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• The range of optimum cutter spacing is identified for various rock types and UCS values. • Two formulas are developed for the normal force index (NFI) and rolling force index (RFI). • Cutter linear speed is identified as an influential factor for both NFI and RFI. • Fn-p diagram is developed to correlate between TBM operational limits and actual performance. • Optimum layout designs of TBMs are studied in various geological conditions. In this paper, the influence of rock type and uniaxial compressive strength on the cutter penetration is investigated to provide a basic guideline for the optimum field cutter spacing. The successfully utilized cutterhead layout designs are also studied in various rock types and different categories of tunnel sizes for projects with relatively high performance. The results of the conducted analyses show that the maximum cutter penetration in uniaxial compressive strength values below 50 and above 150 MPa is achieved when the cutter spacing is close to 90 and below 80 mm respectively. The study on the layout design characteristics of the cutterhead shows the evenly distributed scheme is more used with success even in softer rocks (when the rock mass condition is good). In softer rocks, the extension of the openings may have to be well over 50% of the cutterhead radius to maximize its performance. It is also found that the linear speed of the cutters has a direct correlation with two major parameters of normal force index (NFI) and rolling force index (RFI). In this regard, two formulas are generated using statistical analysis of the data from around 260 tunnel projects to evaluate both NFI and RFI. The corresponding formulas have coefficients of determination of 77 and 68% respectively. These formulas are used in an optimization process to maximize cutter penetration using various operational constraints (cutter load capacity, cutterhead torque limit, cutter geometry constrains, and cutterhead penetration rate limits). The new findings of this study can provide a foundation to improve the design process of hard rock TBMs and to optimize their performance considering various project setting parameters. [ABSTRACT FROM AUTHOR]

• The new balancing method utilizes normal, rolling, and side force components. • The new design involves a symmetrical and uniform distribution of the cutters. • The results ensure the minimum off-axis moments with no boundary conflicts. Optimization in TBM cutterhead design is essential for increasing its performance. Lace design for the cutters, buckets, and manholes in the cutterhead, is one of the major considerations in the design of the hard rock TBMs. An optimum lace design is necessary to avoid cutterhead deviation, vibration, and stress concentration during its operation. TBM manufacturers usually utilize two common lace designs of radial and spiral configurations. Despite the presence of many advantages for these two designs, each of them has its own disadvantages which may cause difficulties in achieving an efficient design of the cutterhead. This paper introduces a new TBM cutterhead lace design in which all three normal, side, and rolling forces are considered. The new force and moment balancing relationships are presented. With the consideration of the problems of the radial and spiral configurations, a new method of "uniformly distributed lace design" is introduced and the steps of achieving the final layout of the cutterhead is explained with its required parameters. On the basis of an example, a comparative study is made among three methods of applying radial, spiral, and uniformly distributed lace designs. The results show that the new method is very efficient in both uniformly and symmetrically distributing the cutters, buckets, and manholes on the cutterhead surface with no boundary conflicts. It also has the advantage to have low unbalanced forces and moments. [ABSTRACT FROM AUTHOR]

• RCM test results show the minimum specific energy occurs at around S / A c o n of 0.1. • Graphical and statistical methods are used to introduce formulas for A c o n , A r and R i. • A procedure is outlined to calculate optimum θ , S , and F n for the peripheral cutters. One of the most important goals in the design of the TBMs is to optimize the arrangement of the peripheral cutters on the cutterhead layout. Peripheral cutters refer to the cutters installed on the curved area near the periphery of the TBM cutterhead. This optimization is essential to improve TBM performance (e.g. penetration rate) and to control the interaction of the cutters (e.g. cutter normal force) with the tunnel face. The actual penetration of the peripheral cutters in the tunnel face is relatively lower which leads to lower applied normal force. To avoid ridge formation between these cutters and to prevent high asymmetric forces applied to the flanks of the cutters, it is necessary to gradually reduce the cutter spacing in the peripheral region of the cutterhead. The evaluation of the design specifications of the peripheral cutters, including spacing, tilt angle, and normal force is typically relying on experience and engineering judgment. To improve such strategies and to achieve an efficient design for the cutterhead lace design, an optimization method is introduced based on the statistical analysis of the cutterhead design details of various TBMs from around the world, as well as the principal of using the optimum ratio of spacing to the cutter contact area (S/A con). The results of this method provide the optimum spacing of disc cutters and their corresponding tilt angles and normal forces for the peripheral cutters. In developing relationships for the peripheral cutters' normal forces, graphical methods are utilized to calculate the actual cutter contact area and the actual cutter indentation area for different values of cutter tip width, cutterhead curvature radius, and tilt angle. In this regard, a multivariate regression formula is presented to evaluate the actual indentation area. To illustrate the steps presented in this method, an example is provided and the details of the design procedure and its final results are explained. The results of the proposed method establish a new foundation to improve the design process of hard-rock TBMs to help prevent structural damages and low performance. [ABSTRACT FROM AUTHOR]