coal mining subsidence surface point subsidence process.

Background

The surface subsidence caused by coal mining is a complex time and space process, and as the working face advances, the relative positions of the stope face and the surface point at different times are different, and the influence of mining on the surface point is also different. The movement of the surface point goes through the whole process from the beginning of the movement to the violent movement and finally to the stop of the movement. In the production practice, some situations are often encountered, namely, the actual problem cannot be solved well only according to the subsidence rule after the ground surface is stabilized, and the dynamic rule of the movement deformation must be further researched. For example, in an over-mining condition, a subsidence basin exhibits a flat bottom, within which the subsidence is the same, with only minimal deformation of the ground surface, but it cannot be assumed that the building in this area is not subject to deformation or damage because every point in the area is subject to dynamic deformation during the advancement of the work surface, which, although temporary, can also cause damage to the building. When coal is mined under a building, the starting time of the mining influence of the building and the ground surface moving deformation amount in different periods need to be determined at any time so as to take proper measures for the building, such as strengthening observation, strengthening, temporary emigration or changing purposes. Therefore, the development of the dynamic prediction research of the surface mining subsidence becomes a research hotspot of experts and scholars in the field, but due to the complexity and the difficulty in accurate description of the dynamic development process of the surface mining subsidence, the existing quantitative prediction research of the dynamic development rule of the surface mining subsidence is not sufficient, the existing function model cannot simultaneously and correctly express the characteristics of the surface subsidence process and the speed and the acceleration of the surface subsidence process, and a corresponding effective model parameter solving method is not provided. The invention provides a dynamic prediction method for the subsidence process of a coal mining subsidence ground surface point, so as to further improve the research on the dynamic development rule of the ground surface mining subsidence.

Most of the coal mining subsidence earth surface point subsidence process dynamic prediction methods are combined with a probability integration method and a relevant time function to construct a relevant model, wherein the probability integration method is relatively complete, and research work is mainly carried out around the time function. The current studies on the function of time are mainly: the knohe (1952) establishes a knohe time function model (formula (1)) based on the Mitscherlich growth law, wherein the model has only one parameter and is effective for predicting dynamic subsidence, inclination, curvature, horizontal movement and horizontal deformation of the earth surface, but is not good in reflecting the change rule of the subsidence speed and acceleration of the earth surface. In view of the defects of the Knothe time function, Sroka (1982) -1983) constructs a double-parameter time function which can better reflect the change rule of the ground subsidence speed and the acceleration. However, the influence of underground mining is not instantly transferred to the ground surface, and generally, when the working face advances to the mining depth of 0.25-0.5 times from the open cut hole, the influence of underground mining appears on the ground surface, and the dual-parameter time function cannot be well reflected in the aspect. For this reason, Kowalski proposes a generalized time function from the viewpoint that surface mining appears to lag underground mining, which has three parameters and can better reflect the whole process of surface movement deformation theoretically. However, although the dual-parameter time function and the generalized time function have a theoretical advantage over the Knothe time function, the parameters are relatively difficult to determine under different geological mining conditions due to the large number of parameters contained in the two. When the subsidence speed of the earth surface point is supposed to reach the maximum value, the subsidence amount of the earth surface point is about equal to half of the maximum value of the point, a segmented Knothe time function is constructed, the accuracy of the Knothe time function for dynamically predicting the earth surface movement deformation is improved to a certain extent by the aid of the time function model, and the application range of the Knothe time function is expanded; meanwhile, the model has the defects, such as: the time function value does not coincide with the theoretical value at the segmentation point, the maximum value of the time function cannot converge to 1, and so on. Liuyu Cheng et al directly processed the Knothe time function with the k power, with this improvement the Knothe time function, the time function after the improvement has had great improvement to the characteristics of describing the surface mining subsidence, still has certain defect, such as: in the literature the authors have shown that the model can only express surface mining subsidence efficiently when k ≧ 3, which if large also results in the improved model not converging to 1; in addition, the authors did not delve into the physical significance of the model parameters. The segmented knotte time function is optimized by Zhang soldier, Cuximin and the like, the defects of the original model are overcome, but the optimized knotte time function inherits the inherent defects of the original model, namely when the sinking speed of the surface point reaches the maximum value, the sinking amount of the surface point is equal to half of the maximum value of the point, and the viewpoint has certain deviation with the actual surface sinking rule; in addition, it is not easy to determine when the surface point reaches the maximum sinking velocity. Therefore, there is a limitation to apply the optimized Knothe time function to develop the relevant prediction. In addition, by referring to relevant documents, the applicant finds that the researches do not provide a corresponding effective and practical time function model parameter solving method.

In the formula (I), the compound is shown in the specification,is a Knothe time function; c is a time factor influence coefficient related to the mechanical property of the overburden stratum, and the dimension of the time factor influence coefficient is 1/a; t is the time elapsed after the unit was mined.

In view of the above, the present application discloses a dynamic prediction method for a coal mining subsidence surface point subsidence process by creating a new time function and combining with a probability integration method, and the expression effect of the dynamic prediction method for the coal mining subsidence surface point subsidence process of the present invention is shown in fig. 1.

Disclosure of Invention

From mineFrom mining subsidence science, it can be known that the dynamic prediction method for the coal mining subsidence surface point subsidence process has the following characteristics: (1) it should be possible to effectively express that surface mining appears to lag underground mining; (2) should express a gradual approach from 0 to a maximum over time; (3) when the initial time t is equal to 0, the sinking speed and the acceleration are equal to zero; (4) in the middle stage of movement, the sinking velocity should be 0 → + v_max→ 0, the sinking acceleration should be from 0 → + a_max→0→-a_maxOn the other hand, when the time variable t → infinity is → 0, both the sinking velocity and the acceleration tend to zero.

According to the characteristics, the applicant constructs a dynamic prediction method of the coal mining subsidence earth surface point subsidence process by looking up related documents and repeated experimental research, creating a new time function model and combining a classical probability integration method, wherein the dynamic prediction method is shown as a formula (1); and a parameter solving method of the created time function is given.

The invention aims to provide a dynamic prediction method capable of accurately describing the subsidence process of a coal mining subsidence earth surface point, aiming at the problems that the complexity and the difficult accurate description of the dynamic development process of the earth surface mining subsidence are realized, the characteristics of the earth surface subsidence process and the speed and the acceleration of the earth surface subsidence process cannot be simultaneously and correctly expressed by the conventional function model, and the current situation that a corresponding model parameter effective solving method is not provided.

The invention is realized by the following technical scheme:

a dynamic prediction method for a coal mining subsidence earth surface point subsidence process can simultaneously express the characteristics of earth surface point subsidence, subsidence speed and acceleration, and construct a dynamic prediction time function for the coal mining earth surface point subsidence process;

the specific method comprises the following steps:

a. constructing a dynamic prediction time function of the coal mining surface point sinking process, as shown in a formula (2),

b. the first derivative of the formula (2) on t is solved to obtain a formula (3), and the formula (3) can effectively express the sinking speed characteristic of the mining surface point;

c. calculating a second derivative of t by the formula (2) to obtain a formula (4), wherein the formula (4) can effectively express the sinking acceleration characteristic of the mining surface point;

d. a dynamic prediction function of a coal mining subsidence surface point subsidence process is shown as a formula (1),

wherein W (x, y) is the maximum subsidence value of the coal mining subsidence earth surface point with the coordinate of (x, y); q is the surface subsidence coefficient; m is the coal seam mining thickness; alpha is the coal bed inclination angle; r is the main influence radius of the surface mining subsidence prediction probability integration method; d is the goaf area; eta and zeta are the length and width of the goaf respectively; t is the time elapsed for mining the surface point; c and n are time factor influence coefficients related to mechanical properties of the overburden stratum, c mainly describes dynamic characteristics of a coal mining subsidence surface point sinking process, and n mainly describes time characteristics of mining surface point appearance lagging underground mining.

According to the dynamic prediction method for the coal mining subsidence surface point subsidence process, the time factor influence coefficient c related to the mechanical property of the overburden rock is obtained by the following steps:

degenerating equation (2), i.e., if n is 1, equation (2) degenerates to the classical Knothe time function (equation (5)), and the parameter c is determined from equation (6);

Φ(t)＝1-e^-ct (5)

wherein H₀And in the average mining depth, tan beta is a main influence angle tangent value of the surface mining subsidence prediction probability integration method, v is a working face advancing speed, and r is a main influence radius of the surface mining subsidence prediction probability integration method.

According to the dynamic prediction method for the coal mining subsidence surface point subsidence process, the time factor influence coefficient n related to the mechanical property of the overburden rock is obtained by the following steps:

when the size of the underground goaf reaches 3/8H₀The surface begins to sink, and the surface begins to sink is marked by the surface sinking of 10mm, so the following formula holds:

wherein, W₀Is the maximum subsidence value of the earth's surface, W₀M is the coal seam mining thickness, q is the surface subsidence coefficient, a is the coal seam dip angle, v is the working face advancing speed, H₀Mean depth of cut.

By adopting the steps, the invention has the beneficial effects that:

the invention takes the measured subsidence data of the observation line of the surface trend of a certain working surface of a certain mine as an example, and contrasts and analyzes the measured data and the predicted value in the mining process based on the dynamic prediction method of the subsidence process of the coal mining subsidence surface point. In order to keep the generality, the method selects one of the initial subsidence period, the active period and the basic stable period of the earth surface to carry out comparative analysis on the whole; for a specific observation point, the invention takes the 26 th point (the point is positioned right above the working surface) as an example for comparative analysis. The geological mining parameters of the working face are shown in table 1, and the surface subsidence dynamic prediction parameters obtained based on table 1 and the formulas (6) and (7) in the invention are shown in table 2.

TABLE 1 face geological mining parameters

Name (R)	Numerical value
		Long trend (m)	571
Breadth of inclination (m)	164
		Average depth of harvest (m)	260
Average thickness (mm)	8800
		Coal bed dip angle (°)	5
Stoping speed (m/d)	2

TABLE 2 surface mobility dynamic prediction parameters

Parameter name	Parameter value
		Coefficient of subsidence	0.79
Main influence of tangent	1.5
		Mining impact propagation angle coefficient	0.7
Inflection offset	0.15H0
		Coefficient of horizontal movement	0.35
c value	6.6
		Value of n	4

The comparison between the measured data and the predicted value is respectively shown in fig. 4 and 5, in order to further quantitatively analyze the prediction effect, the standard error and the relative standard error are introduced for analysis, respectively shown in formula (8) and formula (9), and the specific comparison result is shown in table 3, so that the difference between the predicted value and the measured value is small, and the reliability of the prediction result is high as shown in table 3.

In the formula, m represents an error in the predicted value, f represents an intermediate error in the predicted value, d represents a predicted value correction number, and n represents a prediction frequency.

TABLE 4 prediction accuracy analysis

	m	f
			Initial stage	9	1.4
Active period	65	1.9
			Stationary phase	180	3.6
Point No. 26	59	1.4

The prediction method established by the invention can effectively express all the characteristics of the coal mining subsidence surface point subsidence process, namely: (1) the method can effectively express that the surface mining appearance lags behind underground mining; (2) the function value should gradually approach 1 from 0 with increasing time; (3) when the initial time t is equal to 0, the sinking speed and the acceleration are equal to zero; (4) in the middle stage of movement, the sinking velocity should be 0 → + v_max→ 0, the sinking acceleration should be from 0 → + a_max→0→-a_maxOn the other hand, when the time variable t → infinity is → 0, both the sinking velocity and the acceleration tend to zero.

Drawings

FIG. 1 is a graph of the effect of the surface mining subsidence time function created by the present invention.

FIG. 2 is a graph showing the effect of parameter c of the present invention on the predicted time function of surface mining subsidence.

FIG. 3 is a graph showing the effect of parameter n of the present invention on the value of the estimated time function of surface mining subsidence.

Fig. 4 is a comparison graph of measured data and predicted values at the initial stage of surface subsidence.

FIG. 5 is a comparison of measured data and predicted values of the active period of subsidence of the earth's surface.

FIG. 6 is a comparison of measured data and predicted values during a stabilization period of a subsidence of the earth's surface.

Fig. 7 is a comparison graph of the measured value and the predicted value of the point 26 directly above the ground surface.

Detailed Description

A dynamic prediction method for a coal mining subsidence earth surface point subsidence process is established, and overcomes the defects that the prior method can not effectively express the actual situation that the mining earth surface point subsidence appears to lag behind underground mining and can not simultaneously and effectively express the earth surface point subsidence, subsidence speed and acceleration characteristics; and a parameter solving method of the time function of the coal mining subsidence earth surface point subsidence process dynamic prediction method is constructed.

The dynamic prediction method for the coal mining subsidence earth surface point subsidence process can simultaneously express the characteristics of the subsidence, the subsidence speed and the acceleration of the earth surface point, and construct a dynamic prediction time function of the coal mining earth surface point subsidence process;

the specific method comprises the following steps:

according to the dynamic development rule of the surface mining subsidence, the dynamic prediction method of the coal mining subsidence surface point subsidence process has the following characteristics: (1) it should be possible to effectively express that surface mining appears to lag underground mining; (2) increasing over time should express a gradual approach from 0 to a maximum; (3) when the initial time t is equal to 0, the sinking speed and the acceleration are equal to zero; (4) in the middle stage of movement, the sinking velocity should be 0 → + v_max→ 0, the sinking acceleration should be from 0 → + a_max→0→-a_maxOn the other hand, when the time variable t → infinity is → 0, both the sinking velocity and the acceleration tend to zero.

According to the characteristics, the applicant constructs a dynamic prediction method for the coal mining subsidence earth surface point subsidence process by looking up relevant documents and repeated experimental research, constructing a new time function model and combining a classical probability integration method, wherein the dynamic prediction method is shown as a formula (1).

The method is characterized in that a dynamic prediction time function in the coal mining surface point sinking process is constructed, as shown in a formula (2), and is organically combined with a classical probability integration method. The first derivative of the formula (2) on t is solved to obtain a formula (3), and the formula (3) can effectively express the sinking speed characteristic of the mining surface point; and (3) calculating a second derivative of t by using the formula (2) to obtain a formula (4), wherein the formula (4) can effectively express the sinking acceleration characteristic of the mining surface point. The images of the formula (2), the formula (3) and the formula (4) are shown in fig. 1, and it can be known from the figure that the constructed prediction method can perfectly describe the four characteristics of the coal mining subsidence ground subsidence process.

Wherein W (x, y) is the maximum subsidence value of the coal mining subsidence earth surface point with the coordinate of (x, y); q is the surface subsidence coefficient; m is the coal seam mining thickness; alpha is the coal bed inclination angle; r is the main influence radius of the surface mining subsidence prediction probability integration method; d is the goaf area; eta and zeta are the length and width of the goaf respectively; t is the time elapsed for mining the surface point; c and n are time factor influence coefficients related to mechanical properties of the overburden stratum, c mainly describes dynamic characteristics of a coal mining subsidence surface point sinking process, and n mainly describes time characteristics of mining surface point appearance lagging underground mining.

As shown in the formula (1), the prediction method mainly comprises two parts, namely a classical probability integration method W (x, y) and a time function established by the method, wherein the physical meaning and the obtaining method of each parameter in the probability integration method are clear, and the method is not described in detail. The following description mainly relates to the physical meaning of each parameter of the time function. Fig. 2 shows the effect of the parameter c on the prediction method value according to the present invention when n is 3, from which it can be seen that the total time of subsidence is longer as the value of c is smaller, and the duration of subsidence is 3 years when c is 0.2; the larger the value of c is, the shorter the ground surface subsidence time is, and when c is 1.6, the ground surface subsidence duration is only 1 year; with the increasing value of c, the total time of the surface subsidence is shortened, that is, the parameter c plays a role in controlling the total time of the surface subsidence in the prediction method of the invention, so that the parameter c mainly describes the process characteristics of the surface dynamic subsidence. Fig. 3 shows the effect of the parameter n on the prediction method value when c is 1.6, and it can be seen from the figure that the time when the surface starts sinking gradually lags significantly behind the coal seam excavation starting time as the value of n increases, and when n is 1, the model degenerates to a Knothe time function, and the surface sinking is synchronized with the coal seam excavation time; when n is 2, the earth surface sinking lags behind the excavation time by 0.05 year; when n is 3, the ground surface subsidence lags behind the excavation time by 0.125 years, and when n is 4, the ground surface subsidence lags behind the excavation time by 0.2 years; when n is 5, the ground surface subsidence lags behind the excavation time by 0.3 year; when n is 6, the earth surface subsidence lags behind the excavation time by 0.36 year; the parameter n in the model can effectively express the characteristic that the surface mining appearance lags behind the underground mining. In addition, it can be seen from the figure that as the parameter n is increased, the surface subsidence duration is also shortened.

From the above analysis, the parameter n mainly expresses the characteristic that mining surface points appear to lag behind underground mining, and the parameter c mainly describes the process characteristic of surface dynamic subsidence in the model. Therefore, when the time function model parameters are obtained, the model can be subjected to degradation treatment according to the physical significance of each parameter, and each parameter is obtained respectively.

According to the dynamic prediction method for the coal mining subsidence surface point subsidence process, the time factor influence coefficient c related to the mechanical property of the overburden rock is obtained by the following steps:

degenerating equation (2), i.e., if n is 1, equation (2) degenerates to the classical Knothe time function (equation (5)), and the parameter c is determined from equation (6);

Φ(t)＝1-e^-ct (5)

wherein H₀And in the average mining depth, tan beta is a main influence angle tangent value of the surface mining subsidence prediction probability integration method, v is a working face advancing speed, and r is a main influence radius of the surface mining subsidence prediction probability integration method.

According to the dynamic prediction method for the coal mining subsidence surface point subsidence process, the time factor influence coefficient n related to the mechanical property of the overburden rock is obtained by the following steps:

when the size of the underground goaf reaches 3/8H₀The surface begins to sink, and the surface begins to sink is marked by the surface sinking of 10mm, so the following formula holds:

wherein, W₀Is the maximum subsidence value of the earth's surface, W₀M is the coal seam mining thickness, q is the surface subsidence coefficient, a is the coal seam dip angle, v is the working face advancing speed, H₀Mean depth of cut.

By adopting the steps, the invention has the beneficial effects that:

the invention takes the measured subsidence data of the observation line of the surface trend of a certain working surface of a certain mine as an example, and contrasts and analyzes the measured data and the predicted value in the mining process based on the dynamic prediction method of the subsidence process of the coal mining subsidence surface point. In order to keep the generality, the method selects one of the initial subsidence period, the active period and the basic stable period of the earth surface to carry out comparative analysis on the whole; for a specific observation point, the invention takes the 26 th point (the point is positioned right above the working surface) as an example for comparative analysis. The geological mining parameters of the working face are shown in table 1, and the surface subsidence dynamic prediction parameters obtained based on table 1 and the formulas (6) and (7) in the invention are shown in table 2.

TABLE 1 face geological mining parameters

Name (R)	Numerical value
		Long trend (m)	571
Breadth of inclination (m)	164
		Average depth of harvest (m)	260
Average thickness (mm)	8800
		Coal bed dip angle (°)	5
Stoping speed (m/d)	2

TABLE 2 surface mobility dynamic prediction parameters

The comparison between the measured data and the predicted value is respectively shown in fig. 4 and 5, in order to further quantitatively analyze the prediction effect, the standard error and the relative standard error are introduced for analysis, respectively shown in formula (8) and formula (9), and the specific comparison result is shown in table 3, so that the difference between the predicted value and the measured value is small, and the reliability of the prediction result is high as shown in table 3.

In the formula, m represents an error in the predicted value, f represents an intermediate error in the predicted value, d represents a predicted value correction number, and n represents a prediction frequency.

TABLE 4 prediction accuracy analysis

	m	f
			Initial stage	9	1.4
Active period	65	1.9
			Stationary phase	180	3.6
Point No. 26	59	1.4

The new prediction method established by the invention can effectively express all the characteristics of the coal mining subsidence surface point subsidence process, namely: (1) the method can effectively express that the surface mining appearance lags behind underground mining; (2) the function value should gradually approach 1 from 0 with the increase of time; (3) when the initial time t is equal to 0, the sinking speed and the acceleration are equal to zero; (4) in the middle stage of movement, the sinking velocity should be 0 → + v_max→ 0, the sinking acceleration should be from 0 → + a_max→0→-a_maxOn the other hand, when the time variable t → infinity is → 0, both the sinking velocity and the acceleration tend to zero.

The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various changes and modifications can be made without departing from the overall concept of the invention, and these should be considered as the protection scope of the present invention, which will not affect the effect of the implementation of the present invention and the practicability of the patent.