Boolean-Based Surface Procedure for the External Heat Transfer Analysis of Dams during Construction

Algorithm 1

Boolean-based surface procedure.

(1)  Read surface sets already been defined, 𝑆₁, 𝑆₂, 𝑆₃ and 𝑆₄, according to Section 4.2.

(2)  Detect outlet hole surfaces in the dam body, and store them as 𝑆₅, according to Algorithm 3.

(3)  Detect joint surfaces between adjacent monoliths, and store them as 𝑆₆, according to Algorithm 3.

(4)  Detect foundation surfaces between dam and rock, and store them as S_rock, according to Algorithm 3.

(5)  Kill all the dam elements.   // the elements whose lift_ID   >  0.

(6)  for   𝑖=1,2,…,𝑠𝑡𝑒𝑝𝑠   do

(7)      Activate the lift cast at this step.     // the elements whose lift_ID = 𝑖.

(8)      Recognize external surfaces of activated elements, store them as S_all according to Algorithm 2.

(9)      Look for the element surfaces with lift_ID = 𝑖  from S_all, and note them as S_lift.

(10)     S_rock = S_rock ∧  S_all.

(11)     S_up   = (S_lift ∧  S ₃) ∨  S_up.

(12)     S_down = (S_lift  ∧  S ₄) ∨S_down.

(13)     S_joint   =   𝑆₆  ∧  S_all.

(14)     S_hole   =   𝑆₅   ∧  S_all.

(15)     𝑆_𝑡𝑜𝑝=𝑆_𝑎𝑙𝑙−𝑆_𝑢𝑝−𝑆_𝑑𝑜𝑤𝑛−𝑆_𝑗𝑜𝑖𝑛𝑡−𝑆_ℎ𝑜𝑙𝑒.

(16)     Set boundary conditions according to Table 2

(17)     Seek the highest elevation 𝑧 of nodes in the latest cast lift, which is noted as z_h.

(18)     𝑧_mono   [mono_ID   [𝑖]] = z_h.  // change the top elevation of the new-rise monolith.

(19)     for   𝑗=1,2,…,𝑖𝑛𝑐𝑠   [𝑖].      // increments of this step

(20)          Finite element solver.

(21)     end  loop   𝑗.

(22)  end  loop   𝑖.