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💉 Calculators

Annular Grout Volume (Backfill)

Calculate the theoretical annular backfill grout volume per lining ring of a mechanized tunnel, V = (π/4)·(De² − Di²)·L, from the excavation diameter De (the TBM cutterhead cutting diameter), the segment ring outer diameter Di and the ring length L. Behind the TBM shield an annular gap forms (between excavated ground and lining, from overcut and shield taper) that must be filled immediately with grout injected through the tail. This filling is essential: it prevents ground relaxation (reducing volume loss and surface settlement), locks the ring in place and ensures uniform ground-lining contact. Actual injected volume exceeds theoretical (factor 1.1-1.5). Enter the excavation and ring diameters and the ring length.

Result

Volume de injeção anular (backfill)

Atrás do escudo de uma tuneladora, entre o solo recém-escavado e o anel de aduelas de concreto que forma o revestimento, abre-se inevitavelmente um vão anular (tail gap) — resultado do sobrecorte da cabeça de corte (que corta um diâmetro ligeiramente maior que o escudo para a máquina poder manobrar) e da conicidade do próprio escudo. Esse vão precisa ser preenchido imediatamente, à medida que o anel sai da proteção da cauda do escudo, com argamassa de injeção (backfill grouting) bombeada por linhas na cauda. O volume teórico por anel é V = (π/4)·(De² − Di²)·L, a partir do diâmetro de escavação De, do diâmetro externo do anel Di e do comprimento do anel L — geometricamente, a coroa circular entre os dois diâmetros, multiplicada pelo comprimento. Esse preenchimento é absolutamente crítico e cumpre três funções simultâneas: (1) impede o relaxamento do maciço para dentro do vão, o que é a principal forma de controlar a perda de volume e os recalques de superfície; (2) trava o anel de revestimento na posição correta, evitando que flutue, desalinhe ou se deforme sob a pressão do solo; e (3) garante o contato uniforme solo-revestimento, distribuindo as cargas e evitando concentrações de tensão que trincariam as aduelas. O volume real injetado supera o teórico por um fator de 1,1 a 1,5, devido a perdas, sobrecorte variável e penetração da argamassa nas fissuras do maciço. Controlar volume e pressão de injeção em tempo real, sincronizados com o avanço, é parte essencial da operação de uma TBM moderna. Informe os diâmetros de escavação e do anel e o comprimento do anel.

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Tunnel Volume Loss

Calculate the volume loss of a tunnel excavation, VL = Vs ÷ (π·D²/4)·100, the percentage ratio between the settlement trough volume per metre Vs (m³/m) and the excavated cross-section area (from diameter D). Volume loss quantifies how much soil 'disappeared' relative to the theoretical tunnel volume — caused by face relaxation, overexcavation, tail-gap closure behind the TBM shield and consolidation. It is the key control parameter for urban excavation: well-run EPB/slurry TBMs achieve 0.5-1.5% in soils; values above 2-3% indicate problems and excessive settlement. Enter the trough volume and the tunnel diameter.

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Injection Shot Volume

Compute the shot volume of a plastic part by dividing the injected mass by the molten material density. The shot is the total volume of plastic injected per cycle (parts + runners), a parameter that must fit the injection barrel capacity. Together with the machine capacity, it defines how many cavities can be filled per cycle. Enter the injected mass (g) and the material density (g/cm³).

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Tunnel Support Pressure

Calculate the support pressure a tunnel lining must resist, pv = γ·Hp, from the rock mass unit weight γ (kN/m³) and the rock load height Hp (m) — typically from Terzaghi's method or geomechanical classifications (RMR, Q-system). Support pressure is the vertical stress the loosened rock zone exerts on the support (shotcrete, steel sets, final lining), and it drives the structural design of the lining. In shallow tunnels the load may be the full overburden; in deep tunnels, arching reduces it to a fraction. Estimating it correctly is decisive: underestimating leads to collapse, overestimating raises cost. Enter the unit weight and the rock load height.

The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.