Study on Reasonable Stopping and Time-Sharing Partition Support of Fully Mechanized Top Coal Caving Face Under the Interference of Stopping Line in Close-Up Coal Seam

Close-distance coal seams are widely distributed in China, and there is a problem of stopping mining in a large number of working faces. Taking Yanzishan mine as the engineering background, the mined-out area and the remaining end-mining coal pillar of No.4 coal seam (upper coal seam) mined in advance caused strong interference to the stopping mining of N316 working face of No.3 coal seam under it. Through field observation, laboratory experiment, and support data collection, the mechanical parameters of coal and rock mass and periodic weighting condition of the working face were mastered, and numerical simulation and similar model experiments were carried out. Three positional relationships between the stopping position of the underlying N316 working face and the upper stopping line were obtained: “externally staggered with the upper stopping line” (ESUL), “overlapped with upper stopping line” (OUL), and “internally staggered with the upper stop line” (ISUL, ISUL-SD for shorter internal staggered distances, ISUL-LD for longer ones). The formation and evolution of the stress arch structure of ESUL → OUL → ISUL-SD → ISUL-LD are obtained from the analysis: ① ESUL: there is a double stress arch structure of goaf side and end-mining coal pillar side in the overburden and stress superposition appears in the middle arch foot (stopping mining place). ② OUL: it evolved into a single arch structure of goaf-solid coal, and the stress at the stop of mining was relatively minimum. ③ ISUL-SD: it is still a single arch structure, and the stress at the stop of mining is still small. ④ ISUL-LD: the double stress arch is regenerated and stress superposition occurs at the front arch foot (stopping mining place). At the same time, the morphological evolution process of stress arch is as follows: “front and back stress arches, superimposed with middle arch foot” → “front arch gradually decreases” → “front arch dies, and two arches merge into single arch” → “single arch gradually increases” → “two arches are regenerated, superimposed with front arch foot”. On-the-spot analysis from the combination of stress and overburden structure: ① ESUL: the stress concentration degree is the highest above the stopping space, and the overburden block in the large-scale caving zone directly acts on the support, which makes the stopping operation difficult. ② OUL: although the stress environment is the best, the overlying key blocks will have hidden dangers of overall rotation or sliding instability. ③ ISUL-SD: the stress environment is good, and the overlying rock can realize the stable structure of the cantilever plate (the internal staggered distance is less than the periodic weighting step), and the mining is stopped at this position to realize the safe and smooth withdrawal of the support. ④ ISUL-LD: it is basically consistent with stopping mining when single-layer coal is used but is limited by the limited length of the end-mining coal pillar. In addition, the self-digging retracement channel is designed to serve the whole retracement process, and the idea of time-sharing partition support for a large cross-section of mining stoppage and its corresponding scheme is put forward according to the retracement process. Through the simulation of prestressed field and field practice, the roof overlying rock structure is stable during the whole retracement period, thus realizing the safe and smooth mining stoppage and retracement of the working face.

A mathematical assessment of the efficiency of quarantining and contact tracing in curbing the COVID-19 epidemic

In our model of the COVID-19 epidemic, infected individuals can be of four types, according whether they are asymptomatic (A) or symptomatic (I), and use a contact tracing mobile phone application (Y ) or not (N). We denote by R0 the average number of secondary infections from a random infected individual. We investigate the effect of non-digital interventions (voluntary isolation upon symptom onset, quarantining private contacts) and of digital interventions (contact tracing thanks to the app), depending on the willingness to quarantine, parameterized by four cooperating probabilities. For a given ‘effective’ R0 obtained with non-digital interventions, we use non-negative matrix theory and stopping line techniques to characterize mathematically the minimal fraction y0 of app users needed to curb the epidemic, i.e., for the epidemic to die out with probability 1. We show that under a wide range of scenarios, the threshold y0 as a function of R0 rises steeply from 0 at R0 = 1 to prohibitively large values (of the order of 60−70% up) whenever R0 is above 1.3. Our results show that moderate rates of adoption of a contact tracing app can reduce R0 but are by no means sufficient to reduce it below 1 unless it is already very close to 1 thanks to non-digital interventions.

A mathematically rigorous assessment of the efficiency of quarantining and contact tracing in curbing the COVID-19 epidemic

In our model of the COVID-19 epidemic, infected individuals can be of four types, according whether they are asymptomatic (A) or symptomatic (I), and use a contact tracing mobile phone app (Y) or not (N). We denote by f the fraction of A’s, by y the fraction of Y’s and by R0 the average number of secondary infections from a random infected individual.We investigate the effect of non-electronic interventions (voluntary isolation upon symptom onset, quarantining private contacts) and of electronic interventions (contact tracing thanks to the app), depending on the willingness to quarantine, parameterized by four cooperating probabilities.For a given ‘effective’ R0 obtained with non-electronic interventions, we use nonnegative matrix theory and stopping line techniques to characterize mathematically the minimal fraction y0 of app users needed to curb the epidemic. We show that under a wide range of scenarios, the threshold y0 as a function of R0 rises steeply from 0 at R0= 1 to prohibitively large values (of the order of 60 – 70% up) whenever R0 is above 1.3. Our results show that moderate rates of adoption of a contact tracing app can reduce R0 but are by no means sufficient to reduce it below 1 unless it is already very close to 1 thanks to non-electronic interventions.

Sequential analysis and design of fixed-precision sampling of Lake Kariba fishes using Taylor’s power law

Taylor’s power law (TPL), which states that the variance of abundance is a power function of mean abundance, has been used to design sampling of agricultural pests and fish species. We show that TPL holds for means and variances of abundance of accumulated fish samples in the fished and unfished areas separately of Lake Kariba (between Zambia and Zimbabwe), measuring abundance indices by number and weight separately. We use TPL parameters estimated from sequentially accumulated samples to update a stopping line of fixed precision 0.1 after each new sample from a sampling day. In these Lake Kariba data, depending on the sampling area and abundance measure, our updated stopping-line method requires 21% to 41% of the number of sampling days and 19% to 40% of the number of samples that are planned a priori and performed under systematic sampling. Our novel method yields mean abundance estimates similar to those from systematic sampling and provides a conservative approach to reaching a fixed sampling precision level with reduced sampling labor and time. Using mixed-effect modeling for cumulative means and variances with either number or weight from both fished and unfished areas, we find that fishing increases the slope of TPL. This study provides the conceptual framework and an empirical case study for implementing a sequential sampling method for fish assemblages of an inland lake. The possible limitations and applications of our method for sampling in other environments are discussed.

Numerical Simulation Study on Setting Stopping Line of Working Face in Shuguang Mine

The surrounding rock deformation of pedestrian roadway was serious under the influence of the working face. And it has affected the safety and normal use of roadway. To ensure the long-term stability of the pedestrian roadway surrounding rock and increase the coal recovery rate of working face, the paper studied the position of stopping line of 1203 working face by numerical simulation. The results show that setting 115m wide of security coal pillar between 1203 working face and pedestrian roadway that the area of stress concentration near the working face has less effect on the pedestrian roadway could better control the surrounding rock stability of the pedestrian roadway and meet the need of the long-term normal production use. It narrows the width of security coal pillar, increase the coal resources recovery rate and achieve the better economic benefits.