Rock Bolt Pattern Support Pressure and Dead-Weight Check

The relation is what makes patterns comparable: a 5 ft pattern of 15 ton bolts and a 4 ft pattern of 10 ton bolts are not the same thing, and the division says which is stronger in one line. A 4 by 4 ft pattern of 12,000 lb bolts is 16 sq ft each and 750 psf of support, 5.21 psi. THEN THE DEAD-WEIGHT CHECK, which is the minimum useful test and the one that decides whether a pattern is a pattern. Six feet of loosened zone in 165 pcf rock weighs 990 psf, and 750 psf does not hold it -- a ratio of 0.76, a FAIL. Carrying that zone at this bolt capacity takes a 3.48 ft square pattern, not a 4 ft one, and because support pressure falls as the SQUARE of spacing, opening the pattern costs far more than it looks: 5 ft gives 480 psf and 6 ft gives 333, against the same 990 requirement. BOLT LENGTH IS TIED TO SPACING, roughly twice it, because bolts closer together than half their length interact to build a compressed rock beam -- the actual mechanism in bedded ground -- while bolts spaced further apart act as individual anchors and do not. Length is also tied to the span, about a third of it, and the longer of the two governs. A pressure conversion and a dead-weight screen, not a ground support design. It does not determine the loosened-zone height, which depends on rock mass quality, span, stress, and excavation method and which is the input that dominates the answer; empirical systems such as Q, RMR, or the GSI-based approaches, or a numerical analysis, are what establish it. It does not evaluate bolt type and anchorage -- mechanical, resin, friction, cable -- corrosion protection and design life, pull testing and quality assurance, the interaction between bolts and shotcrete or mesh, dynamic loading in burst-prone ground, or wedge and block analysis, which in jointed rock usually governs bolt length and orientation rather than any pressure criterion. Ground support is a life-safety system: MSHA ground control requirements, the site's ground control plan, and a qualified geotechnical engineer govern.

support pressure = bolt working capacity / (spacing x spacing); the dead-weight requirement = rock unit weight x loosened-zone height; the spacing for a target pressure = sqrt(capacity / target); bolt length is the longer of about twice the spacing and about a third of the span.

The tributary-area support pressure relation and the dead-weight screen by name, with the bolt-length rules of thumb. A screen, not a ground support design: MSHA ground control requirements, the site's ground control plan, and a qualified geotechnical engineer govern.

Division and a square root on the user's own pattern and rock data; no ground control standard is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: bolt_capacity_lb, spacing_1_ft, spacing_2_ft, span_ft, rock_unit_weight_pcf, loosened_zone_ft, target_support_psf, area_per_bolt_sqft, support_psf, support_psi, dead_weight_required_psf, dead_weight_ratio, spacing_for_target_ft, bolt_length_ft

• Support pressure falls as the SQUARE of spacing so opening a pattern by a foot costs far more than it lookstributary area mechanics
• Dead weight is the minimum test a pattern that cannot hold the loosened zone is not a patternground control practice
• The loosened-zone height dominates and it comes from a rock mass classification or an analysis, not from thisground control plan