An analytical study of the hazards of geological problems in engineering geological investigation

By a regionalized variable we mean a random field with three rectangular coordinates (Xu,Xv,Xw) of a spatial point X as independent variables Z(Xu,Xv,Xw)=Z(X) . When an observation is made of it, a sample of it is obtained Z(X), which is an ordinary ternary real-valued function or spatial point function. The duality of the regionalized variable is manifested by viewing it as a random field (dependent on the coordinates (Xu,Xv,Xw) ) before the observation, and as a spatial point function (i.e., with a specific value at a specific coordinate) after the observation.

G. Matron defines a regionalized variable as: a real function with a numerical value in space which takes a definite value at each point in space, i.e., the value of the function changes when moving from one point to the next. From a geological point of view, regionalized variables have the following properties: 1)

Spatial limitation: that is, it is limited to a specific space (e.g., within a certain geological unit), which is called the geometrical domain of regionalization, and the regionalized variable is defined in terms of geometrical support.

In geostatistical research, the variation function is used to represent the spatial structure of the regionalized variables within the statistical range, and when calculating the variation function, it is necessary to have a number of samples of the pair of regionalized variables Z(x) and Z(x + h), and in practice (especially in geology and mining) there is only one pair of such samples, i.e., only one pair of data can be obtained from the points x and x + h (because it is not possible to obtain a second sample from precisely the same point), i.e., there is only one pair of samples. In other words, the values of the regionalization variables are unique and cannot be repeated. To overcome this difficulty, the following smooth and implicit assumptions are proposed. 1)

Smooth assumption

Let there be a random function Z whose spatial distribution law does not change by translation, i.e., if for any vector h; the relation: (1)G(z1,z2,…,x1,x2,…)=G(z1,z2,…,x1+h,x2+h,…)

When holds, then this random function Z is a smooth random function, exactly, two k-dimensional vectors of random variables {Z(x1,x2,…,xk)} and {Z(x1+h,x2+h,…,xk+h)} have the same law of distribution, no matter how large the displacement vector h is. In layman’s terms, the correlation between Z(x) and Z(x + h) within a uniform statistical band does not depend on their particular location within the band. This smoothness assumption requires at least that the moments of all orders of Z(x) exist and are smooth, which is difficult to fulfill in practice. In linear geostatistical studies, it is sufficient to assume that its 1st and 2nd order moments exist and are smooth, hence the second order smooth or weakly smooth assumption.

A regionalized variable is said to satisfy second-order smoothness when it satisfies the following two conditions: (1)

The expectation of the regionalized variable Z(X) exists and is equal to a constant throughout the study area: (2)E[Z(x)]=m∀c

When h = 0, the above equation becomes: (4)Var[Z(x)]=C(0)∀x

That is, it has finite prior variance.

A smooth covariance means that the variance and variance functions are smooth. (5)C(h)=C(0)−γ(h) 2)

Implications assumption

In practice, sometimes the covariance function does not exist, and thus there is no finite a priori variance, that is, it can not satisfy the second-order smooth assumption mentioned above, for example, some natural phenomena and stochastic functions, which are infinitely discrete, that is, there is no covariance and no a priori variance but there is a variance function, in this case, we can relax the conditions, such as only considering the increment of grade without considering the grade itself, which is the basic idea of the assumption of entailment. A regionalized variable Z(x) is said to satisfy the implication assumption when the increment Z(x) − Z(x + h) of the regionalized variable satisfies the following two conditions: (1)

The mathematical expectation of the increment Z(x) − Z(x + h) of the regionalization variable Z(x) is 0 throughout the study area, i.e. (6)E[Z(x)−Z(x+h)]=0,∀x,∀h

That is, the variance of the regionalized variable Z(x) is required to exist and be smooth.

The implication assumption can be understood as follows: the increment Z(x) − Z(x + h) of the random function Z(x) depends only on the vector h (mode and direction) that separates them and not on the specific location x, such that each pair of data Z(x), Z(x + h) separated by the vector h can be viewed as a sample of a different value of the pair of random variables {Z(x1),Z(x2)} , and the estimator γ^*(h) of the variance function γ(h) is: (8)γ˙(h)=12N(h)∑i=1N(h)[Z(xi)−Z(xi+h)]2

where N(h) is the number of data pairs partitioned by h.

A random function is said to obey the quasi-smooth (or quasi-implicit) assumption if it is smooth (or implicit) only in a neighborhood of finite size (e.g., a range with a radius of a. The quasi-smooth or quasi-implicit assumption is a compromise that takes into account both the scale of the similarity of a given phenomenon and how much data is valid. In practice, smoothness can be obtained by narrowing the range of the quasi-smooth band b, while the structural function (covariance or variance function) can only be used for a limited distance |h|≤b , for example, the limit b is the diameter of the estimated neighborhood, or it can be the range of a homogeneous band, and the regionalized variables Z(x) and Z(x + h) can not be considered to belong to the same homogeneous band when |h|>b . In this case the structural function C(h) or γ(h) is only locally smooth, so, we call second-order smoothness restricted to the range of |h|≤b quasi-smooth, and implicitness restricted to the range of |h|≤b quasi-implicit. We can use this idea to identify appropriately sized moving neighborhoods in which the mathematical expectation and covariance (or variance function) of the random function are smooth and in which there is enough valid data to make statistical inferences. Clearly, the smooth or embedded assumption can be understood as a relative concept.

Groundwater samples were taken from boreholes at three locations in the project area: point A, point B and point C. The samples were analyzed in accordance with the relevant investigation standards. The corrosivity of the water samples obtained from the analysis according to the relevant investigation standards is shown in Table 1. From Table 1, it is concluded that the concrete structure is moderately corroded by surface water and groundwater, the steel structure is weakly corroded by surface water and groundwater, and the reinforcing bars in the concrete will not be corroded by both.

Visual resistivity tests were carried out on the transmission pipeline laying lines as shown in Table 2.

From Table 2, the pipeline laying line on the soil on the steel structure has a slightly ~ strong corrosive, so in the construction of the project should be the implementation of anti-corrosion measures for water pipelines.

In this paper, through the investigation, a total of five bad geologic bodies, numbered 1~5, were found within the survey area, and the location and burial depth of each bad geologic body on the survey line are shown in Table 3.

As can be seen from Table 3, No.1 anomaly is inferred to be a jointed fissure development area.

Anomaly No.2 is inferred to be an area of nodal fissure and dissolution development, dominated by nodal fissure development, and there is dissolution development phenomenon near the L4 line, and there may be dissolution holes in the underlying rock layer.

Anomaly No.3 is inferred to be an area of nodal fissure and dissolution development, dominated by nodal fissure development, and there may be cavities in the underlying rock layer near the L5 line.

Anomaly No. 4 is inferred to be an area of jointed fissure and dissolution development, mainly characterized by jointed fissure development, and there may be cavities in the underlying rock layer in individual areas within the scope of the anomaly.

Anomaly No.5 is inferred to be an area of nodal fissure and dissolution development, dominated by nodal fissure development, with dissolution development phenomenon near line L11, and cavities exist in the underlying rock layer, which have been exposed on the surface, and the size of the development of the cavities is inferred to be about 6.2m in the north-south direction, 3.1m in the east-west direction, and the depth of the cavities is about 8.2m, and the development of dissolution phenomenon is inferred to exist near line L8, and there are probably cavities in the underlying rock layer.

It can be seen that the adverse geology developed in the site is karst, where groundwater interacts with dissolvable rocks, leading to rock dissolution.

In order to find out the water permeability of various types of rock bodies in the water transmission tunnel of this water supply project, water pressure and water injection tests were carried out near the depth of the tunnel for different stratigraphic lithologies during the preliminary stage of investigation, except for the shallow depth near the inlet, where the lithology is strongly weathered rock, and the rest of the tunnel body is mostly weakly weathered rock, and locally, slightly weathered rock. Table 4 displays the water permeability statistics for the rock near the cave body.

According to Table 4, within the range of 5 times the diameter of the cave body and the roof, the strongly weathered bedrock is mostly moderately permeable, and locally may be strongly permeable; the weakly weathered bedrock is divided into basalt and chert, among which, the weakly weathered basalt is generally slightly-weakly permeable, while the chert is generally very strongly permeable, and the individual segments with better integrity are slightly-weakly permeable, but it is unrepresentative.

In water conservation and hydropower projects, the permeability of rock bodies is generally expressed by the result of water pressure tests, which is called rock body permeability (q), which is the unit of Lu Rong (Lu). 1Lu means that the flow rate of water pressed into the rock body is 1.0L/s for 1m of rock body under the pressure of 1MPa.

The permeability characteristics of the rock body in accordance with its 2 × 4 × 3 = 24 categories, in order to further analyze the permeability of the rock body, this paper according to a basin 25 water conservancy and hydropower projects of 4561 groups of rock body of the results of the water pressure test data, statistics to get the results of the permeability of the different categories of rock body as shown in Table 5 and Table 6.

The statistical results in Table 5 and Table 6 show that: 1)

The permeability of similar rock bodies containing soluble rock fractions is greater than that of rock bodies without soluble salt fractions, which is due to the karst-like action of the anastase-containing rock bodies.

The relationship between water permeability (q) and lithology and weathering state of different rock bodies is shown in Figure 5.

Figure 5.

Different permeability, lithology and weathering state of rock mass

From the figure, it can be seen that the fresh rock bodies are weakly permeable rock bodies with permeability less than 5Lu except for sandstone and sandstone-mudstone interbedded with soluble rock with permeability greater than 5Lu; while the strongly weathered and weakly weathered rock bodies, whether it is a class a or b, have permeability ranging from 20 to 80Lu, which is moderately permeable rock bodies.

It can be concluded that near-surface weathered rock bodies are generally moderately permeable and fresh rock bodies are generally weakly permeable, and the permeability characteristics of rock bodies have a “shell-core binary” structure from the weathered rock bodies within the weathered crust near the surface to the fresh rock bodies underneath them. The weathered rock mass is a permeable “shell”, and the fresh rock mass is a relatively impermeable “core”, this structure is determined by the geological process formed by the permeable zone of the alluvial rock mass, in the investigation and design of rock mass leakage and seepage prevention, as long as the permeability characteristics of the permeable “shell” and the upper boundary of the relatively impervious “core” can be analyzed and calculated accordingly and the anti-seepage design can be carried out.