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Pre-stressed cables were found to be a viable approach of reinforcing anti-dip bedding rock slopes (ABRSs) in the Wenchuan earthquake. However, the dynamic response law and failure mechanism of reinforced ABRSs are still unclear, which was studied using the Universal Distinct Element Code (UDEC) method in this work. A numerical model of a typical ABRS was first built up using UDEC. Then, a comparison of the dynamic response of reinforced and unreinforced ABRSs was carried out. Moreover, a systematic parameter study was performed to investigate the effect of cable inclination, cable spacing, and pre-stressed force on the reinforcement effect. The results show that pre-stressed cables can be very effective in controlling the deformation and improving the dynamic stability of ABRSs subjected to dynamic loading. For both unreinforced and reinforced ABRSs, a remarkable acceleration amplification occurs on the surface of the slope from half of the slope height upwards. A small cable inclination and a high pre-stressed force are recommended in the seismic reinforcement design of ABRSs. The results of this work could guide the design of reinforcement of ABRS in earthquake-prone areas.

Talus deposits naturally form to a certain height in the toes of slopes because of the accumulation of collapsed material and small landslides. However, the stability of concealed cataclin...

A cusp catastrophic model was developed for the pillar-and-roof support system based on the simplified mechanical model of the support system and the improved stress-strain relationship for gypsum....

As a result of earthquakes, the deformation and failure caused by anti-dip bedding rock slopes are large, and their seismic dynamic response law is complex. Using the three-dimensional discrete element numerical analysis software 3DEC, the influence of seismic wave parameters on the dynamic response of anti-dip bedding rock slopes was systematically studied, with special focus on the influence of the angle between seismic wave incidence direction and slope trend on the dynamic response of anti-dip bedding rock slopes under three-dimensional conditions. The orthogonal test was designed to conduct sensitivity analysis of five seismic parameters, including seismic wave amplitude, incidence angle of the S-wave, frequency, duration, and the time difference between the P-wave’s and the S-wave’s peak. The results revealed that the S-wave’s amplitude As and the holding time T of the seismic wave are positively correlated with the acceleration amplification factor of the slope, and the incident direction γ of the S-wave is negatively correlated with the acceleration amplification factor of the slope. The increase of seismic wave frequency f and the time difference Δt between the P-wave’s and the S-wave’s peak lead to the first increase and then decrease of the Y-directional displacement of the slope. The sensitivity of each seismic wave parameter to the Y-directional acceleration amplification factor at the shoulder of anti-dip bedding rock slopes in earthquake conditions is ordered as follows: S-wave’s amplitude As > frequency f > S-wave’s incidence angle γ > the time difference Δt > holding time T. the study results provide reference and basis for stability evaluation and engineering design of anti-dip bedding rock slopes in areas with high seismic intensity.

In this study, a comprehensive assessment on the generation mechanism, distribution characteristics, and extension rules of structure cracks was conducted by in situ monitoring and field investigation in the Chengchao Iron Mine. Structure cracks are affected by many factors, e.g., surface deformation, structure strength, occurrence position, and machine vibration. They initially occur in a structure when the strength of the structure is not enough to resist the inner strain as surface deformation increases. In contrast, increases in width and length of structure crack exert stress release in the structure and thus decrease structure deformation surrounding the crack. A great ground crack may adversely aggravate structure cracking and release the stress of surrounding rock masses. In addition, micro cracks in rock masses provide favorable conditions for the generation and extension of cracks, resulting that cracks occur in shaft walls more easily and extend towards the deeper. The initial distribution of cracks is generally consistent with such micro cracks. Subsequently, cracks in deep rock masses will extend along the strike of the mined-out area as surface deformation increases. Sensibilities to cracking of structures are changed by their different strain resistances and become stronger from bolt-shotcrete shaft, bolt-shotcrete tunnel, and brick-concrete building to brick wall. Based on distribution characteristics of cracks and wave velocity in rock masses, the overlaying strata affected by underground mining can be divided into four zones: broken zone, broken transition zone, crack generation zone, and micro deformation zone.

Biplanar failure is the most common instability type of footwall slopes, with a steeply dipping joint (typically the bedding plane) and a gently dipping joint (i.e., the daylighting toe joi...

In 2014, a cutting slope was excavated in Guizhou Province in China during the construction of the YanDe highway when a previously unknown ancient landslide was encountered. It has subsequently been named the ‘Longjiayan ancient landslide’. Large surface cracks and severe building damage occurred, as well as apparent ground subsidence. This work reports the results of a comprehensive investigation performed to identify the mechanism and process of reactivation of the ancient landside. In situ surveys and mapping activities were first carried out to obtain a preliminary delineation of the landslide surface, and 19 boreholes were set up in the reactivation area to determine the landslide structure, as well as create a picture of the sliding surfaces involved. Then, 41 surface cracks and deep displacements in eleven boreholes were monitored for over 40 days. A numerical 2D analysis was also undertaken to back analyze the landside. A conceptual model is proposed for interpreting the mechanisms responsible for reactivation of ancient landslides based on the Longjiayan landslide. Thereafter, based on the formation mechanism of the landslide, detailed reinforcement measures were proposed to control it. The results reveal that the landslide was a retrogressive soil-mass slide involving two sliding surfaces. These surfaces have different depths: one is shallow and located in a silty clay layer; the other is deep and lies in a completely weathered shale layer. The soil mass primarily slid towards the free surface along the deep sliding surface. Up to three failure stages have been identified in the landslide which was triggered by excavation in the toe region. Rainfall and adverse dip direction of weak intercalations further promoted the development of the landslide. During this process, the shallow landslide played a key role in the formation of the deep landslide. Appropriate use of anti-slide piles and water interception/drainage is an effective approach to controlling such landslides.

This paper proposes a disturbance observer based dynamic inversion control law for the wind tunnel free-flight test of the directional static unstable blended-wing-body aircraft. Considering that nonlinear control system is usually affine nonlinear system for control design, thus the original wind tunnel aerodynamic coefficients are transformed into aerodynamic derivative form by the weighted least squares method and transformation errors are regarded as external disturbances. The classical nonlinear dynamic inversion control is widely implemented in the practical engineering but sensitive to the model errors, this paper designs the disturbance observer to estimate the aerodynamic model errors, then compensates the errors in the dynamic inversion control loop. Moreover, this paper analyzes the stability of the control system and estimates tracking error upper bound. Finally, the proposed method is verified by the simulation experiment of the blended-wing-body aircraft.

In this study, a comprehensive assessment of the distribution characteristics of ground cracks in the Chengchao Iron Mine was conducted by field investigation and monitoring. In general, ground cracks are initially distributed around collapse pits, and subsequently extend outwards centered on the mined-out area. Greater ground deformation leads to more developed ground cracks. Ground cracks can be divided into cut-through crack, deep crack and shallow crack based on their downward extension depths. Furthermore, the formation of ground cracks is controlled by both underground mining and geological structures. Ground cracks can be divided into mining-induced crack and tectonic crack based on their main influencing factors. Moreover, many types of ground cracks are caused by different failure modes including tensile failure, shear failure and mixed failure. Ground cracks can be divided into vertical-shear crack, vertical-shear and horizontal-tensile crack, horizontal-tensile crack, horizontal-shear crack and mixed crack based on their formation mechanisms. In particular, the movement line and the break line, defined as e = 2 mm/m and 6 mm/m, respectively, can be reasonably regarded as disturbance boundary and crack boundary in a metal mine. The disturbance zone caused by underground mining can be divided into collapse zone, break zone and movement zone based on the size of ground deformation and the characteristics of ground cracks. Increases in ground crack width and length exert different degrees of stress release on the rock masses outside and inside the crack, thus increasing their deformation difference. In addition, the extension of ground cracks is related to the ground topography and the strength and integrity of the rock masses and soil. Cracks on hilltop are more developed than those on flat land, and cracks will initially appear in rock mass and soil rather than on a concrete structure due to the lower strain resistance of the rock mass and soil. However, concrete structures are more sensitive to cracking than rock mass and soil because of the better integrity of concrete structures.

Underground mining operations using the sublevel caving method often result in discontinuous ground deformations involving surface cracks. Determining the limit of the discontinuous deformation zone is important for the relocation of neighbouring residential areas, mining infrastructure, and the planning of underground mining operations. The limit of the discontinuous deformation zone is characterised by the outermost surface crack, which is a tensile crack when it occurs and is correlated with the horizontal ground tensile strain. In this study, a mathematical procedure combining the horizontal displacement, as periodically monitored by total station and GPS, multiquadric radial basis function (MQ-RBF) interpolation, and continuum mechanics is provided to calculate the strain state at any point on the ground. Then the relationship between a new tensile crack and horizontal ground tensile strain is studied to determine the criterion representing the presence of a new tensile crack. This means that, when the criterion at any point on the ground is satisfied, the point will have the potential to crack. Based on this, the potential discontinuous deformation zone where surface cracks may occur can be identified, potential break angles at representative sections can then be determined. A case study is presented to illustrate the results given by the above methodology. The result shows that when major principal horizontal ground strain e1 at any point on the ground reaches the potential cracking major principal strain, PCMPS (6 mm/m in this case study), the point will have the potential to crack. Subsequently, the area within the outermost contour of the PCMPS can be defined as the potential discontinuous deformation zone. Moreover, the approximate matching of the limits of potential discontinuous deformation zones and surface cracks verifies the reliability of the mathematical procedure and the rationality of the PCMPS in identifying the discontinuous deformation zone. Additionally, in this case study, the potential break angles at two respective sections are significantly different, indicating that the break angles should be further studied and care taken in design of works in these two zones, respectively.

Collapse is a common instability mode of anti-dip rock slopes. This type of failure involves a complex geo-mechanical process. This work investigated the collapse mechanism of an anti-dip rock slope in a granite mine in Shanxi Province, China. A detailed field survey was carried out to analyze the inducing factors and failure process of collapse. Then, discrete element numerical simulations were conducted by the Universal Distinct Element Code (UDEC) to determine the microscopic damage and macroscopic failure of collapse. Through these works, the composite collapse failure mechanism of the anti-dip rock slope was investigated comprehensively. Results show that the structural planes perpendicular to the slope surface and the steep anti-dip structural planes are the prerequisites of collapse. Strength softening of the structural planes caused by rainfall is the triggering factor of collapse. The collapse of such a rock slope can be considered as a composite failure composed of shear sliding, block toppling, and flexural toppling. In addition, the numerical results indicate that the composite failure of shear sliding and block toppling occurs at the toe of and the middle of the slope, followed by flexural toppling failure at the rear edge of the slope. Therefore, the monitoring and treatment of such type of collapses should be concentrated on the composite failure zone where shear sliding and block toppling occur. The high consistency between the numerical results and field observations shows the feasibility and rationality of using UDEC to study such collapse from the microscopic damage to macroscopic failure. The results enrich the type of collapse of anti-dip rock slopes and provide a scientific reference to the design treatment for such slopes.

Crest loads are often encountered in hydropower, highway, open-pit and other engineering rock slopes. Toppling failure is one of the most common deformation failure types of anti-dip bedding rock slopes. Analysis on such failure of anti-dip bedding rock slopes subjected to crest loads has an important influence on engineering practice. Based on the step-by-step analysis approach proposed by Goodman and Bray, a geo-mechanical model was developed, and the related analysis approach was proposed for the toppling failure of anti-dip bedding rock slopes subjected to crest loads. Using the transfer coefficient method, a formulation was derived for calculating the residual thrust of slope toe and the support force required to meet the requirements of the slope stability under crest loads, which provided a scientific reference to design and support for such slopes. Through slope examples, the influence of crest loads on the residual thrust and sliding ratio coefficient was investigated for cases of different block widths and slope cut angles. The results show that there exists a critical block width for such slope. The influence of crest loads on the residual thrust is non-negligible when the block thickness is smaller than the critical value. Moreover, the influence of crest loads on the slope stability increases with the slope cut angle and the sliding ratio coefficient of anti-dip bedding rock slopes increases with the crest loads. Finally, the theoretical solutions and numerical simulations using Universal Distinct Element Code (UDEC) were compared, in which the consistent results show the applicability of both approaches.

In this study, a comprehensive assessment of the overlying strata caving characteristics of mental mines is conducted for the non-pillar sublevel caving method, especially considering the geological features and rock mass characteristics. In general, the overlying strata caving process can be divided into four stages: the intermittent roof caving stage, the crack extension and surface subsidence stage, the karst collapse stage, and the mining-induced collapse stage. Roof caving is an intermittent process, with higher caving occurring in stronger rock masses, and occurs more easily in weaker rock masses. Due to gaps generated in the overlying rock mass, the bulking coefficient of the overlying strata is much greater than the laboratory-measured value; it also varies with the mining advance lines. During the crack extension and surface subsidence stage, the surface deformation is less extensive when the rock strength is greater, and the gradient of surface deformation is lower when the rock mass integrity is lower. Thus, higher mining height and lower rock mass quality result in greater surface deformation. Furthermore, weak planes, such as faults and joints, can help to generate fissures in weathered rock masses; these fissures create passageways for groundwater flow, which accelerates crack extension and connection in reverse. In addition, surface collapses can be divided into karst collapses and mining-induced collapses. Because a large number of fissures and a high karst rate create favorable conditions for karst collapse, significant variations in groundwater levels can induce karst collapse at the surface, with high negative pressure forming in the karst caves. Mining-induced collapses are mainly related to the mining depth, mining height, and the properties of the overlying rock mass. Underground mining is a major factor in surface collapse, and heavy rainfall can induce a delayed but sudden collapse.

Block-flexure toppling failure is frequently encountered in rock slopes. In this paper, we first proposed two theoretical models to calculate the factor of safety against block-flexure toppling, namely, step by step analysis model (LEM-SSAM) and overall analysis model (LEM-OAM). Then, we developed two special MATLAB codes for a quick stability estimation based on the proposed methods, respectively. Next, the universal distinct element code (UDEC) was used to study the failure mechanisms of block-flexure toppling. In order to realistically simulate the excavation of slope and obtain the detailed damage information of joints, we developed two FISH functions in UDEC. Finally, we conducted a comparative analysis of the limit equilibrium method and the numerical simulations through twelve theoretical models. The results show that many aspects of block-flexure toppling failure have been captured using UDEC combined with the developed FISH functions. The LEM-OAM and UDEC agree well while a larger factor of safety is obtained using the LEM-SSAM. It is found that the dip angles and friction angles of the joints dipping steeply into face have a great influence on block-flexure toppling failure while the influence of the cross joint spacing is less significant.

Bi-planar failure is the commonest type of failure in steep and high footwall slopes. This paper presents an investigation of the bi-planar failure mechanism and a stability analysis model for footwall slopes based on the study of eleven diabase mines in Hunyuan County, Shanxi Province, China. First, a detailed investigation of the site and tests were carried out to obtain a geological model and calculation parameters for the slope. Then, the failure process in footwall slopes was investigated by a trigon approach performed using the Universal Distinct Element Code (UDEC) software package. A mechanism was then obtained for bi-planar compression–shear failure by combining the results obtained for the stress, displacement, and crack development. Subsequently, based on the limit equilibrium and frictional plasticity theories, a new columnar mechanical model was proposed for bi-planar footwall slope failure. The results demonstrate that the UDEC trigon approach was well suited to simulating bi-planar failure in steep and high footwall slopes. Employing this approach, a sliding failure surface that initiates, develops, and propagates in the discontinuity and intact rock could be correctly captured and the evolution of the damage in the toe of the slope could be quantitatively investigated. The results also indicate that shear failure first occurs at persistent discontinuities and then compression–shear failure occurs in the intact rocks. In addition, the failure surface of the rock emanates from the toe of the slope, is oriented upwards at an angle to the persistent discontinuity thus forming the through sliding surface (this angle can be determined using frictional plasticity theory). The critical heights and safety factors of footwall slopes could be readily obtained by employing this new columnar mechanical model giving results that are consistent with the results of numerical simulations. Furthermore, the results of a parameter-sensitivity analysis show that the dip angle of the toe breakout surface increases as the slope angle increases. However, the angle between the toe breakout and internal shear surfaces remains unchanged as the slope angle increases. Moreover, the critical height of the footwall slope decreases linearly as the slope angle increases. The method proposed provides theoretical guidance for the stability analysis of steep and high footwall slopes. The results produced should also help engineers to gain a better understanding of the mechanisms of bi-planar failure in such rock slopes.

Considering the class Γ(n, m) of ordered trees with m leaves and n-m internal nodes, a set of generating functions are established for the following problems: (1) the total number nodes with degree r over Γ(n, m), (2) the total path length of nodes over Γ(n, m), and (3) the total number of nodes over Γ(n, m) on level k. Some particular counting fomulas are derived from them.

To perform long range navigation and desired task, AUV is required to describe internal system states and mutual transitions clearly and completely. The mission planning system developed in this project utilizes finite state machine model to analyze and depict AUVpsilas working flow and intricate control logic of all mission stages. An efficient path planning method resulting in a shortest tangent route is presented, and it can be easily computed and implemented. A real-time motion planner using fuzzy logic is designed, it can practice superior dynamic control under imprecise sensor measurement, and it also satisfies real-time constraints and is easy to use. Simulation experiments and sea trials show that the mission planning system can guide AUV to navigate from given start position to remote task area, and precisely locate position and complete task, and it is capable of dealing with complex ocean environment and highly autonomous.

The present paper discusses more about additive enumeration problems over some tree families, especially, the trees with nodes and leaves of given numbers. It establishes a uniform solving scheme for additive enumeration problems over V (ery) simply generated tree families. Based on the uniform scheme, a series of additive enumeration problems over tree families, including leaf path length counting and node path length counting, are solved. The tree families related include: binary tree, t -ary tree and ordered tree.