Introduction

The per capita energy consumption per year is one of the main indicators of developed countries and developing countries such as India; the average energy consumption in India is approximately 1075 kWh per year, which is one-third of the world average demand and is much lower than the International per capita consumption per year. The main sources of energy in developing countries are hydro power, coal and oil, which are not environmental friendly. Therefore, alternative energy sources are required for sustainable development in such countries. To this end, India has planned a three-stage nuclear programme to generate sustainable energy by utilizing indigenously available resources [1]. Accordingly, various nuclear power plants and associated facilities are being constructed in India. The sites for locating these facilities are selected with consideration of various environmental aspects and are often located in virgin sites. Currently, these facilities are being set up similar to complexes, along with provisions for future expansions, which require future construction activities and necessitate deep excavations adjacent to the existing operating plants. Since open excavations are not viable in constraint areas, supported excavation needs to be carried out for reaching the competent strata and locating the facilities. The various supported excavation systems, such as a diaphragm wall, strut wall, and anchored walls, are commonly used in various infrastructure projects.

The current practice of deep excavation followed in the Indian nuclear industry is to design retaining walls during the planning stage and to construct them along with the main plant in constrained areas. Later, controlled backfilling will be carried out around the retaining wall. During the expansion of the facility, excavation will be taken up with the help of this existing retaining wall. Even though, these retaining walls are conventionally designed for strength and stability; the performance of retaining system and engineering backfilling during future excavation needs to be studied to evaluate the settlement of adjacent soil mass. This sort of study will help in identifying critical areas of settlement and precautions to be taken up to limit settlements within the permissible limit of 25 mm required for isolated and strip footings of service supporting structures. Presently, empirical methods to predict the ground surface settlement and displacement of the retaining structures from various case histories were commonly adopted [2,3,4,5,6]. Even though these empirical methods are useful for a preliminary analysis and design of a deep excavation, a site-specific analysis accounting for the stiffness properties of the soil, retaining system and dewatering effect is warranted to identify the area of maximum settlement of soil mass to ensure the safety of the adjacent structures, which are to be supported on this soil mass. This outcome can be achieved by a numerical analysis of the deep excavation using a site-specific strength and stiffness properties of the soil after accounting for the retaining system and continuous dewatering. In the present study, an already constructed retaining wall which is to be used for assisting a future expansion excavation was analysed using the PLAXIS 2D finite element software, and the settlements of backfilled soil mass behind the excavation was predicted using various soil constitutive laws. Stiffness properties were obtained from conventional investigations and calibrated using field observed instrumentation data and further used in prediction of settlement zone. This study indicated that settlement of engineered backfill soil mass is beyond permissible limit during future excavation which can cause damage to the foundations of structures, equipments which will be supported on this backfill soil. This indicated the inadequacy of the present retaining systems and engineering backfilling to control settlement of adjacent soil mass. Thus additional precautions are necessary to prevent the damage of structures which will be supported on this soil mass.

Geology of the Site and the Definition of the Problem

The study area (Fig. 1) is located along the East Coast Peninsula of India and comprises a Crystalline/Archean complex overlain by beach deposits. The site comprises sand followed by silty sand and clay. Hard rock is found to be available at a depth of 15–20 m below the existing ground level. As the part of geotechnical characterization of this NPP site, extensive investigation comprising 142 exploratory boreholes, field and laboratory investigations were carried out and idealized the soil profile (Fig. 2). Geologically, the area is comprised of two distinct formations, namely, the Charnockite rock and more recent sediments [7, 8].

Fig. 1
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Location of the study area

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Fig. 2
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Idealized soil profile

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The open excavations and the supported excavations are the commonly adopted methods/types of deep excavation. While open excavation can be adopted at a virgin site where space is not a constraint, for sites adjacent to existing facilities, a supported excavation system must be adopted. Braced walls, sheet pile walls, contiguous and secant piles, diaphragm walls or slurry trenches, reinforced concrete retaining walls, etc., are commonly used in a supported excavation system. The choice of the type of support depends on various factors, such as soil strata, space availability, and cost. In the present case, 185 m length counterfort retaining wall is conventionally designed for retaining earth for a depth of 23 m and constructed along with the main nuclear establishment to facilitate excavation during future expansion. The schematic details of the counterfort retaining wall section and its location with reference to the present and future excavation is also indicated in Fig. 3. This counterfort wall is constructed along with the main plant building. After the construction of the retaining wall, uniform layer backfilling was carried out on both sides A and B (Fig. 3) of the retaining wall with the material obtained from the same site during excavation achieving 95% of modified proctor compaction thus meeting compaction requirements. A future excavation is planned on the side opposite to the counterfort which is indicated as A in Fig. 3. During the future construction while expanding the facility, the excavation must be carried out in the backfill soil up to the desired depth with the assistance of already constructed retaining wall. However, the effect of this deep excavation on adjacent engineered backfilled soil mass in the zone B is to be addressed to evaluate the efficacy of engineered backfilling in limiting the settlement and to identify any additional precautions required as some of the services and lightly loaded structures will be supported on this backfilled soil.

Fig. 3
figure 3

Details of future excavation system

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Analysis of the Deep Excavation Support System

There are various simplified methods available for predicting the deformations of retaining wall systems and settlement zones adjacent to the deep excavation. Soil type, construction dewatering, and the sequence are the major important factors affecting the performance of a deep excavation [3, 6, 9, 10]. Three zones of settlement profiles are available based on the soil type and the workmanship: Type I, sand and soft to stiff clay with average workmanship; Type II, very soft to soft clay; and Type III, very soft to soft clay to a significant depth below the excavation bottom [6]. Pattern of the settlement adjacent to the excavation depends on the soil type and normalized settlement profiles for estimating the settlement pattern adjacent to the excavation are widely used [3] and methods to predict the ground surface settlement is available in papers [5, 11]. The proposed settlement curves are spandrel and concave types. They predicted the ground settlement by the influence zone, the location of the maximum settlement, and the extent of maximum settlement, and showed that the primary settlement zone generates a larger angular distortion for the adjacent structures.

Influence zone of the settlement is 2–3 times that of the excavation depth according to [6]. An excavation in sandy soil may induce an influence zone of settlement approximately twice the excavation depth [2]. The influence zone for stiff to very stiff clay is three times that of the excavation depth, and that of soft or medium soft clay is twice that of the excavation depth. The shapes of the ground surface settlement produced by an excavation can be categorized into spandrel types and concave types according to [12]. The location of the maximum ground settlement of the concave type would occur at a distance of 0.5 times the depth of the excavation from the wall [4, 13]. Based on various case histories [2] established a relationship between the maximum settlement and the excavation depth in stiff clay, sandy soil, and soft to medium soft clays.

This simplified analysis provides a reasonable description of the settlement profile behind the excavation surface and the displacement of the retaining wall and is developed based on case histories from observed settlements and displacements in various types of soil. In the present case, since the type of soil involved is engineering backfill and continuous dewatering to be adopted for the future excavation, a numerical analysis using the Finite Element software PLAXIS was carried out to study the behaviour of the sequential excavation and dewatering needed for the future expansion of the facility. Towards this goal, the characterization of the engineering backfilling was carried out and stiffness property of backfilled soil was calibrated using field instrumentation data.

Characterization of the Site for Constitutive Models

Constitutive Models

A linear-elastic, perfectly plastic Mohr–Coulomb model (MC) and a Hardening Soil Model (HS) are the commonly used constitutive models for defining soil behaviour. Various researchers [12, 14,15,16,17,18,19,20,21,22,23,24,25,26,27] studied excavation behaviour and predicted the ground surface settlements, wall displacements, earth pressure and bending moment distributions using MC and HS Model. In this present case, both the constitutive models were used to predict the behaviour of the adjacent soil mass while carrying out future excavation in the backfilled soil. Strength and stiffness properties which are the basic requirement for defining a constitutive law were obtained from the field and laboratory investigations. The basic parameters required to define the MC model are the Young’s Modulus (E) and Poisson’s ratio (ʋ). The other parameters required to define this model are friction angle (Φ), cohesion (c) and dilatancy (φ). The higher order models, such as HS Model, accounting for the non-linear behaviour of the soil [28, 29] requires stress dependent stiffness according to a power law (m), secant stiffness (\(E_{{50}}^{{{\text{ref}}}}\)), tangent stiffness (\(E_{{{\text{oed}}}}^{{{\text{ref}}}}\)), unloading stiffness \((E_{{{\text{ur}}}}^{{{\text{ref}}}})\), unloading Poisson ratio \(({\upsilon _{{\text{ur}}}})\), cohesion (c), angle of internal friction (φ) and dilatancy (ψ).

Evaluation of the Strength and Stiffness Properties of Materials

A triaxial test or Oedometer tests are the commonly used tests to evaluate the stiffness properties of soil. In the present study, already excavated material was used for backfilling and these excavated materials were remoulded to the field density for performing oedometer tests. Further after compaction, pressuremeter tests were carried out to determine the field stiffness of backfilled soil. The Consolidation properties of soil samples were determined by allowing vertical drainage in both directions which simulated the field condition. Typical stress–strain curve obtained from Oedometer test (Fig. 4) provides Oedometer stiffness and varies from 2000 to 2800 kN/m2 for three cases.

Fig. 4
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Typical stress–strain curve from oedometer test

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The pressure metre modulus (Ep) provides a direct correlation for the horizontal modulus of the soil and related empirically to the Young’s modulus (E) of the soil as Ep/E = α, [30], in which α is the rheological coefficient [31] and has a value between 0 and 1. For the present case, α is considered to be 0.3. A series of pressure metre tests were carried out on the engineering backfilled soil at an adjacent site where backfill was carried out using the same material and with same compaction specification with an objective to determine deformation modulus of soil. Hole expansion is then determined from measurement of volumetric expansion of the probe. Application of pressure increment was carried up to failure point which corresponds to limit pressure (PL) Pressure metre modulus is then determined using relation (1) between pressure interval (ΔP), radius interval (ΔR), Poisson’s Ratio (ʋ) and intermediate radius (Rav).

$${E_{\text{p}}}=(1+\upsilon )~{R_{{\text{av}}}}\left( {\frac{{\Delta P}}{{\Delta R}}} \right).$$
(1)

The limit pressure obtained shows a variation ranging from 0.7 to 1 MPa and this order of limit pressure obtained matches well with that of silty soils and old fills [32]. Considering this, a site specific correlation between Limit Pressure and Pressuremeter modulus was established with a correlation coefficient of 0.926 (Eq. 2).

$${E_{\text{p}}}={\text{ }}6.397{P_{\text{l}}} - 23.75.$$
(2)

The correlation is given in Fig. 5 and can be used for determination of stiffness properties of backfilled soil. However, considering the limited number of data points, an average value of the limit pressure (PL) of 0.8 MPa, the site specific pressuremeter modulus is 2.7 MPa, and the corresponding modulus of elasticity is 8000 kN/m2. In order to evaluate the insitu stiffness properties of backfilled soil alternatively field observed instrumentation data was used and back calculations were performed and calibrated the actual stiffness property to be used in the analysis which is elaborated in “Validation of Stiffness Property of Backfilled Soil”. The strength properties (Table 1) of excavated material used for backfilling were determined from consolidated drained direct shear test carried out on remoulded soil samples. Shear tests and triaxial tests were also carried out for rock samples as the part of site characterization in rock samples to obtain the strength and stiffness properties (Table 1).

Fig. 5
figure 5

Relation between limit pressure and pressure modulus

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Table 1 Parameters of backfilled soil and weathered rock
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Validation of Stiffness Property of Backfilled Soil

With an attempt to validate the stiffness properties of backfilled soil, excavation carried out in a backfilled soil at the same site involving same material and same compaction specifications, was numerically analysed, displacements were obtained and results were compared with that obtained from field instrumentation. For this excavation, a slope of 1 V: 1 H was adopted for top layer and 1 V: 2 H slope was provided for excavation in silty layers. Excavation of bottom layer was carried out with a slope of 1 V: 1.35 H to reach the required depth of foundation. Intermediate berms of 2.0 m were also provided in two stages to increase the stability of slope. Water table was observed at a depth of 15.0 m below existing ground level. To facilitate the excavation below water table, after reaching the water table level, water table was lowered by continuous dewatering. The sequence of construction of the existing infrastructure, deep excavation and dewatering was analysed defining soil stress–strain behaviour using constitutive laws namely MC and HS Model. The model parameters for analysis were obtained from conventional geotechnical investigation is given in Table 2. Standard penetration value ‘N’ of each layer and other parameters are also given in Table 2.

Table 2 Parameters of soil used for validating instrumentation data
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As undisturbed soil samples were not available, empirical relations between SPT N values and Young’s modulus proposed by [33, 34] were considered for estimating Young’s modulus (E) of various layers encountered at the site. For backfilled soil the stiffness parameters obtained from the previous section was utilized.

As the part of field instrumentation programme, inclinometers were deployed to monitor the excavation slopes and these data were used for calibration of the stiffness properties and numerical model of the excavation. The instrumentation readings obtained during the last phase of excavation was compared with that of numerical analysis using MC Model with the pressuremeter stiffness value of 8000 kPa clearly shows that the model displacement of backfill soil is not matching with the field data (Fig. 6). A series of back analysis was carried out by varying stiffness properties from 8000 to 15,000 kPa and matching horizontal displacement with that obtained from field. Cohesion and angle of internal friction are not sensitive to low level deformations at shallow depth [24] and were not varied in this analysis. As the displacement profile obtained from numerical analysis is not matching, using MC Model (Fig. 6), higher order model namely HS model was used to define constitutive behaviour of backfilled soil and displacements were evaluated. Unloading stiffness and tangent stiffness required for HS model were evaluated using the formulations 3 and 4. Poisson ratio of residual soil was considered as 0.2 and Power for stress level dependency was considered as 0.5.

Fig. 6
figure 6

Comparison of displacement

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$$E_{{{\text{ur}}}}^{{{\text{ref}}}}=3E_{{50}}^{{{\text{ref}}}},$$
(3)
$$E_{{50}}^{{{\text{ref}}}}=1.25E_{{{\text{oed}}}}^{{{\text{ref}}}}.$$
(4)

The surface displacement for an E value of 8000 kPa is 9.5 mm away from excavation. For an E value of 15,000 kPa, surface displacement is 14.9 mm which is 55% higher than the displacement value obtained using E value obtained from Pressuremeter. Displacement obtained using HS Model for various secant moduli E (Fig. 7) shows that, instrumentation values and displacement predicted form numerical analysis fairly matches for an E value between 12,500 to 15,000 kPa using HS model. The stiffness obtained from conventional site investigation programme provides a conservative Young’s modulus and the actual insitu stiffness is 50% higher than that obtained from field.

Fig. 7
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Prediction of settlement from back calculation

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Modelling of the Problem and Numerical Analysis of the Supported Excavation System

The problem defined in the “Geology of the site and the definition of the problem” was modelled in the PLAXIS 2D and analyzed as a plane strain case to study the behaviour of the retaining wall system during a future sequential excavation. The engineered backfilled soil is modelled as 15 noded triangular elements, and the retaining wall is modelled as five noded plate elements (Fig. 8).

Fig. 8
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Excavation scheme

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The extent of boundaries was considered as more than four times the depth of excavation to obtain ground settlement. The depth of model is assumed up to 40 m in hard rock to capture the behaviour of retaining system. The equivalent stiffness of the counterfort was estimated per metre length of the retaining wall and was provided as an input to analysis (Table 3). Since the retaining system was constructed during the previous excavations and backfilling was carried uniformly on both sides of the retaining wall, the process of construction of retaining wall was not modelled in this study as this study is to decipher the behaviour of already constructed conventional retaining wall during deep excavation. And also soil structure interaction effects were not studied. Standard fixities were adopted for the model boundary, where the vertical geometry line in the model is assumed to have a horizontal fixity, and the horizontal geometry line is assumed to have a total fixity. The finite element analysis was carried out using the 12 Point Gauss Integration method.

Table 3 Parameters for counter fort retaining wall
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The stress–strain relation of the backfilled soil is defined using Mohr–Coulomb (MC) model and the HS Model. The basic parameters required to define the MC and HS model is given in Table 3. The counter fort retaining wall is modelled by the Elasto Plastic constitutive law. The stiffness parameters for the HS Models were obtained from formulation (3) and (4). The normal stiffness (EA) and bending stiffness (EI) of the plate element is calculated segment-wise for the stem. The stem is divided into five portions, and the stiffness is calculated accordingly. The spacing of the counter fort is 5.0 m, and the equivalent stiffness of the counterfort per metre length is estimated and used for the analysis. The weight of the concrete is 25 kN/m3.

A drained analysis was carried out to predict the behaviour of the excavation. The initial stresses were generated using the K0 procedure. The initial water table is considered to be 2.0 m depth from the ground level. Each stage of the excavation is defined, and a sequential analysis is carried out. In each stage, a 5.0 m excavation is conducted. After reaching 20 m, i.e., four stages, the last phase of the excavation is 3.7 m. Hence, there are a total of five stages of excavation that are analysed. The water table was lowered to 7 m, 12 m, 17 m, 22 m, and 27 m before each stage, respectively. Stiffness of soil considered for this study corresponds to the field calibrated stiffness which is 1.5e4 kN/m2.

Discussion of Results

The numerical analysis showed surface heaves in front of retaining walls and settlements behind the retaining wall. Settlement increases beyond acceptable limits as the depth of excavation increases and the settlement profiles behind the retaining wall during the last phase of excavation, i.e., after reaching 23.7 m of excavation, obtained from both the MC and HS Model for the field calibrated E value of 15,000 kPa (Fig. 9) shows a settlement of 243 and 397 mm behind excavation, respectively.

Fig. 9
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Settlement profile behind excavation

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The settlement induced by the excavation is of concave type and the primary influence zone of the excavation extends upto 25–30 m from both the models and indicated that the primary influence zone is approximately 1.05–1.25 times the depth of excavation. The location of maximum settlement is 8.8 m from both the models which is less than 11.85 m predicted from the formulation of [4, 13]. This analysis indicated the necessity of a site specific numerical analysis in prediction of deep excavation behaviour and also the requirement of higher order soil models namely HS model in predicting the settlement induced due to deep excavations. The settlement obtained from numerical analysis employing the HS model and the MC model were compared with those from the literature [2, 5] and shown in Figs. 10 and 11.

Fig. 10
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Comparisons of settlement HS model vs empirical methods

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Fig. 11
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Comparison of settlement of MC model with empirical methods

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The analysis also indicates that the numerically predicted results match well with the empirical charts provided by [5] in the primary zone of influence, i.e., up to 25–30 m of distance. However, the settlement in the secondary zone of the influence zone (> 30 m) does not match the empirical charts because of the continuous dewatering adopted for the excavation in the present study. The settlement profile predicted by [2] envelopes the numerical values using both MC and HS model and also the settlement predicted from the charts [5] for the primary settlement zone. However, the numerical model employing site specific analysis indicates a high value of settlement in the secondary settlement zone which is mainly attributable to the proposed continuous dewatering during future excavation. This shows that the empirical methods underestimate the settlements in secondary settlement zone which is mainly due to the effect of continuous dewatering. The settlement predicted from the numerical analysis for the different soil models shows a wide variation of 243–397 mm and is not within the permissible limits of 25–40 mm generally adopted for the design of foundations. This order of settlement will affect the foundations of lightly loaded structures to be located near influence zone and other essential services required. Thus, even though the retaining wall that is already designed for strength and stability will assist the future excavation, the adjacent structures will have settlements beyond the permissible limits of 25–40 mm, which needs to be addressed. Also the study highlighted the effect of dewatering in settlement of secondary zone and inadequacy of stiffness of backfilled soil to control the settlements within the permissible limit.

Remedial Measures

As seen in the previous section, while carrying out future excavation using conventional retaining wall, settlement of already placed backfill with stiffness of 15,000 kPa is beyond the permissible limit Since these settlements can cause structural damages, remedial measures needs to be implemented while carrying out the future excavation to limit the settlement of adjacent soil mass within the permissible range of 25–45 mm. Commonly adopted methods to minimize the settlement are anchoring, strut loads and ground improvement to increase the stiffness properties of soil. In the present study, two analyses were carried out in which the first one considers only strut load and the second one a combination of strut and improvement of stiffness properties of already placed backfill soil. In the model developed and described in the previous sections, a strut load was applied after each stage of excavation. The apparent earth pressure was estimated following [6] and the strut load of 500 kN/m was applied at a distance of 2.5 m from top of the excavation (1st strut load) and subsequently at every 5 m distance from the first strut (2nd to 4th strut load). The 5th strut load of 450 kN/m is applied at a depth of 21.85 m below ground level. The struts need to be constructed after each phase of excavation before commencing excavation. The settlement of adjacent soil mass was evaluated from model for each stage of excavation shows that (Fig. 12) the settlement can be minimized with the application of strut load, however, still higher than the permissible limit of settlement at the last phase of excavation. The maximum settlement at the last stage of excavation with strut load is 67.8 mm at a distance of 13.4 m behind the excavation.

Fig. 12
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Settlement profile behind excavation for various strut locations

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Hence further additional measures are required to limit the settlements within the permissible limits. Towards this, ground improvements are to be taken up to increase the stiffness property of already placed backfill soil along with the application of strut loading. A parametric study was carried out by increasing the insitu stiffness of backfilled soil and settlement of adjacent soil mass was studied. The settlement at the final stage of excavation was found to be 48 and 39 mm for a stiffness value of 20,000 kPa and 25,000 kPa which is compared with that obtained from application of strut load (Fig. 13).

Fig. 13
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Settlement at the end of excavation after remedial measures

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The analysis of results given in “Discussion of Results” and the discussion of remedial measures in “Remedial Measures” shows that the settlement of adjacent soil mass during future excavation with the help of conventional retaining wall will be beyond permissible limits and additional measures like strutting and ground improvement to increase the stiffness of already placed backfilled soil is essential for limiting the settlements of adjacent structures. The region of additional treatment required is around 15 m deep for an area upto 20 m from the edge of retaining wall.

Conclusions

The current practice of deep excavation with the assistance of retaining wall which is being followed in Indian nuclear industry does not address the settlement of adjacent engineered backfilled soil mass. In this study efficacy of engineered backfilling in limiting the settlements during future excavation was evaluated and the major finds of the study are

  • Stiffness properties of engineered backfill soil evaluated from conventional laboratory and field tests underestimate the stiffness of backfilled soil and the actual stiffness of engineered backfill soil is 50% higher than the field value as evaluated from back calculations performed in numerical analysis matching the field and model displacements.

  • Settlements predicted from empirical formulations predict the settlements accurately in primary settlement zones. However, the settlement predicted in the secondary settlement zone is higher than that from empirical formulations due to site-specific dewatering.

  • As the settlement predicted using conventional MC model is smaller than that obtained from HS model, the study also indicated the requirement of advanced models accounting non-linear behaviour of soil and unconservatism involved in using conventional MC model is predicting settlements.

  • As the settlements predicted in both the primary and secondary zone of settlements are higher than that of permissible values, these values needs to be limited to ensure the stability of structures supported on this backfilled soil.

  • Additional improvement methods like placement of struts and improving the stiffness of soil to an extent of 25,000 kPa for a depth of 15 m to an extent of 20 m is essential to limit the settlements within the permissible limit of 40 mm.

  • However, an instrumentation scheme is to be deployed during future excavation to observe the settlement of adjacent soil mass so that remedial measures and corrective actions can be taken at each stage of excavation.