Page - 798 - in Book of Full Papers - Symposium Hydro Engineering

According to the above description, the time-space evolution model of construction entity in the construction space can describe by motion equations, motion trajectories, velocities and accelerations and so on. By establishing the construction space coordinate system, the entity position transformation can express as a single-valued continuous function of time t: P(t)=[x(t) y(t) z(t)] [3] The rotation angle around the x-axis, y-axis, or z-axis is express as: O(t)=[ox(t) oy(t) oz(t)] [4] In order to express the construction entity’s translation and rotation in virtual environment, the vector r(t)=[p(t) o(t)]T is defined to represent the position and direction of the entity at a certain moment. When the construction entity moves, the time is from t1 to t2, its direction and position changes from r(t1) to r(t2). Through the above matrix transformation operation, the three-dimensional spatial movement characteristics of the entity in the construction space can describe. 3. CONSTRUCTION COLLISION DETECTION AND ANALYSIS 3.1. COLLISION CLASSIFICATION AND EVALUATION INDEXES According to entities state, all entities can divide into active entities and passive entities. The position of active entity changes constantly with time. The position of passive entity remains stationary. Therefore, the collision can be simplified into two types:1) Collision between active entities;2) Collisions between active and passive entities. Through the observation and statistical analysis of high arch dam construction process, statistics show that the main types of collisions in construction are show in Table 3. Table 3 Collision types and description Collision Type Explanation Collision 1 Among cable cranes Collision 2 Among bucket and surface machine Collision 3 Between bucket and dam body Collision 4 Between bucket and temporary structure Collision 5 Between bucket and other hoists Collision 6 Among machines in the storehouse Collision 7 Between machines and dam structure The collision means that two entities overlap in the same space at the same time. Different degrees of overlap cause different collision effects. Therefore, the degree of overlap can quantify by the indicators with following indexes: (1) The space area of collision (Sc). Two entities have intersection in space when collisions take place, and the degree of collision can measure intuitively by the calculated area of intersection. 798