Computer Model for Hard Rock Tunnel Boring and Microtunneling Machines
Development of the Model
The development efforts on the CSM model began with a theoretical analysis of cutter penetration into the rock without any adjacent cuts or free-faces. This first step was crucial in understanding stress fields and the resultant fractures that are created beneath the penetrating edge of a disc cutter. Initially, the analysis focused on V-profile disc cutters, but later modified to include the constant-cross section discs as they became the industry standard. In this analysis, various previous theories derived from wedge indentation into rock were used as a guide. This analysis helped confirm the occurrence of a highly stressed crushed zone and the radial tension cracks during cutter penetration into the rock.
The next step was to extend this single cutter analysis into multiple cutter operation to simulate the interaction of adjacent cutting paths on a TBM. This means a free face (cut) exists on one side of the cutter to which the chip formation occurs. In this scenario, the rock under the cutter is again crushed to a fine powder, which behaves in a state of hydrostatic stress, causing radial cracks to form and radiate from this crushed zone or the so-called pressure-bulb. As these cracks are forced to grow, one or more of them reach the neighboring cut, causing rock failure in the form of a chip.
Detailed analysis of this chip formation mechanism aided with high-speed movies taken during cutting and chip surface inspections led to the conclusion that rock failure was occurring in tension. As a result, in the first formulation of the CSM model, rock compressive and tensile strengths were used as input to characterize the rock boreability by disc roller cutters. The compressive strength was used to describe the rock crushing beneath the cutter tip while the tensile strength accounted for the chip formation between adjacent cuts. Hence, using these two rock properties, a correlation was developed between cutter load and the depth of penetration achieved as a function of cutter edge geometry and the cutter diameter. Once the equation relating cutter thrust to penetration was established, the cutter rolling force was determined using a ratio called the cutting coefficient.
The formulation of the initial model was followed with calibration with actual cutting data obtained from laboratory tests performed on the CSM Linear Cutting Machine (LCM). LCM allows testing of full size field cutters under field-simulated conditions in terms of cut spacing, penetration, speed, etc (Figure 4). The accuracy of the model is also being validated continuously with extensive field data from numerous hard rock TBM projects from all over the world.
The following figure is a flow chart, which shows the general steps involved in making performance estimates for TBMs. Once the appropriate rock and geologic data is entered into the model, one of two options can be exercised.
Option 1: If the predictions are to be developed for an existing machine, the model then asks for relevant information about the machine, including cutter type, layout, type of machine, all machine specifications in terms of thrust, torque, power, rpm, etc.
Option 2: If it is desired to use a new machine, the model will then develop the required specifications and provide a cutterhead layout determined to be optimal for the rock and geologic conditions anticipated. This also covers the selection of the best cutter geometry.
Program Description for an Existing Machine
The following figure shows the model window where the machine specifications are entered together with power and thrust efficiency factors.
The model then asks whether the actual cutterhead is layout is available and if so, whether the estimates are to be developed using actual layout or the average cutter spacing. These two approaches in general give very close answers. The only difference is that by using the actual head layout, the model can also calculate individual loads, which vary as transition begins to occur from face to gage cutters.
The next step is to perform the calculations using the force-penetration algorithms built into the model. The model accomplishes the required calculations using an iterative approach. It starts from a low ROP and gradually increases it until one or more cutter or machine limits are reached. It then records the corresponding penetration rate as the maximum achievable ROP for the rock and geologic conditions anticipated. It follows the same procedure for all other rock types to be encountered in the tunnel. All estimates are then summarized and listed in a tabular form.