KR101967978B1 - Apparatus for predicting net penetration rate of shield tunnel boring machine and method thereof - Google Patents

Abstract

The present invention relates to an apparatus and method for predicting a net pumping speed of a shield TBM. According to the present invention, there are provided a database storing a plurality of ground factors measured for the site and a site penetration index of the shield TBM, corresponding to each of the plurality of sites constructed in the past, and a database storing coordinate points corresponding to the plurality of ground factors A clustering unit for fuzzy-clustering the coordinate points of each of the sites into a plurality of clusters by projecting the clusters in an input vector space; A neural network learning unit that learns the neural network by applying a plurality of ground factors and the on-the-spot penetration index, and inputs a plurality of ground factors acquired on the on-site to the learned neural network, An apparatus for estimating a net pumping speed of a shield TBM including a predictor for predicting an exponent is provided.
According to the present invention, by using the ANFIS training model constructed by training the ground penetration index of the shield TBM in the adaptive neuro fuzzy neural network obtained from the past construction site, the site penetration index It is possible to reliably predict the net pumping speed of the shield TBM on the basis of this prediction, and thus the prediction error of the construction cost and the construction time required for the construction site can be greatly reduced.

Description

FIELD OF THE INVENTION [0001] The present invention relates to an apparatus for predicting a net boring speed of a shield TBM,

The present invention relates to an apparatus and method for predicting a net TBM of a shield TBM, and more particularly, to a shield TBM (TBM) capable of reliably predicting a net boring speed of a shield TBM And a method thereof.

In Korea, there is a tendency to construct a lot of tunnel type electric power facilities for the undergroundization of the line for electric supply. The power tunnel is mainly constructed by a mechanical tunnel excavator, or Shield Tunnel Boring Machine (TBM).

It is very important to accurately predict the performance of the shield TBM at the design stage in order to predict reliable construction cost or construction period. Among the performance of the shield TBM, there is typically a net penetration rate (PR). This net pumping speed can be defined as the distance excavating the ground per hour. The net pumping speed is a very important factor because multiplying the net pumping speed by the operation rate of the shield TBM finally calculates the construction period and the construction cost accordingly.

However, in Korea, the net pumping speed of the shield TBM used in the power tunnel is predicted according to the Uniaxial Compressive Strength (USC) of the drilling sample. Predicting net pumping speed only by uniaxial compressive strength does not reflect various characteristics existing in rock mass, which causes increase of prediction error.

Also, there is a case that the net pumping speed of the shield TBM is predicted using the statistical techniques such as regression analysis in Korea, but there is a problem that the complexity of the statistical analysis is high and the correlation between the elements is not so large, so the prediction ability is limited.

The technology that is the background of the present invention is disclosed in Korean Patent No. 0769499 (published on October 24, 2007).

An object of the present invention is to provide an apparatus and method for predicting net pumping speed of a shield TBM that can reliably predict a net pumping speed of a shield TBM used in a field to be applied.

The present invention is characterized by comprising: a database storing, for each of a plurality of sites constructed in the past, a plurality of ground factors measured in response to the site and a site penetration index of a shield TBM; and a coordinate point corresponding to the plurality of ground factors A clustering unit for fuzzy-clustering the coordinate points of the respective sites on a plurality of clusters by projecting in a vector space, and an input node and an output node of an adaptive neuro fuzzy neural network (ANFIS) constructed based on the membership function by the fuzzy clustering A neural network learning unit for learning the neural network by applying the plurality of ground factors and the site penetration index to each of the plurality of ground factors and the plurality of ground factors acquired for the construction target site to the learned neural network, And a predictor for predicting a site penetration index.

In addition, the predictor may estimate the net pumping speed of the shield TBM based on the predicted penetration index and the mechanical factor of the shield TBM.

Also, the predicting unit may calculate the net pumping speed using the following equation.

Where F _n is the thrust per cutter of the shield TBM, RPM is the number of revolutions per minute of the shield TBM, and FPI is the predicted on-site penetration index.

In addition, the plurality of ground factors may include at least two factors of unconfined compressive strength, elastic modulus, elastic wave velocity, rock grade, rock quality index, lean value, and absorption coefficient with respect to the ground.

In addition, the field penetration index (FPI) stored corresponding to the field can be determined by the following equation.

Where F _n is the thrust per cutter of the shield TBM and Pe is the penetration depth per revolution of the cutter head measured at the field.

The present invention further includes a step of storing, in a database, a plurality of ground factors measured in correspondence with the site and a site penetration index of the shield TBM for each of a plurality of sites installed in the site, A step of fuzzy-clustering coordinate points of each of the sites into a plurality of clusters by projecting coordinate points on an input vector space, and input nodes of an adaptive neuro fuzzy neural network (ANFIS) constructed based on the membership function by the fuzzy clustering And applying the plurality of ground factors and the site penetration index to the output nodes to learn the neural network, and inputting a plurality of ground factors acquired for the site to be constructed into the learned neural network, And estimating the net penetration index for the shield TBM.

According to the present invention, by using the ANFIS training model constructed by training the ground penetration index of the shield TBM in the adaptive neuro fuzzy neural network obtained from the past construction site, the site penetration index It is possible to reliably predict the net pumping speed of the shield TBM based on the prediction, and thus the prediction error of the construction cost and the construction time required for the construction site can be greatly reduced.

FIG. 1 is a diagram illustrating a configuration of an apparatus for predicting a net pumping speed of a shield TBM according to an embodiment of the present invention. Referring to FIG.
2 is a diagram illustrating a method of predicting a net pumping speed using the apparatus of FIG.
3 is a diagram illustrating the principle of fuzzy clustering in an embodiment of the present invention.
4 is a diagram illustrating an ANFIS training process in an embodiment of the present invention.
FIG. 5 is a diagram for explaining the tendency of predicting a site penetration index and a net pumping speed in the embodiment of the present invention. FIG.
6 is a view for explaining a net pumping speed prediction method according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those skilled in the art can easily carry out the present invention.

The present invention relates to an apparatus and method for estimating the net pumping speed of a shield TBM, and more particularly, to an apparatus and method for predicting a net pumping speed of a shield TBM, in which reliability of a shield TBM (Shield Tunnel Boring Machine) We suggest a technique that can be predicted.

The net pumping speed is defined as the distance at which the shield TBM excavates the ground per hour. In particular, the net pumping speed is an important design factor for estimating the construction period and the construction cost, and it can be regarded as a very important factor because it can reduce the construction time and construction cost more reliably.

In the embodiment of the present invention, an ANFIS training model is obtained by learning the ground factor (ground data) accumulated in each past construction site and the penetration index of the shield TBM in an adaptive neuro fuzzy inference system (AMFIS) Using the ANFIS training model, it is possible to easily obtain the corresponding site penetration index only by inputting the ground data for the site to be constructed.

The front end of the shield TBM includes a circular cutter head that advances while rotating so as to cut the ground. The cutter head includes a plurality of cutters, and the tunnel is excavated while the ground (rock) is cut by the cutters when the cutter head is rotated.

The Field Penetration Index (FPI) is an element related to the penetration depth of the cutter head. In the embodiment of the present invention, in the case of the initial penetration index used in the neural network learning (construction of the training model), it corresponds to the value obtained through the actual measurement at the time of the past field construction, The index corresponds to the value predicted through the training model.

Based on this, it is possible to estimate the net penetration rate (PR) of the shield TBM by predicting the on-site penetration index (FPI) of the shield TBM for the planned site. That is, the net penetration rate of the shield TBM can be predicted by combining the predicted penetration index and the known mechanical factors of the shield TBM. This will be described in detail later.

As described above, according to the embodiment of the present invention, the site penetration index of the shield TBM for the site to be constructed is predominantly predicted only by the ground factors (ground data) for the current site to be constructed and based on the predicted site penetration index By predicting the net pumping speed of shield TBM in a secondary way, prediction errors of construction period and cost can be significantly reduced.

Hereinafter, an apparatus for predicting net pumping speed of a shield TBM according to an embodiment of the present invention will be described in detail.

FIG. 1 is a view showing a configuration of an apparatus for predicting a net pumping speed of a shield TBM according to an embodiment of the present invention, and FIG. 2 is a diagram illustrating a method of predicting a net pumping speed using the apparatus of FIG.

1 and 2, an apparatus 100 for predicting a net TBM of a shield TBM according to an embodiment of the present invention includes a database 110, a clustering unit 120, a neural network learning unit 130, a predictor 140 ).

First, the database 110 stores and manages a plurality of ground factors and shield penetration indices of the shield TBM measured in response to the field, respectively, for each of the plurality of installed sites (S210).

The database 110 stores and manages the data on the ground penetration index of the TBM and the ground factors obtained from the past construction site, and these data are used as data for training of the adaptive neurofuzzy neural network (ANFIS) do. The ground factor is used as the input vector of the neural network and the field penetration index is used as the output value of the neural network for the input vector. Here, of course, when the construction of the new site is completed, the site data can be continuously added and updated to the database 110.

Uniaxial Compressive Strength, Elastic Modulus, Elastic P-wave, Rock Mass Rating (RMR), and Rock Mass Rating (RMS) Rock Quality Designation (RQD), Lugeon value, and Absorption ratio.

In the embodiment of the present invention, the ground factor used as the training data of the neural network may include at least two factors among the seven factors described above. That is, two or more ground factors can be used to input the neural network.

The following embodiments of the present invention illustrate utilizing two ground factors for convenience of explanation. Of course, as the types of soil parameters vary, the accuracy of prediction of the output of the neural network (field penetration index) can be increased instead of the training complexity.

The unconfined compressive strength is a factor that indicates the strength of the rock mass. The elastic modulus is a factor that indicates the degree of elasticity of the rock. The smaller the value, the greater the degree of deformation. The elastic wave p wave velocity means the p wave propagation velocity of the rock.

The rock grade is a comprehensive factor indicating the rock condition, ranging from 0 to 100. The larger the value, the better the rock condition and the more difficult it is to excavate. The rock quality index is a factor indicating the joint condition (similar to crack) of rock mass, ranging from 0 to 100. The larger the value, the better the rock condition.

The leeway value is a unit expressing the water permeability of the rock. The larger the leeway value, the higher the water permeability of the water. The absorption rate is a factor that expresses the degree of water absorption of the rock. The larger the value, the higher the degree of absorption.

Of course, the database 110 manages the ground factor and the TBM mechanical factor, and manages the aforementioned factors as the ground factor. As a mechanical factor, the total thrust, the per-cutter thrust F _n , , RPM, and number of cutters.

These TBM mechanical factors correspond to measurable factors at the construction site. In the TBM machine factor, the total thrust is the total thrust of the shield TBM, the thrust per cutter (F _n ) is calculated by dividing the total thrust by the number of cutters, and the RPM is the shield TBM (specifically the cutter head) .

Also, the site penetration index (FPI) stored in response to the site is determined by the following equation (1).

로 표현된다.Where F _n is the thrust per cutter of the shield TBM and P _e is the penetration depth per turn of the cutter head of the shield TBM measured in the field. These FPIs

Lt; / RTI >

Of course, as described above, the data used for the actual training (learning) of the data of the database 110 includes only at least two factors selected from a plurality of ground factors, and the TBM mechanical factor only.

Next, based on the data constructed in the database 110, the clustering unit 120 projects one coordinate point (data point) corresponding to a plurality of ground factors for each site into the input vector space, And fuzzy clustering is performed on the coordinate points with a plurality of clusters (S220).

Accordingly, one coordinate point is projected to the corresponding position in the input vector space, and each coordinate point is clustered into a plurality of clusters (a plurality of clusters) through the fuzzy clustering technique.

Fuzzy clustering is a well-known method and its principle is briefly described as follows. Fuzzy clustering is a technique for defining each data (coordinate) to be associated with all clusters using membership function (membership function).

Fuzzy clustering is called soft clustering and is different from hard clustering. Hard clustering means that each piece of data belongs to exactly one cluster (cluster), with a weight of 1 and a weight of 0 for the remaining clusters.

However, the soft clustering, that is, the fuzzy clustering, is a technique in which each data does not belong to a specific cluster but represents how much data belongs to the cluster with respect to the center point of each cluster as a weight.

3 is a diagram illustrating the principle of fuzzy clustering in an embodiment of the present invention. Hereinafter, for convenience of explanation, it is exemplified that fuzzy clustering is performed by projecting two ground factors (ex, uniaxial compressive strength, rock grade) into an input vector space.

When two ground factors (x1, x2) are used, fuzzy clustering is performed in a two-dimensional input vector space as shown in Fig.

At this time, it is assumed that x1 is the uniaxial compressive strength and x2 is the rock grade. The horizontal axis of the two-dimensional vector space represents the x1 value, and the vertical axis represents the x2 value. For each site, when the uniaxial compressive strength (x1) of the site and the coordinate point where the rock grade (x2) meet are projected, N coordinate points corresponding to N sites are plotted.

3 illustrates the classification of each coordinate point into two clusters (group 1 and group 2) using fuzzy clustering. Each cluster shares a certain degree with each other according to the weight, not the completely independent cluster.

The principle of dividing the cluster is as follows. Set the number of clusters to divide and initialize the center of each cluster. In FIG. 3, the number of clusters is set to two.

Equation (2) corresponds to a conventionally known formula used for fuzzy clustering.

Here, K is the number, x _i of the number, n is the observation (coordinate points) of clusters (cluster) is the i th observation, c _k is k the center of the second cluster, d (a, b) ² is between a and b, the distance ≪ / RTI > W _ik is the weight of the i th observations in the kth cluster, and is the real number between 0 and 1 as belonging to the i th observation. P is the fuzzy coefficient, the closer to 1, the less the degree of sharing among the clusters. The degree of sharing between communities increases.

)을 최소화하고, 이와 동시에 군집 간 비유사성을 최대화하기 위하여, 군집의 중심 간 거리의 합을 최대화하는 반복적인 최적화 연산을 통해 군집을 나누게 된다.To summarize the principle of Equation (2), in order to maximize the similarity between observations in a cluster (coordinate points), the sum of the squares of the distances between the i-th observation and the center of the k-th cluster

), And at the same time, to maximize the dissimilarity between the clusters, the clusters are divided through the iterative optimization operation which maximizes the sum of the distances between the centers of the clusters.

The center of gravity of each cluster is calculated by averaging all points with the gravity belonging to the cluster. We can also see that each observation takes into account the weights that are likely to belong to a particular cluster. Also, the data far from the center of the cluster are regarded as noise, and the membership is decreased. On the contrary, the data near the center increases the membership.

As a result of the fuzzy clustering, the membership function for x1 and the membership function for x2 can be obtained as shown in the upper and right side of Fig. In this case, since the two clusters are classified, each belonging function has two fuzzy sets. Referring to FIG. 3, it can be seen that all of the two sets are overlapped. If the left and right sides of the two sets are number 1 and number 2, the belonging function of x1 has two fuzzy sets A1 (left) and A2 (right), and the belonging functions of x2 are B1 (left) Of the fuzzy set.

The purpose of the fuzzy clustering is to set the membership functions and the If_then_ rules that are used in the next ANFIS training phase.

When the fuzzy clustering is completed, the neural network learning unit 130 applies a plurality of ground factors and a site penetration index to the input node and the output node of the adaptive neuro fuzzy neural network (ANFIS) constructed based on the membership function by fuzzy clustering And the neural network is learned (S230).

4 is a diagram illustrating an ANFIS training process in an embodiment of the present invention. In the ANFIS training phase, as shown in FIG. 4, it can be subdivided into five levels including a fuzzy layer, a regular layer, a normalized layer, a reverse fuzzy layer and a total neuron layer.

In the input x1 and x2 of the fuzzy layer, two ground data (uniaxial compressive strength, rock grade) obtained in the past construction site are input, and the field penetration index measured in the field is applied to the output y of the total neuron layer Learning process.

First, when the existing ground data (x1, x2) is input, the fuzzy clustering unit allocates the fuzzy clustering function to each member function initially set in the fuzzy clustering step. Here, the membership function takes the bell-shaped activation function as shown in Equation 3 in the model proposed by Roger Jang, who first proposed ANFIS.

,

,

은 각각 종형 활성화 함수의 중심, 폭 그리고 기울기를 제어하는 전제매개변수(premise parameter)이다. here,

,

,

Is a premise parameter that controls the center, width, and slope of the bell-shaped activation function, respectively.

은 맴버십함수 A1과 B1의 출력값을 할당받게 되며, 수학식 4와 같이 각 출력값을 곱하여 규칙의 강도인

을 출력하게 된다.The output of the bell-shaped activation function is passed to each rule layer. In the rule layer, input is received from the fuzzy layer and the rule's execution intensity is output. Here, a rule means an If_then_ format, an If clause is mainly called a rule rule, and a then clause is a rule rule. Each neuron in the ANFIS rule layer corresponds to a single predicate rule. For example, as shown in FIG. 4

The output values of the member functions A 1 and B 1 are assigned and multiplied by the respective output values as shown in Equation (4)

.

은 규칙층에 있는 모든 출력값을 받아 규칙

의 수행강도를 수학식 5와 같이 계산하여 정규화 수행강도

을 출력한다.The normalization layer normalizes the performance intensity, which is the output value of the rule layer. 4,

Accepts all output values in the rule layer,

Is calculated as shown in Equation (5)

.

으로 출력하게 된다. The inverted fuzzification layer receives the output values of the normalization layer and the ground data x1 and x2 that were initially input, and is applied to the function formula of the rule structure. In this case, the Fuzzy rule is given as a rule function and the Fuzzy rule is systematically generated. In ANFIS, the Fuzzy rule is used. The first inverse fuzzy neuron, for example, is calculated by putting the ground data value into the function of the Sueno type rule adjacency rule (set by the first order linear function) as shown in Equation (6), and then multiplies the normalization rule strength received from the normalization layer Result value

.

,

,

는 각각 첫 번째 역퍼지화 뉴런의 규칙후건부 함수의 계수를 의미하며, 이는 결론매개변수(consequent parameter)라고 불린다. 첫 번째 뉴런 이외의 역퍼지화층의 모든 뉴런도 동일하게 적용된다. here,

,

,

Is the coefficient of the posterior rule of function of the first inverse fuzzy neuron, which is called the consequent parameter. The same applies to all neurons in the reverse fuzzy layer other than the first neuron.

를 출력하게 된다. 도 4의 경우에는

값은 4가 된다.The total neuron layer is added with the output values of all neurons inverse fuzzy as shown in Equation (7)

. In the case of FIG. 4

The value is 4.

값과 현장에 계측된 출력값과의 차이 즉, 오차가 발생하면 역방향으로 인공신경망에서 작동되는 기울기 하강법(gradient descent method) 알고리즘을 이용하여 퍼지화층에 있는 전제매개변수를 재조정하게 된다. 재조정이 완료되면 다시 순방향으로 ANFIS를 작동하게 되며 역퍼지화층의 결론매개변수를 최소제곱추정(least square estimator)으로 재계산하게 된다. 이와 같은 방법으로 오차가 허용범위 안에 들 때까지 반복하여 ANFIS 훈련은 최종적으로 마치게 된다. The final output of ANFIS

When the difference between the value and the measured output value in the field, that is, an error occurs, the precondition parameter in the fuzzy layer is readjusted by using a gradient descent method algorithm operated in the artificial neural network in the reverse direction. Once the rebalance is complete, the ANFIS will operate again in the forward direction and the conclusion parameter of the reverse fuzzy layer will be recalculated as a least square estimator. In this way, the ANFIS training is finally completed until the error falls within the allowable range.

Then, using the learned neural network as described above, inputting only the ground factor for the site to be constructed, that is, the site to be constructed, can predict the site penetration index.

That is, the predicting unit 140 inputs a plurality of ground factors obtained for the site to be constructed to the learned neural network, and predicts a site penetration index (FPI) for the site to be constructed (S240). For example, if only the geotechnical data (unconfined compressive strength, rock grade) of the specific field section to be predicted is input, the field penetration index (FPI) of a specific field section can be quickly and easily predicted at the site design stage using the trained ANFIS model .

Of course, if the optimal thrust and RPM of the shield TBM to be used in the field are estimated, the net pumping speed can be predicted finally.

FIG. 5 is a diagram for explaining the tendency of predicting a site penetration index and a net pumping speed in the embodiment of the present invention. FIG. 5, the predicting unit 140 predicts the initial penetration index first, and then uses the predicted penetration index (FPI) and the mechanical factor (F _n , RPM) of the shield TBM to calculate the shield TBM The net penetration rate is predicted (S250). The concrete calculation formula is as shown in Equation (8).

Where F _n is the thrust per cutter of shield TBM, RPM is the number of revolutions per minute of shield TBM, and FPI is the predicted field penetration index.

6 is a view for explaining a net pumping speed prediction method according to an embodiment of the present invention. The present invention is largely divided into three steps. Step 1 is a step of fuzzy clustering the ground data of the past site, step 2 is a step of inputting the ground data of the site based on the result of the fuzzy clustering, And training the adaptive neuro-fuzzy neural network with the output of the field penetration index as an output.

In step 3, an ANFIS training model is used to derive the result corresponding to the ground data for the site to be constructed, that is, the penetration index of the shield TBM. Further, based on the derived site penetration index, Can be derived.

According to the apparatus and method for estimating the net pumping speed of the shield TBM according to the present invention, the ANFIS training that is constructed by training the ground penetration index of the shield TBM and the ground factors obtained in the past construction site in the adaptive neuro fuzzy neural network It is possible to easily predict the site penetration index using only the ground data of the site to be constructed and to reliably predict the net pumping speed of the shield TBM based on the predicted site penetration index. There is an advantage to reduce.

While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims. Accordingly, the true scope of the present invention should be determined by the technical idea of the appended claims.

100: Prediction speed of pure TBM shield
110: database 120: clustering unit
130: Neural network learning unit 140:

Claims (10)

A database storing a plurality of ground factors measured in response to the site and a site penetration index (FPI) of the shield TBM for each of a plurality of sites constructed in the past;
A clustering unit for projecting one coordinate point corresponding to the plurality of ground factors for each site into an input vector space and then fuzzy clustering the coordinate points of the respective sites with a plurality of clusters;
Applying the plurality of ground factors and the site penetration index to an input node and an output node of an adaptive neuro fuzzy inference system (ANFIS) constructed based on the membership function by the fuzzy clustering, A neural network learning unit for learning a neurofuzzy neural network; And
A plurality of ground factors acquired for the site to be constructed are input to the learned adaptive neuro fuzzy neural network to predict a site penetration index for the site to be constructed and the site penetration index predicted through the adaptive neuro fuzzy neural network FPI ') and a predictor for calculating and estimating a net pumping speed of the shield TBM based on a mechanical factor of the shield TBM,
A plurality of ground factors stored in the database,
And at least two factors of unconfined compressive strength, elastic modulus, elastic wave velocity, rock grade, rock quality index,
The on-site penetration index (FPI)
Is determined with the thrust force (F _n) per cutter of the shield TBM value _{(FPI = F n / P e} ) divided by the cutter head per rotation penetration depth (P _e) of the shield TBM measurement in the field,
Wherein the net pumping speed is predicted by the following equation: < EMI ID =

Where F _n is the thrust per cutter of the shield TBM, RPM is the number of revolutions per minute of the shield TBM, and FPI 'is the predicted on-site penetration index. delete delete delete delete A method for predicting a net pumping speed in a net pumping speed predicting apparatus of shield TBM,
Storing, for each of a plurality of installed sites, a plurality of ground factors measured in response to the site and a site penetration index (FPI) of the shield TBM in a database;
Projecting one coordinate point corresponding to the plurality of ground factors for each site into an input vector space, and fuzzy clustering coordinate points of each of the sites with a plurality of clusters;
Applying the plurality of ground factors and the site penetration index to an input node and an output node of an adaptive neuro fuzzy inference system (ANFIS) constructed based on the membership function by the fuzzy clustering, Learning neural fuzzy neural network;
Inputting a plurality of ground factors acquired for a site to be constructed to the learned adaptive neuro fuzzy neural network to predict a site penetration index for the site to be constructed; And
Computing and estimating a net pumping speed of the shield TBM based on a site penetration index (FPI ') predicted through the adaptive neuro-fuzzy neural network and a mechanical factor of the shield TBM,
A plurality of ground factors stored in the database,
And at least two factors of unconfined compressive strength, elastic modulus, elastic wave velocity, rock grade, rock quality index,
The on-site penetration index (FPI)
Is determined with the thrust force (F _n) per cutter of the shield TBM value _{(FPI = F n / P e} ) divided by the cutter head per rotation penetration depth (P _e) of the shield TBM measurement in the field,
Wherein the net pumping speed is predicted by the following equation: < EMI ID =

Where F _n is the thrust per cutter of the shield TBM, RPM is the number of revolutions per minute of the shield TBM, and FPI 'is the predicted on-site penetration index. delete delete delete delete

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