Determination of non-uniform settlements caused by decompression of soil in the excavation

The article is offered refined and simplified methods for determination of non-uniform settlements caused by decompression of soil in the excavation. The results of the calculations executed taking into account the done suggestions and in the program Plaxis are presented. The results of the calculations are compared with the results of experimental observations given in the literature. The influence of the excavation parameters on the non-uniform settlements is investigated. Present a proposal for adjustment of the conditions, which require consideration of soil decompression in the excavation.


Introduction
At excavations as a result of removing the load from the weight of the extracted soil, the lower layers of soil undergo decompression and, as a consequence, the bottom of the excavation is lifted. The lifting of bottom of the excavation depends on its depth and sizes in plan, texture and mechanical characteristics of soils , the presence of enclosing structures of the excavation, the duration of work on the excavation and the construction of the building, etc. [1,2].
Since the decompression of the soil massif along the depth in the central part of the excavation will be larger than at the edges (Fig.1b), then under subsequent loading it will give a large settlement, which in turn can lead to additional small but non-uniform settlements with a tendency to the deflection of the building [3,4]. from dead weight pressure of soil before construction begins σ'zg (Fig. 1a); from dead weight pressure of soil extracted from the excavation σz (Fig. 1b); from dead weight pressure of soil after excavation σzu (Fig. 1b); from dead weight pressure of soil after the construction of the building σzg; from external load after the construction of the building σzp (Fig. 1c); total after the construction of the building σz (Fig. 1c).
In ordinary engineering-geological conditions, non-uniform settlements caused by decompression of soil in the excavation usually does not have a significant effect on the stress-strain state (SSS) of building constructions. In this regard, the current regulatory documents for design of soil bases and foundations [5,6] allow to ignore the settlements from decompression at a depth of excavation of less than 5 m. However, in difficult engineering-geological conditions, when under the influence of various factors, the occurrence of significant uneven deformations of the base may occur, consideration of the settlements caused by decompression of soil can both reduce the overall unevenness and aggravate it [7,8].
Recently, numerical methods for determining the SSS of a soil massif with the help of specialized geotechnical software using the finite element method (FEM) [2,3,9] and various elastic and elastic-plastic models of the soil base have become increasingly popular [10,11,12,13,14,15]. Nevertheless, analytical methods of calculation and at the moment have not lost relevance, since they are most fully developed in regulatory documents [5,6] for almost all types of difficult engineering-geological conditions, are well confirmed by experimental data [16,17] and are one of the ways verification of the results of numerical calculation methods. A widely used method of layer-by-layer summation to determine the settlement of the bases continues to be improved [18] and by applying the deformation characteristics of the soil, which are determined taking into account its stress state [19,20], it is possible to significantly improve the accuracy of the determination of the settlement.
It should be noted that the formula (1) used in the current regulatory documents [5,6] at the size of the excavation significantly exceeding the size of the foundation has a certain incorrectness caused by taking into account the unloading of the bases during excavation. , , , where non-dimensional coefficient, equal 0.8; When using this formula under certain conditions, for example, with the surface of the planning practically coinciding with the surface of the natural relief, the great depth of excavation and the size of the excavation, which substantially exceed size of the foundation, in the layers of the lower zone of the compressible stratum may arise negative vertical stresses from the external load.

Ei
In this case, the negative settlements of these elementary layers are not fully compensated by a component that takes into account the decompression of the soil during the excavation. An increase in the compressible stratum, caused, for example, by the influence of neighboring foundations, in this situation leads to a paradoxical decrease of the settlements. As a result, the settlement, determined in accordance with [5,6], is significantly less than in accordance with [21].
Previously, this incorrectness was eliminated by zeroing the stresses zγ,і, if they exceeded the stresses zp,i ( §2.231 [22]), however, in the current regulatory documents this indication is absent.
Consider the formula (1) in the following form 0 ,0 ,0 ,0 where 0 ,0 zg pp    additional pressure in the level of the foundation base; paverage pressure on the foundation base; 'zg,0vertical stress from dead weight pressure of soil extracted from the excavation in the level of the foundation base; icoefficient that takes into account the distribution of stresses from external load in depth, depending on the size of the foundation; 'icoefficient that takes into account the distribution of stresses from the dead weight pressure of soil extracted from the excavation, in depth, depending on the size of the excavation.
Under the conditions described above, with increasing depth, the damping of the stresses from the external load  will be more intense than that stresses from the dead weight pressure of soil extracted from the excavation ,0 zg i      (Fig. 2). This situation is possible in the absence of backfilling of the excavation, but then the component taking into account the decompression of the soil overstates the settlement, since in it the load from the dead weight of the soil above the foundation base is accepted acting throughout the area of the excavation. Depending on the ratio of mean pressure and vertical stress from the dead weight pressure of soil extracted from the excavation p /'zg,0, according to the norms [5,6], the calculated compressible stratum can be either larger or smaller than the actual zone of soil decompression.
Analysis of experimental observations of stratified decompression deformations shows that the bulk of the deformations are realized in the upper zone of the unloaded base. About 90% of the elastic deformation occurs within a depth slightly exceeding the size of the unloaded area [23].

Methods
To eliminate these incorrectness, it is proposed to present the total settlement in the form of separately determined components from additional vertical stresses and elastic deformations caused by unloading the foundation during the excavation, with an appropriate division into elementary layers. pk s s s  where sksettlement at a pressure equal to natural pressure, determined using deformation modulus of soil across the branch of secondary loading; sрsettlement with a further increase in pressure to its full value, determined using deformation modulus of soil across the branch of primary loading. , , , where nnumber of elementary layers located within the depth of the unconsolidated zone of the soil; of the whole area of the excavation with uniform pressure p < 'zg,0 [24] , 1 , ,0 where za,ivertical stress along the vertical axis considered, taking into account the influence of all differently loaded areas within the bottom of the excavation.
As a limitation of the depth of the unconsolidated zone of the soil take condition zγ,і ≤ k·zg,і, where k accepted 0.2-0.5 depending on the width of the excavation.
Graphically, the dependence of the settlement of the i-th elementary layer of soil on the stresses acting in it is shown in Fig. 3.   Fig. 3. Dependence of the precipitation of the i-th elementary layer on the stresses acting in it: sgsettlement from the action of its own weight of the soil, which occurred during the formation of the soil massif Non-uniform settlements caused by decompression of soil during the development of the excavation is determined taking into account the location of foundations in the excavation.
Vertical stress from dead weight pressure of soil extracted from the excavation taking into account the location of the calculated vertical in the excavation plan is determined by the formula , ,0 z i i zg       (8) where 'coefficient taking into account the distribution of stresses over the depth, determined by the method of corner points along the calculated vertical line passing through the center of the foundation base, depending on the size of the excavation and the location of the calculated vertical (Fig. 4) ηj = lj / bjaspect ratio of the j-th area of the excavation; ξj,і = zі / bjrelative depth for the j-th area of the excavation.

Results and Discussion
The results of measuring lifting of the excavation bottom with natural slopes of 10 m depth with dimensions in the plan of 47.7 × 86 m at three points are given in [25]: at the center of the excavation and at distances from the center ≈9 m and ≈20 m. In this work, for the indicated parameters of the excavation, lifting of the excavation bottom was determined at these points according to the proposed method and in the Plaxis software (Fig. 5). Numerical modeling in Plaxis is performed in a flat formulation of the problem using the model Hardening Soil (HS) as the most suitable for performing such calculations [11,13,26,27].
Modules of elastic deformation of soil layers were adopted from the condition of ensuring the coincidence of the lifting in the center of the excavation.

Fig. 5. Vertical displacements soil massif
The nonuniformities of the settlements obtained by proposed method and in Plaxis showed good convergence with the experimental values. The proposed method using the elastic half-space model overestimated the nonuniformities, and Plaxis with the HS model understated it. The value of the unconsolidated zone was also smaller in the Plaxis with the HS model Also, in accordance with the proposed method, was investigated the influence of such factors as the parameters of the excavation (sizes in plan and depth) (Fig. 6) and the mechanical properties of the soil (density and modulus of elastic deformations) on the scheme of non-uniform settlements from soil decompression. Non-uniform settlements from decompression of soil in the outer zones of the excavation is much higher than in the central part . To describe the scheme of non-uniform  settlements from soil decompression with relatively uniform soil bedding, can take the  conditional radius of curvature, defined by formula   2  2  2 , , , where sk,c and sk,bsettlement from decompression of soil, respectively, of points in the center and on the edge of the excavation bottom; Bwidth of excavation.
In this case, the settlement from the decompression of the soil at the point of the crosssection of the excavation located at a distance x from the center can be found from The error of the non-uniform settlements, determined from formulas (10, 11) with respect to the experimental data given in Table 1, does not exceed 5%.

Conclusions
The proposed method for determining the unevenness of settlements caused by soil decompression allows: regardless of the size of the foundation for the given parameters of the excavation, determine the maximum settlement from the decompression of the soil in the center of the excavation; determine by the simplified formulas (10, 11) the non-uniform settlements caused by the decompression of the soil with sufficient accuracy to make a decision on the need to take it into account; if necessary, refine the non-uniform settlements by using formulas (5)(6)(7)(8)(9). In current regulatory documents for the design of base of foundations, the decompression of the soil in the excavation is allowed to be ignored at a depth of excavation less than 5 m [6,5]. However, according to the authors, under certain conditions other criteria should be used: for buildings that are particularly sensitive to non-uniform settlements in difficult geotechnical conditions can be ignored if the conditional radius of curvature, defined by formula (10), R ≥ 20 km; for dense clay soils with explicit elastic properties at the base it is proposed to use the condition where σz,0total vertical stress in the level of the foundation base after the construction of the building; , el EErespectively, the averaged values of the modulus of the total and elastic deformation within the zone of soil decompression, which in the first approximation can be taken equal to the width of the excavation.