Methodology for Determining the Productivity of a Set of Machines in the Excavation of Frozen Soils
Abstract Generated abstract
The paper develops a methodology for calculating the productivity of machine sets used to excavate frozen soils, where work consists of loosening by ripping machines and removal by excavating machines. It distinguishes sequential and parallel-sequential organization of operations, deriving relationships for excavation time, machine productivity, permissible reserves of loosened soil, and constraints imposed by refreezing. The method accounts for machine dimensions, trench or foundation pit geometry, excavation and loosening technology, freezing depth, and the relative productivities of the ripper and excavator. The resulting formulas and tabulated procedure are intended to determine the necessary work front, assess whether particular machine combinations can operate together, and estimate overall set productivity under technical, technological, soil, and climatic conditions.
Full Text
Proceedings of the Tomsk Polytechnic Institute, Decorated with the Order of the October Revolution and the Order of the Red Banner of Labor, named after S. M. Kirov
Volume 299 1976
Methodology for Determining the Productivity of a Set of Machines in the Excavation of Frozen Soils
N. A. Dubrovsky
(Presented by the scientific seminar of the Department of Industrial Economics and Enterprise Organization)
The excavation of frozen soils includes loosening, performed by ripping machines, and removal of the soil by excavating machines. Loosening and removal of soil may be performed sequentially or in a parallel-sequential manner.
When the operations are performed sequentially, the duration of soil excavation \(T_n\) is determined as the sum of the time spent on loosening \(T_1\) and removal \(T_2\), i.e.,
\[ T_n = T_1 + T_2 . \tag{1} \]
The values of \(T_1\) and \(T_2\) can be determined from the relations
\[ T_1 = \frac{V}{Q_{ij}}, \tag{2} \]
\[ T_2 = \frac{V}{Q_{\varphi j}}, \tag{3} \]
where \(V\) is the volume of soil being excavated, m\(^3\);
\(Q_{ij}\), \(Q_{\varphi j}\) are, respectively, the productivities of the ripping machine and the excavating machine, m\(^3\)/h.
Knowing the volume \(V\) and the duration of soil excavation, one can determine the productivity of the set of machines
\[ Q_n = \frac{V}{T_n}, \ \text{m}^3/\text{h}. \tag{4} \]
When operations are performed sequentially on sites with significant volumes of work and when loosening and removal are not coordinated, the soil prepared for removal freezes again. To prevent this, the following condition must be observed:
\[ (T_1 + T_p) \leq T_{\mathrm{sm}} \geq (T_2 + T_p), \tag{5} \]
where \(T_{\mathrm{sm}}\) is the time required for the soil prepared for removal to freeze again;
\(T_p\) is the interval of time between the end of loosening and the beginning of removal.
Parallel-sequential performance of operations can be carried out when there is a backlog, which at any moment in time
of the joint operation of the machines must be greater than a certain minimum permissible value.
The size of the reserve depends on such factors as:
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Machine dimensions. As the horizontal overall dimensions of the machines increase, their working zone increases.
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Configuration of the object being excavated. When excavating trenches whose width is less than the maximum possible cutting width of the excavating machine, the reserve area may be determined from the expression:
\[ F_z=(L_{r.z}+L_r)L_{\mathrm{pot}}, \tag{6} \]
where \(L_{r.z}\) is the length of the working zone of the excavating machine;
\(L_r\) is the minimum permissible gap between the excavating machine and the ripping machine;
\(L_{\mathrm{pot}}\) is the width of the trench.
The reserve area when excavating foundation pits may be determined from the relations
\[ F_z=(L_{r.z}+L_r)L_{\mathrm{pok}}, \tag{7} \]
\[ F_z=b_zL_z, \tag{8} \]
\[ F_z=(L_{r.z}+L_r)L_z, \tag{9} \]
where \(L_{\mathrm{pok}}\) is the width of the foundation pit;
\(b_z\) is the cutting width of the excavating machine;
\(L_z\) is the length of the cut;
\(H_{\mathrm{pr}}\) is the depth of freezing.
The volume of the reserve varies in proportion to the depth of freezing, since the reserve area for the specified machine dimensions remains constant:
\[ V_z=F_z\cdot H_{\mathrm{pr}},\ \mathrm{m}^3,\quad \text{where } H_{\mathrm{pr}} \text{ is the depth of freezing.} \tag{10} \]
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Technology for preparing frozen soil for excavation. Thus, when loosening a foundation pit by transverse cuts (furrows, passes), the reserve area is determined according to relation (7), and when loosening by longitudinal cuts, according to relation (8).
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Technology for excavating frozen soil. When a foundation pit is excavated transversely, the reserve area is determined according to relation (7). If the foundation pit is excavated by longitudinal cuts and soil excavation is carried out across the cut, then the reserve area must be determined according to relation (8). In the case of excavation of a foundation pit by longitudinal cuts and soil excavation along the cut, the reserve area is determined from expression (9).
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Ratio of the productivity of ripping machines and excavating machines. From relations (6)--(10), the minimum permissible reserve value is determined. When \(Q_{ij}=Q_{\varphi j}\), it is sufficient and remains constant throughout the entire period of parallel operation of the machines in the set.
If \(Q_{ij}>Q_{\varphi j}\), then the excavating machine can begin work when a reserve equal to \(V_z\) has been created. However, in the course of joint operation the reserve will increase, and its maximum value may be found from the expression
\[ V_{z\max}=V_z+\tau\,(Q_{ij}-Q_{\varphi j}), \tag{11} \]
where \(\tau\) is the time of parallel operation of the machines in the set during ripping and excavation.
The value of \(V_{z\max}\) must not exceed the amount of excavation that the excavating machine can provide before the loosened soil refreezes.
In the case \(Q_{ij}<Q_{\varphi j}\), the amount of advance continuously decreases during parallel operation. But since, in order to ensure normal joint operation of the machines in the set, the advance must not be less than \(V_z\), then, in order to satisfy this condition, by the start of operation of the excavating machine it is necessary to create an advance whose magnitude is determined from the relation
\[ V_{z\max}=V_z+r\left(Q_{\varphi j}-Q_{ij}\right). \tag{12} \]
Table
| Name of indicators | Relations for determining indicators at productivity ratios \(Q_{ij}>Q_{\varphi j}\) | Relations for determining indicators at productivity ratios \(Q_{ij}=Q_{\varphi j}\) | Relations for determining indicators at productivity ratios \(Q_{ij}<Q_{\varphi j}\) |
|---|---|---|---|
| Type of excavating machine | \(\varphi\) | \(\varphi\) | \(\varphi\) |
| Productivity of the machine | \(Q_{\varphi j}\) | \(Q_{\varphi j}\) | \(Q_{\varphi j}\) |
| Type of ripper | \(i\) | \(i\) | \(i\) |
| Ratio of loosened frozen soil by the working member of the ripper to that prepared for excavation | \(S\) | \(S\) | \(S\) |
| Productivity of the ripper | \(Q_{ij}\) | \(Q_{ij}\) | \(Q_{ij}\) |
| Minimum permissible amount of advance | \(V_z\) | \(V_z\) | \(V_z\) |
| Time of operation of only machines of one type (minimum possible) | \(T'_1=\dfrac{V_z}{Q_{ij}}\) | \(T'_1\) or \(T'_2\) | \(T'_2=\dfrac{V_z}{Q_{\varphi j}}\) |
| Possibility of forming a set according to the condition | \((T'_1+T'_p)\leq T_{\mathrm{sm}}\) | \((T'_1+T'_p)\leq T_{\mathrm{sm}}\) or \((T_2+T'_p)\leq T_{\mathrm{sm}}\) |
\((T'_2+T'_p)\leq T_{\mathrm{sm}}\) |
| Time of soil excavation | \(T_2\) | \(T_2\) | \(T_2\) |
| Time of preparing frozen soil for excavation | \(T_1\) | \(T_1\) | \(T_1\) |
| Time of joint operation of the machines | \(\tau=T_1-(T'_1+T'_p)\) | \(\tau\) | \(\tau=T_2-(T'_2+T'_p)\) |
| Time of operation of only machines of one type | \(T'_2=T_2-\tau\) | \(T'_1=T_1-\tau\) | |
| Possibility of forming sets according to the condition | \(T'_2\leq T_{\mathrm{sm}}\) | — | \(T'_1\leq T_{\mathrm{sm}}\) |
| Time of developing the specified volume of soil | \(T=T_2+T'_1+T'_p\) | — | \(T=T_1+T'_2+T'_p\) |
| Productivity of the set | \(Q=\dfrac{V}{T}\) | \(Q=\dfrac{V}{T}\) | \(Q=\dfrac{V}{T}\) |
Note. \(T'_p\) is the time interval between the possible and the actual start of operation of the excavating machine.
Having thus determined the required size of the work front, it is possible to determine the productivity of a set of machines under parallel-sequential loosening and excavation of soil.
The sequence and relationships for determining the productivity of the set are given in the table.
Thus, the proposed methodology and relationships make it possible to:
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Determine the required size of the work front, which makes it possible to carry out parallel-sequential operations for loosening and excavating frozen soil.
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Relationships (6)—(12) can be used to determine the required size of the work front when developing frozen soils by any methods.
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Determine the possibility of forming sets for developing frozen soils from various loosening machines and excavating machines.
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Determine the productivity of sets of machines, taking into account the combined influence of technical and technological factors, soil characteristics, and climatic conditions.