# Q-slope

The Q-slope method for rock slope engineering and rock mass classification is developed by Barton and Bar.[1][2][3] It expresses the quality of the rock mass for slope stability using the Q-slope value, from which long-term stable, reinforcement-free slope angles can be derived.

The Q-slope value can be determined with:

${\displaystyle Q_{slope}=\left({\frac {RQD}{J_{n}}}\right)\times {\left({\frac {J_{r}}{J_{a}}}\right)_{0}}\times \left({\frac {J_{wice}}{SRF_{slope}}}\right)}$

Q-slope utilizes similar parameters to the Q-system[4] which has been used for over 40 years in the design of ground support for tunnels and underground excavations. The first four parameters, RQD (rock quality designation), Jn (joint set number), Jr (joint roughness number) and Ja (joint alteration number) are the same as in the Q-system. However, the frictional resistance pair Jr and Ja can apply, when needed, to individual sides of a potentially unstable wedges. Simply applied orientation factors (0), like (Jr/Ja)1x0.7 for set J1 and (Jr/Ja)2x0.9 for set J2, provide estimates of overall whole-wedge frictional resistance reduction, if appropriate. The Q-system term Jw is replaced with Jwice, and takes into account a wider range of environmental conditions appropriate to rock slopes, which are exposed to the environment indefinitely. The conditions include the extremes of erosive intense rainfall, ice wedging, as may seasonally occur at opposite ends of the rock-type and regional spectrum. There are also slope-relevant SRF (strength reduction factor) categories.

Multiplication of these terms results in the Q-slope value, which can range between 0.001 (exceptionally poor) to 1000 (exceptionally good) for different rock masses.

A simple formula for the steepest slope angle (β), in degrees, not requiring reinforcement or support is given by:

${\displaystyle \beta =20\log _{10}Q_{slope}+65^{\circ }}$

Q-slope is intended for use in reinforcement-free site access road cuts, roads or railway cuttings, or individual benches in open cast mines. It is based on over 200 case studies in slopes ranging from 35 to 90 degrees in fresh hard rock slopes as well as weak, weathered and saprolitic rock slopes.[1][2][3][5]

Rock slope design techniques have been derived using Q-slope and geophysical survey data, primarily based on Vp (P-wave velocity).[6]

Q-slope is not intended as a substitute for conventional and more detailed slope stability analyses, where these are warranted.

## References

1. ^ a b Barton, N.R.; Bar, N. (2015). "Introducing the Q-slope method and its intended use within civil and mining engineering projects". In Schubert W (ed.), Future Development of Rock Mechanics; Proc. ISRM reg. symp. Eurock 2015 & 64th Geomechanics Colloquium, Salzburg 7–10 October 2015. OGG, pp. 157-162.
2. ^ a b Bar, N.; Barton, N.R. (2016). "Empirical slope design for hard and soft rocks using Q-slope". In Proc. 50th US Rock Mechanics / Geomechanics Symposium, Houston 26–29 June 2016. ARMA, 8p.
3. ^ a b Bar, N.; Barton, N.R. (2017). "The Q-slope Method for Rock Slope Engineering". Rock Mechanics & Rock Engineering, Vol 50, Springer, Vienna, https://doi.org/10.1007/s00603-017-1305-0.
4. ^ Barton, N.R.; Lien, R.; Lunde, J. (1974). "Engineering classification of rock masses for the design of tunnel support". Rock Mechanics and rock engineering. Vol. 6, Springer-Verlag, pp. 189-236.
5. ^ Bar, N.; Barton, N.R.; Ryan, C.A. (2016). "Application of the Q-slope method to highly weathered and saprolitic rocks in Far North Queensland". In Ulusay et al. (eds.), Rock Mechanics and Rock Engineering: From the Past to the Future Development of Rock Mechanics; Taylor & Francis Group, London, pp. 585-590.
6. ^ Bar, N.; Barton, N.R. (2018). "Rock Slope Design using Q-slope and Geophysical Survey Data". Periodica Polytechnica Civil Engineering. doi:10.3311/PPci.12287.
Bayesian information criterion

In statistics, the Bayesian information criterion (BIC) or Schwarz information criterion (also SIC, SBC, SBIC) is a criterion for model selection among a finite set of models; the model with the lowest BIC is preferred. It is based, in part, on the likelihood function and it is closely related to the Akaike information criterion (AIC).

When fitting models, it is possible to increase the likelihood by adding parameters, but doing so may result in overfitting. Both BIC and AIC attempt to resolve this problem by introducing a penalty term for the number of parameters in the model; the penalty term is larger in BIC than in AIC.

The BIC was developed by Gideon E. Schwarz and published in a 1978 paper, where he gave a Bayesian argument for adopting it.

Geotechnical engineering

Geotechnical engineering is the branch of civil engineering concerned with the engineering behavior of earth materials. Geotechnical engineering is important in civil engineering, but also has applications in military, mining, petroleum and other engineering disciplines that are concerned with construction occurring on the surface or within the ground. Geotechnical engineering uses principles of soil mechanics and rock mechanics to investigate subsurface conditions and materials; determine the relevant physical/mechanical and chemical properties of these materials; evaluate stability of natural slopes and man-made soil deposits; assess risks posed by site conditions; design earthworks and structure foundations; and monitor site conditions, earthwork and foundation construction.A typical geotechnical engineering project begins with a review of project needs to define the required material properties. Then follows a site investigation of soil, rock, fault distribution and bedrock properties on and below an area of interest to determine their engineering properties including how they will interact with, on or in a proposed construction. Site investigations are needed to gain an understanding of the area in or on which the engineering will take place. Investigations can include the assessment of the risk to humans, property and the environment from natural hazards such as earthquakes, landslides, sinkholes, soil liquefaction, debris flows and rockfalls.

A geotechnical engineer then determines and designs the type of foundations, earthworks, and/or pavement subgrades required for the intended man-made structures to be built. Foundations are designed and constructed for structures of various sizes such as high-rise buildings, bridges, medium to large commercial buildings, and smaller structures where the soil conditions do not allow code-based design.

Foundations built for above-ground structures include shallow and deep foundations. Retaining structures include earth-filled dams and retaining walls. Earthworks include embankments, tunnels, dikes and levees, channels, reservoirs, deposition of hazardous waste and sanitary landfills.

Geotechnical engineering is also related to coastal and ocean engineering. Coastal engineering can involve the design and construction of wharves, marinas, and jetties. Ocean engineering can involve foundation and anchor systems for offshore structures such as oil platforms.

The fields of geotechnical engineering and engineering geology are closely related, and have large areas of overlap. However, the field of geotechnical engineering is a specialty of engineering, where the field of engineering geology is a specialty of geology. Coming from the fields of engineering and science, respectively, the two may approach the same subject, such as soil classification, with different methods.

Rock mass classification

Rock mass classification systems are used for various engineering design and stability analysis. These are based on empirical relations between rock mass parameters and engineering applications, such as tunnels, slopes, foundations, and excavatability. The first rock mass classification system in geotechnical engineering was proposed in 1946 for tunnels with steel set support.

Rockfall

A rockfall or rock-fall refers to quantities of rock falling freely from a cliff face. The term is also used for collapse of rock from roof or walls of mine or quarry workings. A rockfall is a fragment of rock (a block) detached by sliding, toppling, or falling, that falls along a vertical or sub-vertical cliff, proceeds down slope by bouncing and flying along ballistic trajectories or by rolling on talus or debris slopes,” (Varnes, 1978). Alternatively, a "rockfall is the natural downward motion of a detached block or series of blocks with a small volume involving free falling, bouncing, rolling, and sliding". The mode of failure differs from that of a rockslide.

SMR classification

Slope Mass Rating or SMR is a rock mass classification scheme developed by Manuel Romana to describe the strength of an individual rock outcrop or slope. The system is founded upon the more widely used RMR scheme, which is modified with quantitative guidelines to the rate the influence of adverse joint orientations (e.g. joints dipping steeply out of the slope).

Slope stability

Slope stability refers to the condition of inclined soil or rock slopes to withstand or undergo movement. The stability condition of slopes is a subject of study and research in soil mechanics, geotechnical engineering and engineering geology. Slope stability analyses include static and dynamic, analytical or empirical methods to evaluate the stability of earth and rock-fill dams, embankments, excavated slopes, and natural slopes in soil and rock. The analyses are generally aimed at understanding the causes of an occurred slope failure, or the factors that can potentially trigger a slope movement, resulting in a landslide, as well as at preventing the initiation of such movement, slowing it down or arresting it through mitigation countermeasures.

The stability of a slope is essentially controlled by the ratio between the available shear strength and the acting shear stress, which can be expressed in terms of a safety factor if these quantities are integrated over a potential (or actual) sliding surface. A slope can be globally stable if the safety factor, computed along any potential sliding surface running from the top of the slope to its toe, is always larger than 1. The smallest value of the safety factor will be taken as representing the global stability condition of the slope. Similarly, a slope can be locally stable if a safety factor larger than 1 is computed along any potential sliding surface running through a limited portion of the slope (for instance only within its toe). Values of the global or local safety factors close to 1 (typically comprised between 1 and 1.3, depending on regulations) indicate marginally stable slopes that require attention, monitoring and/or an engineering intervention (slope stabilization) to increase the safety factor and reduce the probability of a slope movement.

A previously stable slope can be affected by a number of predisposing factors or processes that make the safety factor decrease - either by increasing the shear stress or by decreasing the shear strength - and can ultimately result in slope failure. Factors that can trigger slope failure include hydrologic events (such as intense or prolonged rainfall, rapid snowmelt, progressive soil saturation, increase of water pressure within the slope), earthquakes (including aftershocks), internal erosion (piping), surface or toe erosion, artificial slope loading (for instance due to the construction of a building), slope cutting (for instance to make space for roadways, railways or buildings), or slope flooding (for instance by filling an artificial lake after damming a river).

Slope stability analysis

Slope stability analysis is performed to assess the safe design of a human-made or natural slopes (e.g. embankments, road cuts, open-pit mining, excavations, landfills etc.) and the equilibrium conditions. Slope stability is the resistance of inclined surface to failure by sliding or collapsing. The main objectives of slope stability analysis are finding endangered areas, investigation of potential failure mechanisms, determination of the slope sensitivity to different triggering mechanisms, designing of optimal slopes with regard to safety, reliability and economics, designing possible remedial measures, e.g. barriers and stabilization.Successful design of the slope requires geological information and site characteristics, e.g. properties of soil/rock mass, slope geometry, groundwater conditions, alternation of materials by faulting, joint or discontinuity systems, movements and tension in joints, earthquake activity etc. The presence of water has a detrimental effect on slope stability. Water pressure acting in the pore spaces, fractures or other discontinuities in the materials that make up the pit slope will reduce the strength of those materials.

Choice of correct analysis technique depends on both site conditions and the potential mode of failure, with careful consideration being given to the varying strengths, weaknesses and limitations inherent in each methodology.Before the computer age stability analysis was performed graphically or by using a hand-held calculator. Today engineers have a lot of possibilities to use analysis software, ranges from simple limit equilibrium techniques through to computational limit analysis approaches (e.g. Finite element limit analysis, Discontinuity layout optimization) to complex and sophisticated numerical solutions (finite-/distinct-element codes). The engineer must fully understand limitations of each technique. For example, limit equilibrium is most commonly used and simple solution method, but it can become inadequate if the slope fails by complex mechanisms (e.g. internal deformation and brittle fracture, progressive creep, liquefaction of weaker soil layers, etc.). In these cases more sophisticated numerical modelling techniques should be utilised. Also, even for very simple slopes, the results obtained with typical limit equilibrium methods currently in use (Bishop, Spencer, etc.) may differ considerably. In addition, the use of the risk assessment concept is increasing today. Risk assessment is concerned with both the consequence of slope failure and the probability of failure (both require an understanding of the failure mechanism).Within the last decade (2003) Slope Stability Radar has been developed to remotely scan a rock slope to monitor the spatial deformation of the face. Small movements of a rough wall can be detected with sub-millimeter accuracy by using interferometry techniques.