To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively...To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively） are presented. Algorithm I is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm II, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm I. The implementation, for algorithm II or I, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.展开更多
Norwegian hydropower industry has more than 100 years of experiences in constructing more than4000 km-long unlined pressure shafts and tunnels with maximum static head of 1047 m（equivalent to almost 10.5 MPa） reache...Norwegian hydropower industry has more than 100 years of experiences in constructing more than4000 km-long unlined pressure shafts and tunnels with maximum static head of 1047 m（equivalent to almost 10.5 MPa） reached at unlined pressure tunnel of Nye Tyin project. Experiences gained from construction and operation of these unlined pressure shafts and tunnels were the foundation to develop design criteria and principles applied in Norway and some other countries. In addition to the confinement criteria, Norwegian state-of-the-art design principle for unlined pressure shaft and tunnel is that the minor principal stress at the location of unlined pressure shaft or tunnel should be more than the water pressure in the shaft or tunnel. This condition of the minor principal stress is prerequisite for the hydraulic jacking/splitting not to occur through joints and fractures in rock mass. Another common problem in unlined pressure shafts and tunnels is water leakage through hydraulically splitted joints or pre-existing open joints. This article reviews some of the first attempts of the use of unlined pressure shaft and tunnel concepts in Norway, highlights major failure cases and two successful cases of significance, applies Norwegian criteria to the cases and reviews and evaluates triggering factors for failure.This article further evaluates detailed engineering geology of failure cases and also assesses common geological features that could have aggravated the failure. The minor principal stress is investigated and quantified along unlined shaft and tunnel alignment of six selected project cases by using threedimensional numerical model. Furthermore, conditions of failure through pre-existing open joints by hydraulic jacking and leakage are assessed by using two-dimensional fluid flow analysis. Finally, both favorable and unfavorable ground conditions required for the applicability of Norwegian confinement criteria in locating the unlined pressure shafts and tunnels for geotectonic environment different from that of Norway are highlighted.展开更多
文摘To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively） are presented. Algorithm I is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm II, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm I. The implementation, for algorithm II or I, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.
文摘Norwegian hydropower industry has more than 100 years of experiences in constructing more than4000 km-long unlined pressure shafts and tunnels with maximum static head of 1047 m（equivalent to almost 10.5 MPa） reached at unlined pressure tunnel of Nye Tyin project. Experiences gained from construction and operation of these unlined pressure shafts and tunnels were the foundation to develop design criteria and principles applied in Norway and some other countries. In addition to the confinement criteria, Norwegian state-of-the-art design principle for unlined pressure shaft and tunnel is that the minor principal stress at the location of unlined pressure shaft or tunnel should be more than the water pressure in the shaft or tunnel. This condition of the minor principal stress is prerequisite for the hydraulic jacking/splitting not to occur through joints and fractures in rock mass. Another common problem in unlined pressure shafts and tunnels is water leakage through hydraulically splitted joints or pre-existing open joints. This article reviews some of the first attempts of the use of unlined pressure shaft and tunnel concepts in Norway, highlights major failure cases and two successful cases of significance, applies Norwegian criteria to the cases and reviews and evaluates triggering factors for failure.This article further evaluates detailed engineering geology of failure cases and also assesses common geological features that could have aggravated the failure. The minor principal stress is investigated and quantified along unlined shaft and tunnel alignment of six selected project cases by using threedimensional numerical model. Furthermore, conditions of failure through pre-existing open joints by hydraulic jacking and leakage are assessed by using two-dimensional fluid flow analysis. Finally, both favorable and unfavorable ground conditions required for the applicability of Norwegian confinement criteria in locating the unlined pressure shafts and tunnels for geotectonic environment different from that of Norway are highlighted.
