The effect of temperature in underground openings is related to the thermal properties of rocks, which at certain depths may exceed the minimum standards of comfort to human work, thus causing thermal and other environmental risks. To evaluate this influence a mathematical model was developed upon the concept of heat transference from the rock mass to the ventilation air flowing in the underground space. The model was applied to the underground mine of San Rafael located in the eastern mountain range of southern Peru, at an altitude of 5 299 m above sea level, with underground works located 1,000 m deep, where water temperatures are around 40°C, thus generating high air thermal values (up to 34°C). The study allowed to determine the geothermal degree of the mine field (89.46 m/°C), the thermal conductivity of local rocks (2.25 W/m °C) and led to evaluate the required corrective procedures by means of injecting 26.3 to 35.0 m3/s of cool air, in order to attenuate those values to the recommended ones of 29°C to 26.5°C, respectively.

1. DEVELOPMENT OF A MATHEMATICAL MODEL
1.1 The concepts of geothermal gradient and degree

The length of vertical depth corresponding to the increase of one degree Celsius is known as geothermal gradient and the average increase of temperature per meter of depth is called geothermal degree. At a certain depth from the surface (15 m according to Hartman, 1992; or around 20 m to 40 m as predicted by Vutukuri, 1986), the temperature of surface rock masses varies during the year in function of the changes of air temperature until a depth known as thermal neutral layer (Fig. 1). For greater depths rock temperatures increase gradually due to the central heat of the Earth, but with variations from place to place, as a consequence of rock types, volcanic proximity, chemical reactions, radioactivity, etc.

2. CASE STUDY IN PERU

The San Rafael mine belongs to the Peruvian company Minsur S.A. and is located southwest of the San Bartolome de Quenamari mountain (altitude 5,299 m), in the Eastern Mountains of Southern Peru, politically belonging to the district of Antauta, province of Melgar and department of Puno. This mine is geographically located at the coordinates 70° 19'' longitude West and 14°14'' latitude South. The mine is the only producer of tin in Peru, with an ore production of 2 500 tons per day, averaging 5.23% of Sn.

2.1. Rock mass and the underground environment

Geology of San Rafael mine involves silts and quartzite rocks of the tertiary Sandia formation with the intrusion of two granites. In the neighborhood there are rocks of the upper Paleozoic. In the Sandia formation silts have dark gray colors with muscovite in the cleavage plans where quartzites are intercalated with silts. The mineralized veins and ore bodies are located in the intrusive orebody of San Rafael (Fig. 2) along the NE - SW direction, with a length of 1000 m to 800 m, a width of300 m and depth of up to 2000 m.

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