Experience in Collapse Risk Assessment of Building on Covered Karst Landscapes in Russia

Abstract

Problems that arise during development of terranes with carbonate and sulfate-covered karst are discussed herein and are based on experiences in Russia, where karst terranes constitute one third of the total territory. Different karst hazards are considered with respect to various types of construction and facilities. Karst hazards caused by sinkholes are classified according to specific sinkhole development intensity (ten categories) and average sinkhole diameter (eight categories). Some examples of accidents causing damage to buildings are presented and the reasons for the accidents are discussed. The main stochastic laws describing sinkhole development are considered. A method of evaluation of karst collapse risk and assessment of the risk level is presented. Application of this method helps to plan an antikarst protection program with both capital and maintenance types of prevention activity.

1 Introduction

Information presented herein is based on long-term research into issues involving engineering and construction in karst terranes in Russia (Tolmachev 2006). Russian engineers first encountered serious karst-related problems at the end of the nineteenth century during construction and operation of railways in the Volga River catchment basin and in the Urals region. That was the time when engineering karstology originated as an applied multidisciplinary science combining engineering and construction-related theory, and it later included economics, jurisprudence, and environmental study (Tolmachev 1999). The term engineering karstology was formally adopted in Russia in 1947 at the Molotov Karst Conference (Proceedings 1947). To the best of our knowledge, this term is not used outside Russia, but there are some very similar terms, such as applied karst geology (Beck 1993) or engineering geology of karst (Reuter and Tolmachev 1990). Similar to engineering karstology are the trends dealing with geotechnical aspects of construction in karst regions (Sowers 1996; Aderhold 2005).

Russia has nearly 70 years of experience quantitatively assessing hazards for the purpose of development on karst terranes. The main focus was on the karst collapse hazard in covered sulfate-carbonate karst at the depth of 20–80 m. The presence of subsurface karst features is an essential (though not the only) prerequisite for the development of this hazard. In practice, it is difficult and often impossible to locate voids and fissures and to identify their shape and dimensions between these depths. Despite this uncertainty, the karst collapse hazard must be taken into consideration by civil engineers during development. Consequently, Russian researchers, while developing methods of karst collapse hazard assessment, have attempted to both meet the needs of practical engineering and enhance the understanding of surficial karst development mechanisms (e.g., stochastic mechanism of sinkhole development and processes in the overburden). Such attempts can be seen in the evolution of karst hazard and risk assessment methods. However, other aspects of karst hazards exist, and depending on the natural and technogenic situation, some of these may become more important when considering particular economic tasks.

Analysis of karst hazard and risk assessment methods worldwide shows that researchers and engineers follow the same approaches. We assume that the Russian experience described here can be helpful for specialists in other countries. Some important developments in knowledge have only been discussed in Russian publications, which are not easily accessible to foreign researchers.

There exist numerous approaches to karst hazard assessment in Russia. We suggest that the method described below is the most efficient approach available. It presents a solution to the problems of risk assessment for building in karst areas and constitutes the basis of Russian national standards and is also the officially recognized methodology.

As a Russian case study, we will concentrate on work undertaken in that country, and although we recognize there are other hazards and approaches investigated elsewhere, these will not be covered in the chapter. The other aspects of karst hazard and risk assessment are discussed in different chapters of this text. These include:

• Technogenic impacts on karst hazard parameters

• Techniques of zoning of territories according to the level of karst hazard in various natural and technogenic conditions

• Mechanisms of sinkhole development

• Use of geosciences investigation techniques (geomorphological, structural, and lithological mapping, bedrock core drilling, geophysical methods, etc.)

In Russia, engineering karstology evolved mainly from traditional karstology. New research methods for karst study were developed; various forecast techniques for prediction of karst development were created to be incorporated into the construction design in karst regions and even a new specific terminology arose. Engineering karstology deals essentially with the problems of civil engineering in karst regions within the framework of an integral system that is “Karst Engineering” (Tolmachev et al. 1986; Tolmachev and Reuter 1990; Tolmachev and Leonenko 2005). The nature of karst development in Russia, with its subsurface and superficial effects, has been studied within this system. Research has mainly focused on covered karst in carbonate and sulfate rock. In the investigation of subsurface karst features, special attention is paid to the development of voids and deconsolidated areas in the overburden (Tolmachev et al. 1982; Khomenko 1986, 2003). During the investigation of superficial karst features, the emphasis is placed on sinkholes and the conditions of their development (formation mechanisms, spatial and timing stochastic characteristics).

Most Russian engineers and officials perceive general karst hazards and the karst collapse hazard as one and the same, and this simplification often leads to development-related problems on karst territories. The failure to appreciate the distinction between karst risk and karst hazard has often resulted in serious design and engineering mistakes. Nevertheless, it is necessary to recognize that for many areas of Russia with deep karst (over 20 m in depth), the most significant threat of damage to buildings and facilities with shallow foundations is posed by a sudden collapse of foundations. For this reason, most attention will be given to the problem of the collapse (sinkhole) hazard.

One of the crucial issues for construction in karst regions is karst risk assessment. The approach taken in assessment varies depending on the type of structures or facilities, their overall importance, degree of their impact on the environment, their size, and construction characteristics. Designers and contractors stress the importance of karst risk assessment for helping guide the development of structural, building, and operational characteristics of the construction. Their consideration of karst risk assessment is especially important when considering the potential negative impacts of karst development to local economies, societies, and the environment.

Engineering karstology assumes that the results obtained by research should be rendered to engineers through new building codes and specifications. Documentation of this kind first appeared in Russia in 1967, and since that time, a system of standardized requirements including codes of practice, guidelines, and recommendations have been developed. Some of these official documents are adopted throughout Russia while others are valid only for separate regions or departments (Tolmachev and Leonenko 2001). Examples of these documents are:

• Recommendations on Foundation Engineering on Karst Territories (1985)

• Recommendations on the Use of Engineering/Geological Information for Selection of Antikarst Protection Methods (1987)¹

• Basic Track Maintenance Instructions for Karst Hazardous Terranes (1997)

• The chapter, “Engineering Geological Site Investigations in Karst Terranes,” and the code of practice, “Engineering Geological Site Investigations for Construction” (2000)

• Technical regulation “Engineering, Design, Construction and Operation of Structures in Karst Terranes in Nizhny Novgorod Region” (2010)

We have been instrumental in the development of the above documents. The 2010 document was written in accordance with recent Federal Laws of the Russian Federation, such as “On Technical Regulation,” “Urban Planning Code of the Russian Federation,” “On Environmental Protection,” and “On Safety of Structures and Facilities,” all of which put forward a binding requirement to assess natural risk in order to assure construction does not exceed safe limits.

2 Types of Karst Hazard

Negative impacts of karst on economic activity and, above all, on construction work can be described in various ways which are related to specific karst hazards. Table 4.1 describes the types of karst hazard that may be reflected in decisions made in the course of economic development. As a rule, designers of buildings and facilities take into consideration only one type of karst hazard or a combination of two. However, when designing major structures that can cause significant hazard to the health and safety of the population, all of the risk factors outlined in Table 4.1 must be considered.

Table 4.1 Types of karst hazard

Karst hazard Type A and B always require a specific approach to the construction and operation of water supply and drainage systems in cities and towns (e.g., appropriate routing of pipelines, pipe material selection, water leakage control). As a general rule, failure to account for karst-suffusion processes in planning water withdrawals increases the frequency of karst development not only at the particular water removal site but also within adjacent areas (Khomenko 1986, 2003). Water leaks usually lead to local increases in karst hazard Type A and B (Figs. 4.1 and 4.2).

Fig. 4.1

Types and subtypes of karst danger 1 Source of pollution 2 Water-permeable soils 3 Low permeability soils 4 Karstified rock 5 Rock base 6 Karst-induced joints in the soil 7 Karst cavity 8 Friable soil area under a sinkhole 9 Increased infiltration area 10 Disintergrated soils in the rim of the subsidence mold 11Moving direction of underground water pollutants 12 Subsurface disintergrated area 13 Compressible soil

Fig. 4.2

Development of a karst-suffosion sinkhole induced by a heating main leakage in Dzerzhinsk (2009)

Hazard Type A, B, and C are especially important for determining the price of land. All things being equal, the price of land in a karst zone will inevitably be much lower compared to a nonkarst area, especially since the contractor will have to bear considerable additional expenses in order to reduce karst risks. This circumstance is especially important for developers of city planning projects.

Notions of karst hazard and karst risk are closely connected with the insurance of construction in karst territories. The need for insurance may arise for locations with the Type B hazard. Unfortunately, insurance of construction against karst risks is not used in Russia, even though the methodology for probabilistic assessment of karst hazard was proposed long ago. In part, this absence can be explained by general immaturity of insurance in Russia, as well as by a certain exotic character of karst issues to the national insurance companies. This situation is contrasted with the practice in karst areas of the USA (which has sinkhole insurance coverage) (Salomone 1984; Zisman 2005). The American experience should be used in Russia as much as possible, especially in terms of interaction between the participants of the insurance process in the following order: geologist, designer, karstologist, insurance agent, and customer. Introduction of insurance procedures will have economic impacts in development of karst regions and will obviously cause some new problems with concepts and methodology. It will be necessary to develop new terms or to correct some of the accepted terminology in order to establish legal precedents that are legally verifiable, clear and comprehensive for customers and experts from insurance companies.

In the process of construction of buildings and engineered facilities in karst terranes, a number of specific aspects of karst hazard of Types A, B, and C should be considered.

2.1 Karst Hazard Type A

When a Type A hazard is identified, one must consider the various pathways that pollution may take in entering the geological environment of covered karst. These are described as follows (Mamonova and Tolmachev 1997; Tolmachev et al. 2005):

• The increased rate of pollution of the geological environment is observed in locations of newly developed sinkholes, as well as old sinkholes, in the rims of the subsidence depression, and in the areas of active subsurface karst.

• Water pollutants may penetrate through karst joints to areas many kilometers away from the source of pollution.

• Pollution of underground water can be described as a pulse process dependent on the dynamics of subterranean and superficial karst development.

• Water pollutant penetration rates through karst joints are several times higher in comparison with the values observed in other water-bearing formations.

• Under certain circumstances, pollution traveling through solution pipes in karst terranes may result in a substantial increase of dissolution rate of karst rock.

• The net process may lead to reduction of the soil load-bearing capacity and, therefore, to conditions which facilitate formation of karst features.

In the siting of locations for landfills, the main criterion of Type A in Table 4.1 is to predict a volume of potential pollutant V _p (m³ per 100 years occurring in an area of 1 ha). This is the potential quantity of pollutant that may penetrate beneath the landfill through existing and newly formed karst features (Tolmachev et al. 2005). Depending on the values of V _p, karst areas can be classified according to their potential environmental vulnerability into a number of conventional subgroups using the units discussed below:

(1) (V _p  <  10); (2) (V _p  =  10–50); (3) (V _p  =  50–100); (4) (V _p  =  100–500); (5) (V _p  =  500–1,000); (6) (V _p  =  1,000–5,000); (7) (V _p  =  5,000–10,000); etc.

Values of V_p are usually estimated using the results of probability analysis of the features of the developing karst and the distribution of their predicted dimensions. For more details, see Tolmachev et al. (2005).

2.2 Karst Hazard Type B

For covered karst areas with Type B karst hazard, risk should be assessed by accounting for specific features and mechanisms that may occur during the life of the facility. For the majority of buildings and facilities, karst features can be grouped in decreasing order of potential risk: (1) soil or rock collapse, (2) local subsidence developed in the vicinity of the construction, (3) old sinkholes located close to the construction, (4) differential foundation settlements caused by karst processes, (5) slow subsidence of soil and (6) karst (karst-suffosion) induced slumps. This arrangement allows further subdivision of Type B karst hazard into subtypes (Fig. 4.1b).

Subtype B ₁ (collapse sinkholes) is characterized by the following factors:

• Temporally, collapses are usually immediate events, though occasionally, they are preceded by slumps, concentric fissures on the ground surface, etc.

• Collapse development process has a pronounced probabilistic character (in time and space, i.e., diameter, depth, and volume).

• Often, collapses occur on the same spot or in close vicinity to previous collapses.

• The area around a fresh collapse is characterized by considerably reduced soil load-bearing capacity and increased water permeability.

• The shape of a depression formed by a collapse of the ground surface does not stay the same and changes rather quickly (depending on the kind of soil) with the diameter growing and the depth decreasing, which eventually results in a conical appearance of the sinkhole.

In Russia, the following parameters of the prediction of sinkhole development are used for karst hazard assessment:

• Specific intensity (frequency) of sinkhole development (λ), related to a unit area (as 1 km² or 1 ha) per unit time (as 1 year or 1 century) or theoretical intensity of sinkhole development on the area occupied by construction during a given time period (e.g., predicted service life, pre-reconstruction period of operation).

• Average (d_c) and the largest (d_max) dimensions of sinkholes. In order to solve many practical design problems, empirical (histograms) and theoretical curves of sinkhole diameter distribution may be needed. It is necessary to consider that sinkhole diameter distribution for vast territories (with nonuniform conditions of collapse development) in most cases is described by the lognormal law. In small areas (e.g., construction sites) with practically homogeneous conditions affecting the dimensions of sinkholes, diameter distribution is close to normal (Gaussian distribution).

• Current percentage of the total area of a sinkhole for a given territory and potential vulnerability of this territory during a given period of time (e.g., for 100 years).

As a rule, the assessment of sinkhole development probability includes zoning of the territory based on specific intensity of sinkhole development λ and average sinkhole diameter d_c. For the purpose of zoning, Russian national building specifications recommend a classification with six categories of endangered territories according to the parameter λ, and four categories according to d_c. This classification promotes a much more systematized arrangement of engineering/geological research. However, nearly 40 years of experience revealed a number of weaknesses in use of these categories, especially with respect to their objectivity and applicability for design purposes (Tolmachev and Leonenko 2005; Tolmachev 2009). Recently, a more detailed system of differentiation of sinkhole danger categories was created (Tables 4.2 and 4.3). It has worked well in trial cases and was approved for other karst-endangered territories in Nizhny Novgorod region.

Table 4.2 Karst hazard categories according to the predicted specific intensity of sinkhole development (λ, the number of collapses on 1 ha per 100 years)

Table 4.3 Karst hazard categories according to predicted average diameter of a sinkhole (d _c, m)

The karst hazard resulting from local subsidence (Subtype B ₂ ) is characterized by the following features:

• Development of local subsidence of the ground surface (and under buildings or other construction) can take from several days to several months.

• Final diameters of local subsidence of the ground surface, as a rule, can extend to several decameters at comparatively small depths (about 1 or 2 m).

• In the zone of local subsidence, a significant horizontal shifting of the soil is observed.

• The rim of the local subsidence is characterized by low soil load-bearing capacity and high water permeability.

Hazard assessment of local subsidence for vast territories should be done together with the karst collapse hazard assessment. However, karst hazard assessment for construction sites should be done separately from karst collapse hazard assessment.

A karst hazard caused by an old sinkhole on construction (Subtype B ₃ ) is characterized as follows:

• The zone beneath the sinkhole and around it retains high probability of another collapse, a new local subsidence or a slump. Anthropogenic effects (due to dynamic and static loads, water leakage from pipelines, etc.) bring the probability value of new collapse very close to one.

• The zone in the immediate vicinity of the sinkhole has low soil load-bearing capacity and high water permeability.

Threat of differential foundation settlement (Subtype B ₄ ) is usually considered under the following conditions:

• Karstified rock with filled sinkholes and joints

• Shallow covered karst overlain by karstified rock of depression, vertical channels, layers of dolomitic lime, and other karst abnormalities

• Deep covered karst with buried karst sinkholes, deconsolidated areas, and other karst (karst-suffusion) deformities in the compressible burden

Karst hazard created by slow subsidence (Subtype B ₅ ) is characterized by the following features:

• Slow depression of the ground surface (several years or decades).

• Rate of subsidence is irregular in different parts of the depression and can vary from several millimeters to several centimeters per year. Revival and dampening periods can be observed.

• Shapes of subsidence depressions are irregular and their diameters can reach several hundred meters.

• On the rims of the subsidence depressions, there are areas of rock with deconsolidated surface layers which facilitate seepage of rain and industrial water into the soil, thereby increasing the probability of new sinkholes in these locations.

• In the subsidence zone, horizontal and vertical deformation can be found in the same area.

Design of construction in areas where karst subsidence is probable requires knowledge of the interdependence between the construction and its foundation with the help of methods that consider mechanisms of subsidence development, their predicted rates and duration. Such methods are common for mines. In this case, the most important design parameter is the subsidence depression slope (i, mm/m). Depending on this parameter, the total area of the subsidence depression can be subdivided into the following sections:

(1) i  <  5, (2) i  =  5–7, (3) i  =  7–10, (4) i  =  10–20, (5) i  >  20

Hazards related to karst (karst-suffosion) soil slumps (Subtype B ₆ ) can be characterized by the following features:

• Like collapses, slumps are formed instantly.

• Slump dimensions seldom exceed 1–2 m and their depth is up to 0.3 m.

• Most often, karst slumps occur after prolonged soaking of soil and due to dynamic and static loads imposed by construction.

• In some situations, karst slumps can be followed by collapses.

• Quantitative assessment of karst slump parameters is difficult and in most cases not necessary. From the practical point of view, designers just need to be aware of the probability of slump formation in the location in which they work. If slumps are the only type of predicted karst features, karst hazard will be determined as Category 1 in Table 4.2 (without the need for separate estimation of slump formation intensity).

• In the course of construction and operation of structures or facilities, it is extremely important to register the exact place and time of this type of depression, as it may be a serious symptom of new karst collapses or local subsidence.

In a karst region, when developers consider the most appropriate sites for large-scale construction, they need to know the results of preliminary zoning of the location according to the proportion of the total area of all karst features at the surface (α, %/km²). Locations can be classified according to α in the following way: (1) α  <  5%, (2) α  =  5–25%, (3) α  =  25–50%, (4) α  =  50–75%, (5) α  >  75% (Aderhold 2005).

2.3 Karst Hazard Type C

Type C can be subdivided into the following subtypes:

• Subtype C ₁ is created by the additional load from deep foundations that threaten the roofs of karst cavities. In the absence of anthropogenic impacts, such cavities are classified as stable. Serious problems usually arise as early as the stage of foundation building.

• Subtype C ₂ typically has subterranean karst deformations (voids, disintegrated areas, etc.) in the compressible overburden.

• Subtype C ₃ is characterized by increased karst water inflow toward underground facilities during construction or service life.

Subterranean karst features are considered potentially hazardous for any structure. These hazards can be determined through identification of probable deformation types and analysis of expected structural loads. Hazard assessment of the subsurface karst features identified by research should also be performed to account for their potential impact on development during the service life of the construction. Karst features in the overburden, especially in sand, demonstrate considerable dynamics. It is also necessary to perform special karstological monitoring with the use of geophysical methods.

3 Examples of Structural Damage to Construction in Karst Regions

In the European part of Russia, the proportion of territory where karst presents real danger for buildings and facilities is equal to a quarter of the total area. Karstified rock (predominantly, limestone, dolomite, and gypsum) is found here mainly at the depth of 20–80 m. Generally, it is overlain by clay and/or sandy soil which are often saturated with water. Presence of water makes karst suffosion highly probable. At the surface, karst manifests itself in the form of sinkholes, local subsidence, or slowly developing vast subsidence. Of the karst manifestations mentioned, the highest level of hazard is related to sinkholes due to abruptness of their occurrence.

Sinkholes and local subsidence often cause accidents with damage to residential and industrial buildings, water supply systems, pipelines, railways, and motorways (Figs. 4.3, 4.4, and 4.5). Large-scale accidents happened recently in a number of Russian cities (Dzerzhinsk, Nizhny Novgorod, Pavlovo, Moscow, Bereznyaky, Kungurr, Ufa, Kazan), on the Gorky and Sverdlovsk railways and on the main pipeline in the Perm region. Fortunately, there was no loss of life in any of the accidents.

Fig. 4.3

Collapse of a residential building in Nizhny Novgorod region (1959)

Fig. 4.4

Collapse of a building in the historical part of Kazan (1977)

Fig. 4.5

Sinkhole in the village of Rastrigino, Vladimir region (1972)

In 1992, a catastrophic karst sinkhole, more than 10 m deep and 32 m wide (Fig. 4.6), destroyed an industrial facility of a machine-building plant in Dzerzhinsk. It took only 20 min to demolish a 125 m long structure along a row of columns. Direct economic losses were equivalent to ∼$30 million, and there were indirect losses as the production shop did not function for approximately 2 months. The dramatic event was found to be a consequence of serious engineering and administrative errors made at various stages from selection of the construction site, research and construction work to the operation of the industrial plant. The building was designed as a frame on isolated foundations. When the plant was being designed in 1963–1964, the specialists involved in the project were under pressure from the administrative authorities who imposed very strict cost demands. The cost was mainly reduced at the expense of antikarst protection during construction.

Fig. 4.6

Collapse of an industrial building in Dzerzhinsk (1992)

In 1993, local karst subsidence occurred in the form of a sinkhole with a diameter of up to 20 m, threatening a chlorine warehouse for a water supply station in Nizhny Novgorod. The station building did not have any antikarst protection. Subsidence took only several days, during which the building was promptly disassembled to avoid its progressive destruction.

In 1993, a six-story civil building in Ufa was damaged to the point that it was uninhabitable and had to be demolished. The damage was caused by multiple local subsidences in the zone of buried karst sinkholes which had not been identified by the exploration at the project stage. Destructive deformation continued for 14 years after the building was completed in 1979, despite continuous attempts to prevent the collapse (jacking by sectional piles, securing of the foundation bed, etc.). The lessons learnt from this event are discussed in Mulyukov et al. (2006).

Sinkholes and local subsidence are highly hazardous for railways as they cause not only economic but other serious problems as well. Karst-induced events on the Gorky railway are good illustrative examples. In 1994, a freight train accident took place on a section of a single-way line, Arzamas–Krasny Uzel. The cause of the accident was a comparatively small 2.5 m karst sinkhole which developed under the train. Railway operation in that direction was stopped for several days. Some rail carriages with sulfuric acid were broken in the accident, and it caused local pollution. In 1995, on the 395th km of the two-way railway from Moscow to Nizhny Novgorod, not far from Dzerzhinsk station, a local karst-suffosion subsidence formed on the surface. Its diameter was 35 m, and although its center was 20 m away from the track, one of the lines sank 15 cm along a length of 25 m. As a result, train operation was interrupted on one track for 12 h, and on the other track, the speed limit of 15 km/h was instituted and remained unchanged for several months until the remedial work was completed. It is interesting to mention that two accidents caused by sinkholes occurred at the same location in 1943 and 1960.

In 2000, on a single track of Kazan-Yoshkar-Ola railway, a large local subsidence damaged more than 100 m of track. The rail track sank 1 m and shifted horizontally toward the center of the sinkhole by up to 0.5 m. The train operation in all directions was stopped and did not start for several days.

The above examples show the high vulnerability of the railway tracks in karst terranes, characterized by high probability of sinkholes. Typically, collapses take place simultaneously with train motion. As antikarst protection during construction is not applicable for rail tracks (unlike structures with foundations), and grouting of karst cavities is not efficient enough, the main safety measures taken are maintenance-related ones (special karst monitoring of the track, arrangement of alarm, and restrictive signalization). New, high-speed traffic programs need to deal with this aspect of safety. In certain cases, karst hazards may present a major obstacle for implementation of the program.

Karst and karst-suffosion processes are extremely sensitive to various anthropogenic effects from construction and operation of industrial plants and facilities which can cause karst deformations. The following examples illustrate this statement.

In 1996, on the property of a chemical plant in Dzerzhinsk, a karst sinkhole appeared with the diameter of 9 m and the depth of 3.5 m. It caused serious damage to an underground water pipeline and brought the operation of some workshops to a halt for several days. The direct cause of the event was leakage from the pipeline which provoked intensification of the karst-suffosion process. In 1998, a 16 m wide and 8 m deep karst sinkhole developed in the center of Pavlovo (a town in Nizhny Novgorod region) and a sewage collector was damaged. The reason for the collapse was long-term leakage of aggressive water penetrating into the soil and karstified rock. Another disaster in 1999 with destruction of a main pipeline section in the karst area of Perm Krai happened because trench work explosions had been used for laying pipes. These explosions greatly increased sinkhole development in the shallow karstified gypsum (Kutepov et al. 2004).

Accidents related to karst development during construction work are often caused by a combination of errors of various types. Nevertheless, the results of studies (Tolmachev 2005; Leonenko and Tolmachev 2006; Mulyukov et al. 2006; Sorochan and Tolmachev 2007) showed the most significant reasons for these events. These are arranged below in ascending percentage of the total number of accidents:

• Unprofessional interference of contractors or administrative bodies in research and engineering activity (10%)

• Inappropriate karstological monitoring during operation of the construction (10%)

• Engineering errors (15%)

• Omission of specialized (karstological) research (20%)

• Exploration errors, including lack of knowledge of karst processes (20%)

• Inadequate interaction between researchers and designers (25%). This item was identified outside Russia and in one of the publications described by Bachus (2005)

In the Nizhny Novgorod region, the highest karst risk exists in the city of Dzerzhinsk, which is why in 1952 the Academy of Sciences of the Soviet Union founded a karst station there (at present joint stock company, Antikarst and Shore Protection). Since that time, every karst occurrence has been registered on a regular basis along with data on the damage to construction. The table below presents the distribution of events and damage to construction (N) caused by 72 karst deformations in the territory of Dzerzhinsk between 1953 and 2006 (Table 4.4).

Table 4.4 Distribution of karst deformations in dzerzhinsk district causing damage to construction

On average, this territory has 1.3 sinkholes annually causing damage to construction. Their total number (72) includes all known instances of damage to buildings, roads, railways, pipelines, etc. It also includes 14 disasters with complete destruction of various industrial sites, which gives the frequency of one disaster every 4 years. The majority of instances of complete destruction (11 out of 14) were the consequences of a sudden karst sinkhole. The distribution of these cases of destruction is close to the law of stochastic events (Poisson law), and the distribution parameter is equal to 0.26. As it was shown earlier (Tolmachev 1968), distribution of independent karst collapses is also described by the Poisson law. For the Dzerzhinsk karst district, the distribution parameter reaches the value of 4.5.

4 Stochastic Laws for Sinkhole Development

4.1 Probabilistic and Stochastic Properties of Sinkhole Diameters

Sinkhole diameter is one parameter that predetermines the occurrence of a karst hazard, so prediction of probable diameters is one of the most important tasks of the engineering exploration in karst territories. There are a number of approaches to prediction which use various models and methods of forecasting. Theoretical and estimation methods incorporating deterministic geomechanical models are rarely used and only in comparatively simple engineering and geological conditions. In our opinion, forecasting of this kind only gives a rough approximation and other techniques should also be used. The probabilistic statistical method of forecasting based on the statistical analysis of the sizes of sinkholes is the most objectively and widely used (Methodology 1966; Recommendations 1987; Tolmachev et al. 1986). This method, used to predict a sinkhole diameter d, consists of constructing a distribution curve and the estimation of the statistical parameters necessary for further definition of karst failure parameters: arithmetical mean value d _c, standard deviation S, and maximal diameter d _max.

The minimum number of karst sinkholes n _d for constructing a distribution curve can be defined by the formula:

$$ {n}_{\text{d}}={\left({t}_{\text{d}}\right)}^{2}·{K}_{\text{var}}/{({e}_{\text{d}})}^{2},$$

(4.1)

where K _var – variation ratio, ε _d – admissible error or acceptable relative deviation from arithmetical mean of the limited retrieval from mathematical expectation with a given probability P _t, t _d – normalization factor characterizing probability P _t.

For engineering and geological tasks, it can be assumed that ε _d  =  0.1 and P _t  =  0.95 (t _d  =  2), and then

$$ {K}_{\text{var}}=S/{d}_{\text{c}}$$

(4.2)

Value of K _var can be preliminarily identified by the in situ measurement of the sinkhole diameter. If the number of sinkholes obtained by the formula exceeds the actual number of sinkholes in a certain area, the conclusion is that there was not a large enough representative sample to provide accurate results within error limits. Consequently, results can be improved by simply increasing the number of karst sinkholes included in the study, provided these samples belong to the same general array. However, it is important to realize that increasing the sample size will require a larger area, potentially leading to averaging of nonuniform sites (from the point of view of karst sinkholes dimensions). As a result, the accuracy of the results will be reduced.

To increase the reliability of sinkhole diameter assessment, it is necessary to find theoretical distribution curves corresponding to empirical histograms of sinkhole diameters. Knowledge of the distribution law for karst sinkhole diameters allows us to obtain valid initial data for the structural analysis of karst-proof construction and for the assessment of their efficiency. Figure 4.7 shows one such example of efficiency testing, where the span length is equal to the sinkhole diameter d _d  =  12 m. Reliability of the construction obtained with the empirical and theoretical distribution curves is shown to be P _d  =  0.73 and P _d  =  0.5, respectively. Thus, in this example, the efficiency of the designed construction determined with the use of the histogram is significantly overestimated.

Fig. 4.7

The distribution curve of sinkhole diameters 1 empirical; 2 theoretical

In most cases, the distribution of sinkhole diameter (especially for large areas where natural factors influence sinkhole dimensions) is described by the lognormal law (Fig.4.8). However, for territories that are homogeneous, in which factors are influencing karst sinkhole diameters, the law of diameter distribution tends toward a normal distribution, which appears to be the case for many small karst areas (Tolmachev 1980).

Fig. 4.8

Lognormal distribution curve of sinkhole diameters

In the absence of reliable statistical data concerning sinkhole diameters on the site, construction of a distribution curve will be possible if the distribution parameters d _c and $S=\left({d}_{\mathrm{max}}-{d}_{\text{c}}\right)/3$ are obtained through deterministic models. Here d _c is estimated for average values of the initial data and d _max for the values of the largest sinkhole diameters.

4.2 Space and Time Laws for Karst Sinkhole Development

If in a territory with the area A during time t, the number of new sinkholes is n and the average specific frequency (the intensity ratio, λ) of sinkhole development is equal to:

$$ \lambda =n/A·t$$

(4.3)

The parameter λ will precisely describe the actual intensity of sinkhole ­development for large areas when detailed information on the number and the dates of sinkholes is available. In the majority of cases, time span t is comparatively short; therefore, the value n should be increased at the cost of increasing A. For separate locations, the objective estimation of the parameter λ by field observation data is possible only in cases of rather intensive sinkhole development. It is frequently necessary to know the value of λ for a small area; however, often it has only been estimated for a much larger region. In this case, λ can be determined using probabilistic and statistical calculation (correlation and dispersive analyses, the theory of qualitative attributes, etc.) methods. These methods are based on the analysis of the engineering/geological situation and the use of maps of natural factors influencing the intensity of karst development. For a detailed description of these, see Tolmachev (1980, 1986).

Presence of an underground karst void is an elemental component of sinkhole development. However, some of the karst voids may never impact the surface throughout a structure’s lifespan. For instance, from the results of drilling in Dzerzhinsk karst area, it was found that more than 1,000 karst voids in carbonate and sulfate rock located between 30 and 70 m below the surface; yet, none manifested itself as a sinkhole. Elsewhere in this region, ∼4–5 collapses are documented each year. Consequently, there is certain probability that a karst void will manifest itself on the ground surface as a sinkhole (in the engineering sense of time).

Let us consider an area A, where during a given time interval (e.g., one year) a certain number of karst sinkholes appear, and let us divide it into N arbitrary sites with A/N. The probability of karst sinkhole development occurring on any site chosen at random can be presented as:

$$ {P}_{\text{s}}={P}_{1}·{P}_{2}$$

(4.4)

where P ₁ – the probability of a karst void existing on the area A/N, P ₂ – the probability of the subsequent collapse of the karst void within a given time span. If we increase the number of arbitrary sites and, therefore, reduce their area, probability P ₁ will also get lower. Finally, at N  →  ∞ P ₁  →  0 and P _s  →  0. We will consider only independent sinkholes, i.e., the situation when the appearance of a sinkhole in one location does not change the probability of a similar event in another location, and karst voids collapse one by one.

The theory of probability requires that the following conditions are satisfied: (1) on the area A in time t, certain points be distributed in a statistically regular way with the average density λ _A; (2) the points occur independently; and (3) points appear one by one, not in pairs, or threes, etc., at N  →  ∞ and P _s  →  0

$$ lim\text{\hspace{0.05em}}N{P}_{\text{s}}={\lambda }_{\text{A}},$$

(4.5)

and the probability of X events for the given time interval is equal to

$$ {P}_{\text{SN}}\left(\text{X}\right)=\mathrm{exp}(-{\lambda }_{\text{A}})·{\lambda }_{\text{A}}{}^{\text{X}}/\text{ X}!$$

(4.6)

The distribution law described by this formula is known as the law of rare events or the Poisson law. This statement appears to be applicable for many karst areas (Tolmachev 1968, 1980). American karst scientists Lilly (1979), Raghu and Tiedeman (1984) also claimed that sinkhole development distribution is close to the Poisson law and proved this important statement from the point of view of spatial laws of sinkhole development.

According to a valuable property of this law, mathematical expectation MX and dispersion σ ² are equal to the distribution parameter λ _A, i.e.,

$$ MX={\sigma }^{2}={\lambda }_{\text{A}},$$

(4.7)

or, for a separate sample, they are approximately equal to λ _A, i.e.,

$$ {X}_{\text{c}}\approx S\approx {\lambda }_{\text{A}},$$

(4.8)

where X _c is the arithmetical mean and S is standard deviation.

Consequently, we can assume that the distribution of independent karst sinkholes in a region over a particular time interval is regulated by the Poisson law. The distribution parameter λ _A is the mathematical expectation (arithmetical mean) of the number of independent karst sinkholes in the investigated territory that develop during a given time interval.

If we mark value X _i on the X-axis and the corresponding number of years on the Y-axis, we will get an empirical distribution curve for karst sinkholes for the given area (Fig. 4.9). It shows alignment with the Poisson distribution curve and satisfies assumptions of the Pearson’s chi-square test.

Fig. 4.9

The example of distribution of independent sinkholes development in karstified area of Dzerzhinsk region 1 distribution range; 2 theoretical Poisson`s distribution curve

Known values of λ for the investigated territory with area A can give us the probability of the situation when not a single collapse will occur within a given time t:

$${P}_{0}=\mathrm{exp}\text(-{\lambda }_{\text{A}}).$$

(4.9)

Probability P _1−n of at least one karst collapse occurrence equals

$$ {P}_{1-\text{n}}=1-{P}_{0}.$$

(4.10)

The probability that during a certain time period the area A will be affected by karst sinkholes with the diameters exceeding the estimated sinkhole diameter d is found by

$$ {P}_{\text{A}}=1-\mathrm{exp}[-\lambda ·A·t·\left(1-{P}_{\text{d}}\right)]$$

(4.11)

where, P _d is the probability that the diameter of an appearing sinkhole will not exceed the value d (defined by an integrated diameter distribution curve).

4.3 Methods of Assessment of Karst Territories Using the Criteria of the Hazard of Karst Collapse

There exist several approaches to determine the level of hazard of karst collapse in karst territories. Analysis of separate aspects of these approaches can be found in some publications (Tolmachev et al. 1986; Tolmachev 2009; Tolmachev and Leonenko 2001). From all the known approaches, separate qualitative and quantitative approaches have been most widely used during the development of karst regions.

The qualitative approach is based on the analysis of the karst environment and the natural factors contributing to void collapse. Standard procedure dictates that the investigated territory is divided into two or three areas (or categories) with different qualitatively described karst hazard levels, e.g., “dangerous area, safe area” or “dangerous area, potentially dangerous area, safe area.” While these qualitative characteristics actually reflect comparative hazard, they are often perceived as an absolute definition of karst danger. Their misuse may unreasonably disturb local residents and give the media cause for sensational coverage resulting in contentious public hearings. A preferable situation would be the introduction of neutral description of the land site categories as is done in Germany: Land Niedersachsen now identifies eight digital categories 0, 1,…,7 (Buechner 1991), while Land Hessen identifies eleven categories 1, 2,…,11 (Aderhold 2005). We feel this approach becomes inappropriate when the range of categories widens.

In Russia, a three-stage classification scheme for land areas with respect to their karst hazard was first introduced over 100 years ago and is still often used in spite of recent achievements in karst engineering geology, including a deeper understanding of collapse mechanisms, use of probabilistic methodology for prediction of collapses, GIS-based technologies, and so forth. For the Moscow urban karst territory, this approach was officially adopted some 25 years ago. However, this classification task has not been completed because of insufficient coordination between geological engineers and designers, civil engineers, economists, land-use planners, insurance specialists, and ecologists.

A two-step qualitative classification scheme may be used for general evaluation of vast karst-prone territories in the process of large-scale administrative planning (within the bounds of a whole country or a large region) as has been demonstrated in multiple cases in Russia (Shoigu 2005).

The quantitative approach is to differentiate karst territories by the karst collapse hazard has been known for about 70 years in Russia, but it was not widely used until the Recommendations (1967) were published. Stability categories in karst terranes were supposed to be assigned depending on predicted average frequency (intensity) of karst sinkhole development in a unit area (1 km²) per a unit time (1 year). In accordance with the range of λ values, territories were subdivided into six stability categories: (1) λ  >  1(very unstable), (2) λ  =  0.1−1 (unstable), (3) λ  =  0.05−0.1 (insufficiently stable), (4) λ  =  0.01−0.05 (slightly unstable), (5) λ  <  0.01 (relatively stable), and (6) λ  =  0 (stable). In view of the above discussion, too many categories would lower the utility and value of the classification (Tolmachev and Leonenko 2001).

Intensity ratio of karst sinkhole development is an important parameter reflecting the probability of collapses. However, the intensity ratio alone (without predicted sinkhole dimensions, particularly diameters) does not fully characterize the karst ­hazard for constructions. Civil engineers were dissatisfied with this method of karst collapse probability assessment. That was why Methodological Recommendations of 1986 presented a new classification scheme with four classes based on sinkhole diameter d: (1) d  =  30–20 m, (2) d  =  20–10 m, (3) d  =  10–3 m, (4) d  =  3–0.5 m. However, this approach failed to consider the intensity of karst sinkhole development with time.

These points of concern were corrected by the building specifications “Engineering Exploration for Construction” developed in 1987. This document and the more recent “Code of Practice 11-105-97,” which is now in force, identify the stability categories of karst territories using two predictable parameters: intensity of sinkhole development λ (1–6, no qualitative characteristics added) and average sinkhole diameter d _c: (a)  >  20 m, (b) 10-20 m, (c) 3–-0 m, (d)  <  3 m. Through this approach, engineering exploration became more manageable and focused on the technical aspects. Nevertheless, the practical application of this method over a protracted period revealed further weaknesses:

• 1. The term “stability of the territory” is not a correct engineering term. Originally, it was adopted from the geographical study of karst. In our opinion, it would be more reasonable to use the term “karst collapse hazard” similar to “landslide hazard” and “seismic hazard.” Karst collapse hazard could have a numerical designation in the ascending order (depending on both the intensity of sinkhole development and the average sinkhole diameter).

• 2. The unit which measures the specific ratio of sinkhole development intensity λ(the number of sinkholes on 1 km² per a year) seems difficult for civil engineers to perceive as its origin was again geographical. It would be desirable to modify the unit measure in spatial units more applicable to civil engineering needs. For example, we can use 1 ha (0.01 km²) as a unit area, which covers most construction and the unit time period of 100 years, which corresponds to the expected life of construction. Interaction with designers shows that the resulting unit of measurement is now better understood by engineers. It should be noted that the numeric value of λ remains the same, even with the new unit measure.

Differentiating karst hazards is important for solving various practical and economic problems (Tolmachev et al. 1986). For instance, it provides data for antikarst protection planning, defines the cost of protecting properties from the negative impacts of karst development, assesses the risk of damage to construction in case of karst sinkhole development, and identifies optimal conditions for insurance of construction against karst-induced risk. Thus, the probability of damage to a property with the area of 1 ha during the time span of 100 years can be estimated by the formula:

$$ {P}_{\text{r}}=1-\mathrm{exp}(-{\lambda }_{\text{d}})$$

(4.12)

Here λ _d (predicted value of the intensity ratio of sinkhole development) is obtained using the average and maximal sinkhole diameter. It reflects the probability of karst-induced damage to a unit area (1 ha), including the situations when the sinkhole center lies outside the proposed construction site. Therefore, for the purpose of selection of a potential construction site and comprehensive city planning, it is recommended to use only the categories presented in Table 4.2 for λ  =  λ _d (Tolmachev 2009).

5 Karst Risk Assessment

Karst risk can be understood as the probability of economic, social, and environmental damage, which may be caused by karst collapses, to a territory over time. Using various methods of assessing risk allows for the comparison of construction sites at the selection stage by the value of predicted damage to the structure being designed, as well as antikarst protection planning at the construction and maintenance stages. Damage can also include loss of life and pollution of the environment.

In case of economic damage, karst risk is assessed in the following way:

$$ {R}_{\text{e}}={P}_{\text{r}}D$$

(4.13)

where P _r is the probability of sinkhole development on an area of 1 ha during 100 years (Formula 12) and D is the economic damage caused by deformation or complete destruction of a building as well as costs for remedial work, technological losses, residents resettlement costs among others.

Estimation of D is a difficult economic task, and it does not need to be calculated exactly for every type of construction. On the contrary, large-scale projects, such as new residential areas of the cities, important industrial plants, nuclear power stations, and so forth, are likely to require knowledge of predicted D values. It is even more difficult to define monetary costs associated with social and environmental damage. In practice, the Russian Scientific Society for Risk Analysis suggested in “The Declaration on Allowable Risk Limits” to identify general types of negative karst impacts for various scenarios based on comparative verbal characterization. Consequently, Table 4.5 takes that recommendation and defines allowable risk levels for various types of damage in karst terranes, by showing the value of specific allowable karst risk for a 1 ha economically developed area during 100 years (R _n).

Table 4.5 Allowable karst risk level R_n in different scenarios of negative impacts of karst on future construction and facilities (on 1 ha during 100 years)

For practical purposes, each of these three classes of damage is further divided into the following types:

5.1 Economic Damage

• I. Small scale (up to 10 million rubles)

• II. Medium scale (from 10 to 100 million rubles)

• III. Large scale (from 100 million to 1 billion rubles)

5.2 Environmental Damage

• 1. Improbable pollution

• 2. Probable local pollution

• 3. Probable pollution of large areas

5.3 Social Damage

• a. No threat to human life

• b. Threat to life of a small group of people (up to ten people)

• c. Threat to life of a large group of people (up to 100 people)

Comparison between the values of allowable risk R _n and the values of probability P _r can give us the notion of relative risk level for a certain site of a particular territory and allow appropriate antikarst protection measures to be undertaken. The relative risk level is realistically described by the following expression:

$$ LR={P}_{\text{r}}/{R}_{\text{n}}$$

(4.14)

Antikarst protection activity of an appropriate type helps reduce P _r and/or increase R _n.

Consider the following example. Designers came to a conclusion that it is necessary to build karst-protected foundations for any construction placed on a given site. Such a preventive measure will exclude economic damage in future, as well as environmental and social damage. Let us assume that prior to the use of antikarst foundation design features, negative impacts of karst were assessed as (II-2-a) in the above table, which corresponds to R _n1  =  0.01. It was demonstrated that karst-protected foundation corresponds to the predicted scenario of (I-1-a), where R _n2  =  0.1. Let us also assume that the specific risk (probability) of karst feature occurrence on the construction site became P _r1  =  0.2, and the risk of unacceptable damage to the construction with karst-proof foundations is lowered by 70%, i.e., ${P}_{\text{r2}}=0.2·0.7=0.14$. Thus, relative risk values prior to and following the introduction of antikarst protection can be expressed as $L{R}_{1}=0.2/0.01=20$ and $L{R}_{2}=0.14/0.1=1.4$, correspondingly, i.e., LR ₁ values became 14 times lower. Reduction of the risk P _r2  =  0.14 below the acceptable level R _n2  =  0.1 is now possible due to the maintenance type of antikarst protection activity, including specialized karstological monitoring, raised awareness for construction personnel and other measures. In such cases, the residual risk value P _r0 may be decreased to a level below, which is allowable (P _r0  ≤  R _n2), i.e., the relative specific risk level has now become LR ₀  <  1.

The above approach encourages the combination of antikarst protection measures. When dealing with designers, investors, developers, and especially administrative authorities, there is a need to render the specificity of the approach in a comprehensible way, and for this reason, relative karst risk values for typical buildings and facilities can be subdivided into several classes. Table 4.6 shows an example.

Table 4.6 Karst collapse risk land adequate antikarst protection measures

6 Conclusions

The problem of building on karst areas is mainly associated with karst hazard and karst risk assessment. These two notions are interrelated. In real life, in engineering practice and in publications, they are erroneously used as synonyms. What they have in common is the methodology of probabilistic assessment of karst-related events. However, karst hazard assessment involves probability of karst features development (on a given area during a given period of time) which can bring damage to structures, whereas karst risk assessment deals with probability of any negative impacts from exposure (economic, social, and environmental). Differences between these two notions become evident when the karst hazard is realized by sinkholes developing on the ground surface. In addition, karst hazard assessment is usually performed by geological engineers experienced in applied karstology (engineering karstology), but karst risk assessment is performed by a multidisciplinary team (investors, geologists, civil engineers, economists, building maintenance managers, insurance agents, ecologists, etc.). Quantitative karst risk assessment is only meaningful if we have defined safe limits of karst risk. This gives us grounds for further planning of antikarst protection activities during both facilities construction and operation, for evaluating residual risk and defining protection parameters to achieve allowable risk levels.

Involvement in the karst risk assessment process can fulfill our notion of sustainable development of terranes adopted by the UNO in 1987. This concept is declared in the current legislation of the Russian Federation, although our interaction with local authorities, Russian and foreign investors show that they neglect laws in order to reduce costs. To remedy the situation, we have formulated principles of sustainable development on karst terranes (Sorochan et al. 2010) and included them into the regulations for Nizhny Novgorod region as a product of the karst risk assessment methodology.