interpretation of the behaviour of a system building object - difficult subsoil in modern numerical...

Proceedings of the 11th International Conference on New Trends in Statics and Dynamics of Buildings

October 3-4, 2013 Bratislava, Slovakia Faculty of Civil Engineering STU Bratislava

Slovak Society of Mechanics SAS

INTERPRETATION OF THE BEHAVIOUR OF A SYSTEM BUILDING OBJECT - DIFFICULT SUBSOIL

IN MODERN NUMERICAL MODELING

Jan Fedorowicz1 and Leszek Słowik2

Abstract As a result of mining we can observe deformations of the layer of subsoil which interacts with the building structure. Precisely, there are observed deformations of the ground surface. Observations in situ (i.e. surveying and recorded damage as a result of non-uniform deformation of the structure), however, indicate that we are dealing with the change of state of the ground that is deforming; usually interpreted directly as a change in stiffness resulting from loosening or soil compaction. The actual behaviour of a building object at mining deformed subsoil, however, depends on many factors, including:

- the overconsolidation ratio of the subsoil, - mining forced state of deformation, - weight, size and rigidity of a building, - homogeneity or heterogeneity of the subsoil.

This paper will present the results of numerical simulations and measurements in situ of the building tilted on the ground, which parameters are entered in the computational analysis.

Key Words Mining areas, mining activities revenues, protection of buildings in the areas of mining, numerical analysis, models of inelastic material degradation.

1 INTRODUCTION The characteristic feature of analyses of objects built on areas influenced by mining is the total lack of proposals for numerical methods for proceeding that would yield assessment of behaviour and safety of these objects, featuring, according to the contemporary principles of the geotechnical design, the building-subsoil interactive system. Behaviours of mining subsoils (that is beddings subjected to deformations caused by mining of minerals), registered in the in situ state and forecast with various methods, reveal the complexity of phenomena so great that calling them the "difficult beddings" is fully justified. Resistance of building objects to the effect of the postmine terrain surface deformations is expressed with the capability to transfer these deformations - expressed, in the basic formulation by terrain slope values (T), vertical 1 PhD, DSc. J. Fedorowicz Associate Professor, Department of the Theory of Building Structures, Faculty of Civil Engineering, The Silesian University of Technology, ul. Akademicka 5, 44-101 Gliwice, Poland, phone No.: +48322372268, e-mail: [email protected] 2 MSc Eng Leszek Słowik, Ph.D. student: Instytut Techniki Budowlanej, Oddział Śląski, Katowice, Al. W. Korfantego 191, Tel./FAX: +48 32 730 29 64, [email protected]

11th International Conference on New Trends in Statics and Dynamics of Buildings October 2013, Bratislava

curvature (K), and horizontal deformation (ε) in the subsurface soil layer. The additional factor influencing the building object's response to the subsoil deformations may be also the velocity of its vertical displacements (evaluated usually by values of the twenty-four hours' settlements of the particular points). Velocity of the excavation front gets more and more significant in connection with the mining conditions changing nowadays and with growing depth at which mining is carried out. It affects, according to mining experts, the quantity and distribution of deformations on the terrain surface. This is a known approach and is being developed nowadays again [1,9,10]. In Table 1 below, the maximum values are shown as an example (after work [1]) of the surface deformation coefficients forecasted for various wall advance velocities for mining carried out at depth of H=395m.

wall advance velocity m/day

subsidence velocity dw/dr

mm/day

maximum slope Tmax

mm/m

Maximum deformations εmax

mm/m c →∞

immediate effects

transient effects

c →∞ immediate

effects

transient effects

c →∞ immediate

effects

transient effects

1.5 8.18 5.24 5.49 3.50 2.67/–4 .02 1.45/–4 .02 2.4 13.10 7.20 5.49 3.01 2.67/–4 .02 1.21/–4 .02 3.0 16.38 8.92 5.49 2.98 2.67/–4 .02 1.20/–4 .02 5.0 27.24 13.30 5.49 2.67 2.67/–4 .02 1.05/–4 .02

Table 1. Maximum values of deformation coefficients for mining at depth of H=395m, after [1]

One may notice that increase of the wall advance velocity causes reduction of the slope values and maximum horizontal tensile deformations (retaining the compression deformations). Drawing of settlements' progress is shown for full illustration of the real subsoil behaviour, recorded during during surveying measurements; Fig. 1.

Fig. 1. Progress of subsidences versus time for selected points of the analysed line, after [1]

Generalising, one should state that changes of mining conditions may lead to change of T and ε r parameters' ranges considered for the particular mining category. The danger of "underestimation" of the real effect of these parameters on the building construction arises currently because of the above mentioned reasons. In authors' opinion, to prevent such phenomenon, more advanced descriptions of the soil behaviour in the interaction zone of the building object with the deforming mining subsoil should be used in the forecast building analyses.

time


However, in the geotechnically oriented programs no separate computation paths were developed connected with mining subsoil analyses. Problem of the proper numerical analysis of the building - mining subsoil system (using the classic soil constitutive models, Coulomb-Mohr,or Drucker-Prager ones) is connected probably with the fact that in the deforming mining subsoil effects in the form of changes of soil parameters (φ i c) are difficult to record [e.g., 2, 6, 7]. All, therefore, real problems, requiring carrying out evaluation of threat conditions of the building - mining subsoil system are, in principle, of the authorial character. Therefore, certain solutions are found in the literature of the subject, which may be defined as "intrinsically contradictory". Inappropriateness was pointed out already in [3,5] of the numerical assessment of the building - mining subsoil system safety when the subsoil is described with the elastic plastic model, and the boundary conditions result from separation of the surface deformations into the constituent states (represented by the deformation parameters). Approach to analyses of the building - mining subsoil systems in the excessively conventional way features another, very important problem. For example, the statement does not have to be always true that the significant slope values resulting from mining pose a considerable threat to stability of tall objects with high slenderness ratio, and insignificant one for objects with big dimensions and low slenderness ratio, covering, among others, road embankments. Problems mentioned above are the subject of a more extensive analysis presented in the next chapters. It was demonstrated that:

- defining the appropriate boundary conditions in the subsoil model, and - employment of the relevant constitutive description of soil work

makes it possible to explain certain phenomena observed in the in situ state.

2 BEHAVIOUR PICTURE OF SOIL REPRESENTING MINING SUBSOIL IN (C-M) MODEL

If the surface displacements (and settlements of buildings) in the numerical model of the subsoil (subjected to deformations) would have to be considered as meaningful for the analysis carried out, then we should first take look into two interconnected tasks: � evaluate usability of the commonly used constitutive soil models in simulations of the mining subsoil

behaviour, and � evaluate accuracy with which terrain surface displacements are determined - representing the moving

subsidence trough in the computational model.

Fig. 2. Development of the subsidence trough in the model area (Pg) for transition of the excavation front over

the LSC segment

Forecasted range of the inactive

subsoil area


In Fig. 3 a simple numerical simulation is shown - representing propagation of displacements during development of the subsidence trough in the subsoil zone (Pg). This is the effect of wall progress over the real length Lsc – Fig. 2. Simulation of the subsidence trough progress in model (Pg) is realised by the appropriately specified kinematic Budryk-Knothe boundary conditions. The (C-M) Coulomb-Mohr model was used in analysis. Lack of time parameter in the model was replaced with the notion of the "conventional time", connected with the way in which the displacement boundary conditions are realised - in a directly incremental way (for the quick progress of the mining front, or in the block-incremental way (for the slower front progress).

Fig. 3. Block-incremental realisation of the trough in the Coulomb-Mohr model, successively for a) number of blocks = 6, b) number of blocks n=3

Behaviour of the , analysed as a deformations propagation phenomenon in the model area (Pg), shows the relationship of the reach (and local values) of deformations developing in the model with the realisation method of the kinematic boundary conditions; which may be - greatly simplified - related to the realisation method and progress velocity of the extraction front. However, the real propagation of mining deformations in the numerical model of the subsoil (Pg) is always connected with introduction of the relevant:

- length L of model (Pg), such that the analysed area of interaction with the building would not run a risk of boundary disturbances, and

- height H of model (Pg), containing area of interaction with the subsoil [3,4,5]. Moreover, one should indicate that the boundary conditions realised for areas (Pg) correspond to the displacement functions (u,v) on the model boundary, determined according to the particular mining deformations forecasting theory, e.g., Budryk-Knothe theory. Next, introducing (after specifying the boundary conditions) the relevant constitutive description , taking into account changes of soil state taking place during subsoil deformation, will make it possible - as shown in chapter 3 - to bring the description of behaviour of the building - mining subsoil system to cases of the in situ states.

3 ANALYSIS OF REAL SYSTEM USING (MMC) MODEL FOR MINING SUBSOIL Problems of deviations of the building objects from the vertical occur mostly in the areas with mining influence. These are the extremely difficult cases for modelling the complete building - subsoil system, among others because of the lack of the unambiguous interpretation of the soil work representing the mining subsoil in the main engineering (C-M) model; see chapter 2.


The following thesis was put forward: If in certain soil conditions additional settlement may occur of the building objects due to deformations taking place in the mining subsoil, then there is a significant probability that with the relevant soil stratification or in specially complex mining conditions, the same phenomenon may be revealed in the form of the non-uniform settlement causing building tilt (bigger than the forecasted terrain slope). Effect of the additional settlements that is settlement process of the buildings' structures reinitiated by mining was noticed repeatedly in the in situ observations; however, it was usually attributed to the evident differences between the forecasted and measured values of the vertical terrain displacements. General explanation of this effect in respect to the mining subsoil, based on the critical state mechanics, is given in work [3]. In works [8, 12] cases were discussed of the permanent deviations of buildings from the vertical, it was also shown, based on the assessment of the interaction change under the slanted building that deviation from the vertical may be different from the terrain slope. However, to be able to forecast the object slanting threat, it is proposed to carry out analysis of the soil behaviour in the critical state model (MCC) making interpretation possible of the rigidity reduction of the deforming mining subsoil as the result of the soil state change. Credibility of such analysis is connected; however, with meeting three conditions:

1) Proper identification of the subsoil (along with its history) in the area of its interaction with the construction,

2) determining model parameters properly, and 3) determining boundary conditions of the model properly.

In practice, meeting condition (3) in the engineering analyses may turn out to be most difficult. Character is shown below, which is assumed by the above mentioned conditions specified for the real building object being the subject of the detailed monitoring since 1993 until today [12, 13]. The object under consideration is the 5-storey apartment building built in the pre-fabricated concrete slabs technology, consisting from three segments with the length of L=18.20m and breadth of B=10.00m each. The object is built on in the direct way on the reinforced concrete grate strengthened with two bowstrings. Object localisation is shown in Fig. 4a. Measurement of subsidences along the survey line is shown in Fig. 4b.

Fig. 4, a) object localisation in respect to measurement traverse in the terrain, consistent with the mining direction, b) subsidences of terrain surface along the measurement line

a) b)

fragment of the subsiding trough fitted

with the Budryk-Knothe equation

object localisation


1) Identification of subsoil The rock mass in the analysed region is composed of Carboniferous formation with the Quaternary overburden in the form of gray and brown sandy clay, with a thickness of 0.6-5.0m. Carbon consists mainly of clays and fine-grained sandstones. Area around the location of the investigated object was repeatedly subjected to the influence of mining activities, carried out by the mines' Murcki "and" Staszic ". The total thickness of the mined walls is about 25m. Most of the mining concerned, however, the walls of which the outline was outside the region of location of the building. 2) Determining parameters of the model To describe the model simulating the subsoil behaviour in a critical state it should be noted that the destruction of the soil normally consolidated or slightly preconsolidated, connected with the critical state of critical and advanced plastic flow, is of a purely friction nature [11,14]. This is demonstrated by the course of the envelope of critical states in the effective stress space. Line, considered in the laboratory examinations as a Coulomb-Mohr straight line, in the interpretation of the critical state mechanics is the envelope of the strength peaks. Peak strength characterizes the greatly preconsolidated soils. Figure 5 shows the characteristic surfaces of the critical state model Modified-Cam-Clay (MCC) and the interpretation of the model parameters.

F( 1, 2, 3; i, pco)=0e

ecs

eo

NCLCSL

ln(p)

pco

linia odciążenia

pco

p

q

F(p q; i, pco)=0

CSLM2

3q⋅

p

powierzchnia zniszczenia

p co

q

1

2

3

e=e 1

e=e 2

e=e o początkowa

powierzchnia plastyczności

Fig. 5. Critical state model and interpretation of the model parameters in (p,q,e) space

Successive stages of the procedure are as follows: soil sampling - laboratory test results - determining model parameters, are shown in Fig. 6 (example for the OW1 test bore-hole).

initial

plasticity

surface

damage

surface

unloading line


OCR=2.5, pc=200 kPa, M=1.157,=0.056, =0.017, ecs=0.462,=0.30, K(NC)o=0.4652, q*z=122 kPa

grunt nasyp.

piasek śr.

ił

węgiel k.

ił

OCR=2.5, pc=200 kPa, Cc=0.130, Cs=0.040, ecs=0.462, =29o

OCR=2.5, pc=225 kPa, Cc=0.108, Cs=0.038, ecs=0.405, =23o

PROFIL OW-1

φφ

sin3sin6

−=M

303.2cC=λ

303.2sC=κ

φsin95.0)( −=NCoK

( )11

)()) −−

+⋅= OCRKOCRK NCo

OCo ν

ν

pMpMq

pco 2

222 +=

OCR=2.5, pc=225 kPa, M=0.8985, =0.047, =0.017, ecs=0.405, =0.29, K(NC)o=0.6093, q*z=60 kPa

poziom pos.

ił

)(OCoK

poziom pos.

z [m]

0.5 1.0

0.5480.6360.612

-9

-6-4-20

Fig. 6. Determining (MCC) model parameters

3) Determining boundary conditions of the model The actual slanting of the investigated object (according to the in situ measurements) exceeds by about 10o/oo the terrain slope values T (forecasted and determined along the measurement traverse). Location of the investigated object and the dominating slanting component (parallel to the mining direction and to the measurement traverse from Fig. 4) authorize to carry out numerical simulations of the subsoil behaviour in the (2D) analysis - Figure 7. The task of the preliminary analysis (presented below) is answering the question if the observed building behaviour results from appearing of the phenomenon of the additional settlements of the building due to activation of the particular phenomena in the pre consolidated soil by mining. This phenomenon is understood here as the soil rigidity reduction and transition from the pre consolidation state to the normal consolidation state in the subsoil loosening stage. Discovering this phenomenon would make it possible to refer to the thesis stated in the work (put forth at the beginning of the chapter). Figure 7 shows the satisfactory consistency acquired in the area of the mining subsoil model of the vertical deformations, obtained for the upper edge of the model, with the state of the measured vertical ground displacements (see Fig. 4b) in years 2007-2012. This state is the result of the correlation between the displacement boundary conditions determined in accordance with the Budryk-Knothe theory at the vertical edges and at the bottom edge of the model (at the mining conditions closest to the real state, a = 0.8, g = 2.5m, tan ! = 2.3, H = 460m, n = 1.0), and the model response obtained at the upper edge.

OW-1 PROFILE

made

ground

medium gr. sand clay

hard coal

clay

foundation level

foundation level


Fig. 7. Numerical simulation of the actual terrain surface deformations measured along the measurement line from Fig. 4 in the (2D) analysis

The determined boundary conditions were used for carrying out the preliminary analysis meeting the conditions specified above. Result of analysis showing the mining subsoil behaviour in the (MCC) model in the area of subsoil interaction with the analysed object. In the preliminary analysis: � homogeneous subsoil was introduced, with the clay layer parameters of OCR = 2.5,

dominating in the soil profile, � load from the construction was assumed as qz, equivalent, evenly distributed, applied to

the foundation in the marked area of the subsoil model, � load with the determined, displacement boundary conditions was realised in the

incremental form in four blocks, where the first block was the realisation of the load transferred from the construction to the subsoil.

The analysis result provides the qualitative view of the investigated object behaviour - Fig. 8. This is the realisation of the last block of the displacement boundary conditions, when: � sum of the initial settlement values from load qz and vertical displacements of the object

begins to exceed displacement values of the undeveloped terrain, and � further vertical displacements of the building object, exceeding values measured along the

measurement traverse may be interpreted as the additional unforecasted building displacements (shaded area in Fig. 8); with the tilt visible in the numerical simulation, consistent with the real state.

according to Budryk-Knothe theory

object

localisation

w = measured


Fig. 8. Result of the preliminary analysis assessing behaviour of the examined building object

4 SUMMARY AND CONCLUSIONS Effect of the additional vertical construction displacements, different from displacements of the undeveloped terrain (not loaded with the construction) was noticed repeatedly in the in situ observations. It was treated; however, usually as the evident fact of occurrences of differences between the forecasted, and measured values of the vertical terrain displacements. However, if this phenomenon may be explained with changes of soil rigidity occurring in the mining subsoil, then (according to the thesis put forward in chapter 3) one may also forecast the particular, disadvantageous for the building structure, consequences of this phenomenon. There is, e.g., a big probability that with the relevant subsoil stratification or in the complex mining conditions this phenomenon may demonstrate itself in the form of the uneven settlement causing building tilt (bigger than the forecasted terrain slope). Results of the preliminary analysis are presented in the work, providing picture of the mining subsoil behaviour in the critical state model (MCC) in the area of interaction of the subsoil with the slanted building. The analysis result provides the qualitative; however consistent with the reality, view of the investigated object behaviour - Fig. 8. Credibility of the numerical analysis (especially the one employing the advanced model of the constitutive soil description) is closely connected with: 1) identifying of the subsoil, 2) determining parameters of the constitutive model, and 3) determining boundary conditions of the model. In research analyses, meeting condition (3) correctly, and the proper realisation of the displacement boundary conditions in the model are the base for the correct assessment and forecasting of the buildings' structures - mining subsoil system behaviour.

ACKNOWLEDGEMENT Numerical analyses were performed at ACK CYFRONET Kraków, based on grants MNiSW/SGI3700/PŚląska/054/2010 and MNiSW/SGI3700/PŚląska/056/2010.

(analysis blocks)

left foundation corner

foundation centre

right foundation corner


REFERENCES

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