*2.1. X-linked Syndromic Mental Retardation*

Germline alterations of the ubiquitin-conjugating enzyme E2 A (*UBE2A*) gene coding for the ubiquitin-conjugating enzyme 2A [40] are associated with X-linked syndromic mental retardation, a disease characterized by abnormal intellectual development and dysmorphic features, such as large head, wide mouth, almond-shaped eyes, and onychodystrophy. Patients with this syndrome carry intragenic point mutations or microdeletions of *UBE2A* or larger Xq24 deletions encompassing the *UBE2A* region [45,46]. The *Ube2a* knockout mice present defects in spatial learning tasks, but no other severe phenotypes [81]. This indicates that the mouse model only partially recapitulates the phenotype observed in patients suffering from *UBE2A*-linked mental retardation.

Molecular mechanisms linking *UBE2A* mutations to neurodevelopmental disorders are not fully understood. A study focused on the fly *UBE2A* homolog *Rad6A* implicates defective mobilization of the E3 ligase PARKIN as a cause of abnormal vesicle trafficking and dysregulated clearance of dysfunctional mitochondria in neurons. These abnormalities are suspected to contribute to the neurodevelopmental phenotype in patients with *UBE2A* deficiency syndrome [82]. On the other hand, one of the best-described functions of UBE2A is to promote monoubiquitination of proliferating cell nuclear antigen (PCNA) in a complex with the RING-Type E3 ubiquitin transferase RAD18. PCNA monoubiquitination can be switched to polyubiquitination in the presence of helicase-like transcription factor (HLTF). Two distinct branches of the DNA damage tolerance pathways are

activated by either mono-, or polyubiquitinated PCNA to rescue a stalled replication fork and ensure continuous DNA synthesis. Monoubiquitinated PCNA favors low-fidelity translesion DNA synthesis, whereas PCNA polyubiquitination induces high-fidelity homology-dependent DNA repair [42]. Defects in DNA damage response could explain some of the developmental aspects of X-linked mental retardation [43,44]. *PCNA* mutations in patients also cause ataxia-telangiectasia-like disorder-2, a disease showing development delay [83]. Moreover, the disease-associated G23R mutation of UBE2A disrupts the binding site for RAD18 [84]. This suggests that the UBE2A/RAD18/PCNA axis might be at least partially responsible for the pathogenesis in mental retardation (Figure 1A).

In complex with the E3 ligase ring finger protein 20 (RNF20), UBE2A also promotes the monoubiquitination of histone H2B [41]. Monoubiquitinated H2B not only regulates global transcriptional elongation [85,86] but also plays an essential role in the regulation of inducible genes involved in cell di fferentiation [87–89] and inflammation [90]. However, a potential role of UBE2A-mediated monoubiquitination of H2B in mental retardation is still to be elucidated.

**Figure 1.** The role of monoubiquitination in human diseases. ( **A**) Ubiquitin-conjugating enzyme E2 A (UBE2A) loss of function impairs proliferating cell nuclear antigen (PCNA)-mediated DNA repair that partially explains developmental aspects of X-linked mental retardation. (**B**) Parkinson Protein 2 (PARK2) regulates mitophagy and apoptosis by controlling poly- and monoubiquitination of voltage-dependent anion-selective channel 1 (VDAC1). Dysregulation of VDAC1 ubiquitination contributes to the development of Parkinson's disease. ( **C**) Mutations in Fanconi Anemia complementation group L/T (*FANCL*/*T*) lead to DNA repair deficiency. Monoubiquitinated FA group D2 (FANCD2)/FA complementation group I (FANCI) heterodimer binds DNA, whereas deubiquitination of FANCD2 allows to re-start DNA replication. ( **D**) The Rat sarcoma (RAS) GTPases are monoubiquitinated by the Leucine Zipper Like Transcription Regulator 1 (LZTR1)- Cullin 3 (CUL3) complex, inhibiting RAS association with the membrane and activating of RAS signaling. Hyperactivation of the mitogen activated protein kinase (MAPK) caused by LZTR1 loss of function leads to the Noonan syndrome phenotypes. (**E**) Casitas B-lineage lymphoma (CBL)-mediated monoubiquitination of SH3 domain-containing kinase-binding protein 1 (SH3KBP1) recruits active epidermal growth factor receptor (EGFR) for degradation. *CBL* mutations lead to up-regulation of the MAPK pathway that partially explains its contribution to the development of Noonan syndrome. (**F**) Mutations in E3 ubiquitin-protein ligase Itchy (*ITCH*) impair the monoubiquitination of survival motor neuron (SMN) that dysregulates translocation to Cajal bodies and a ffects post-transcriptional regulation of gene expression, linking ITCH loss of function to the development of spinal muscular atrophy.


**3. United States patent and trademark office**

An important difference of the United States patent system compared to the Brazilian system, for example, is the fact that several are the possible paths in the USPTO after a second or subsequent rejection of some claims in a patent application. The applicant may file a request for continued examination (RCE),9 file for an amendment after final (AAF),10 abandon the application, apply for a continuationin-part,11 or file a request for appeal [7, 8].

Appeals in the United States patent system aim to review objections related to the patentability of claims in a patent application and may be filed after a second action by the office rejecting some of these claims. These procedures, at the administrative level of the USPTO, are conducted by three administrative judges of the Patent Trial and Appeal Board (PTAB), which is the second-instance administrative body responsible for patents in this office. These judges must be people with technical and legal knowledge. The duties of this Board are: (a) to review decisions rejecting claims in patent applications; (b) to review reexamination appeals;12 (c) to conduct derivation proceeding,13

9 Request for Continued Examination (RCE). This is a request to reopen the processing of the patent application yet at first instance through the payment of a specific fee, where the examiner will evaluate the changes in the claims and the arguments presented [8].

10 Amendment after final (AAF). It is the filing of amendments to claims. This procedure, unlike the RCE, is free of charge; however, the examiner has little time to examine it [8].

11 Continuation-in-part. A request for continuation of an original patent application, where a new matter or new claims are included in the application. This procedure does not end the first-instance proceeding for the new matter included.

12 Reexamination. Procedure that can be requested by anyone, at any time during the term of a patent, aiming at reviewing a patent already granted.

13 Derivation proceeding. This is a trial proceeding conducted at the Board to determine whether (i) an inventor named in an earlier application derived the claimed invention from an inventor named in the petitioner's application, and (ii) the earlier application claiming such invention was filed without authorization.

(d) to conduct *inter partes* review;14 and post-grant review.15 Each of these procedures is conducted by a jury composed of at least three members of the board, who shall be appointed by the Director [9].

The USPTO's appeal procedure begins with the submission of a notice of appeal and payment of the required fee within no more than six months after the decision denying the patentability of the claims. Then, within a period of two months, which can be extended in exceptional situations for up to five months, the appeal brief must be filed with the office, including, in addition to the applicant's arguments regarding each of the objections raised by the examiner, other information, such as the name of the interested party, a concise explanation of the matter defined in each independent claim that has been rejected, and an appendix containing a copy of the claims under appeal [10].

A pilot program in progress at the USPTO provides the possibility of filing a pre-appeal request with the notice of appeal, where the applicant may request a review of the decision rejecting the claims. This request may not exceed five pages and must provide a series of succinct, concise, and focused arguments explaining the reasons why the review is being requested. This request is assessed by a panel of three examiners, including the examiner responsible for the decision to reject the claims. There are four possible outcomes for this review: (a) the request will continue under appeal, as the reasons were not sufficient; (b) the first-instance proceeding will be reopened; (c) the claims are accepted and, (d) the pre-appeal request does not meet the requirements and is disregarded [9].

After the appeal brief is filed with the USPTO, it does not immediately enter the jurisdiction of the appeal board. Appeals are first examined at an appeal conference, whose participants are the examiner responsible for the decision to reject the claims him/herself, his/her supervisor, and a third examiner who is able to consider the merits of the matter under appeal. After this procedure, the examiner may introduce new objections to reject the claims and reopen the case at first instance, may reverse the decision denying the claims, or may maintain the appeal, preparing a written response to the reasons for appeal. This reply must discuss all grounds for the challenged decision, enabling the examiner to add new objections to the request, if applicable.

After filing a notice of appeal with the USPTO, the filing of amendments to the application is not a matter of right. For acceptance of such amendments, two deadlines shall be considered and certain criteria shall be met. In the case these amendments are filed on the date or after the notice of appeal and before the appeal brief, such amendments may be accepted, as long as: (a) they cancel claims or comply with any requirement of form expressly set forth in a previous Office action; (b) they present rejected claims in better form for consideration, (c) they show good and sufficient reasons why the amendment is necessary and was not earlier presented.16 Amendments filed on or after the date of filing a brief may not make substantive amendments to the claims, but may be admitted: (a) to cancel claims, where such cancelation does not affect the scope of any other pending claim in the proceeding, or (b) to rewrite dependent claims into independent form.17 Amendments to the application are not accepted after the appeal enters the jurisdiction of the PTAB [10].

Like the filing of amendments to the application, the filing of new evidence or testimonies for inclusion in the application follows certain rules. If these amendments are

14 Inter partes review. It is a trial proceeding conducted at the Board to review the patentability of one or more claims in a patent based on novelty and inventive step and only on the basis of prior art consisting of patents or printed publications.

15 Post-grant review. It is a trial proceeding conducted at the Board to review the patentability of one or more claims on any ground and any matter of the prior art.

16 37 CFR § 1.116.

17 37 CFR § 41.33.

#### *Comparative Analysis of Appeal Procedures in the European, American and Brazilian Patent… DOI: http://dx.doi.org/10.5772/intechopen.98413*

filed at the time of or after filing the notice of appeal, but before the appeal brief, these amendments may be accepted if the examiner understands that: (a) such evidence and/or testimonies surpass all objections under appeal; (b) show good and sufficient reasons as to why the amendment is necessary and was not previously filed. In all other cases, they shall be rejected. New evidence may not be filed together with the brief.

In case a new objection to the application is added to the examiner's written response to the appeal brief, the appellant has two options: apply for a reopening of the proceeding at first instance or request that the appeal is maintained by filing, within two months, a reply to the examiner's opinion. Only after expiration of the deadline to file the reply with the office, the appeal is forwarded to the PTAB. In this reply, no amendments to the claims or new evidence are admitted.

In the American patent system, the appellant may request oral proceedings in circumstances in which the appellant thinks it is necessary or desirable for proper understanding of the appeal. This request is made in writing and shall be accompanied by the payment of a fee, within two months of the date of the examiner's response to the appeal brief, or on the date of filing of his/her reply.

After submission of the reply to the examiner's opinion, with or without oral proceedings, the three PTAB judges shall render the final decision, issuing a written decision, whose outcomes may be: (a) affirmance, a situation in which the examiner's decision of rejecting the claims is fully confirmed; (b) affirmance-in-part, a situation in which the examiner's decision of rejecting at least one of the claims is confirmed, but not all; (c) reversed, when the decision of denying the claims is not confirmed, and (d) new grounds for rejection, a situation in which the PTAB judges understand there are additional reasons for which at least one of the claims is not patentable. In this last case, the appellant has two options: apply for reopening of the proceeding at first instance and file amendments or evidence deemed necessary, or request a review of the case. In the review, the appellant shall define specifically where he or she believes the appeal board was mistaken.

**Figure 2** shows a schematic presentation of the procedures for appeal against rejection in the USPTO.

#### **Figure 2.**

*Schematic representation of the procedure for appeal against rejection in the USPTO.*


applying a broadband frequency sweep in the range 1.6−4.2 kHz. Figure 4a shows the space-frequency analysis of the experimental data. Depending on the frequency, waves stop at different spatial positions, corresponding to the band gap opening.

Moreover, we notice that the amplitude and the wavelength of the mode shapes decrease inside the array, until the amplitude vanishes in correspondence of the position of the resonating element, which is well predicted by numerical results (dashed white line). We then quantify the advantages of such mechanism for energy

**Fig. 4** Space-frequency analysis of the experimental data superimposed to numerical predictions (dashed white line) from dispersion curves. **b** Open circuit output voltage for the graded array and single cell configuration (i.e. the same harvester but without the graded metamaterial), corresponding to the input excitation frequency marked with the red star in (**a**). The graded metamaterial amplifies the output voltage, i.e. the energy harvesting capabilities of the device

harvesting by placing piezoelectic PZT-5H patches (*Ep* = 61 GPa, ν*p* = 0.31, ρ*p*= 7800 kg/m3, dielectric constant ε*T* 33 ε0 = 3500, and piezoelectric coefficient *e*31= −9.2 C/m2) at the position of the 7th cell, denoted with the red star in Fig. 4a.

Figure 4b shows the mean output open circuit voltage for the single cell (i.e. the same resonators but without the graded metamaterial), and graded array, normalized by the measured input velocity, to make sure that the results are displayed under the same conditions. We observe that the graded array gives a mean normalized peak voltage of 41 Vs/m which is 56% higher than the single cell. We notice that such peak is reached with a delay t of approximately 1.3 ms, which is justified by the smooth reduction of the group velocity inside the array.

#### **3 Conclusions**

In conclusion, potential advantages in using graded metamaterials for efficient elastic energy confinement have been demonstrated both numerically and experimentally. The graded metamaterial capability of slowing down waves enables a strong energy transfer to the resonators, which then reflects in enhanced energy harvesting performances. This mechanism can be adopted to create more efficient energy harvesting systems able to self-power, or at least compensate, the power consumption of small electronic devices, using ambient waste energy from vibrations. The possibility to substitute batteries and their chemical waste, with fully sustainable vibration-based energy harvesting systems can play an important role toward Goal 7 of the SDGs for the next generation of affordable and clean energy sensors and small electronic devices.

**Acknowledgements** I would like to acknowledge my supervisors Prof. Alberto Corigliano, Prof. Raffaele Ardito, Prof. Francesco Braghin and Prof. Richard Vaughan Craster for their help throughout this thesis. This research was funded by the H2020 FET-proactive project Metamaterial Enabled Vibration Energy Harvesting (MetaVEH), under Grant Agreement No. 952039.

#### **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Limit Analysis for Masonry Vaults and Domes of Cultural Heritage**

**Maria Chiara Giangregorio**

**Abstract** The scope of this dissertation is the study of masonry shell structures of cultural heritage through limit analysis. The final aim is to set up computational tools, integrated with experimental observations, for use in the interpretation of observed crack patterns and to study the safety of these structures. The kinematic approach is developed to calculate the limit load and the three-dimensional collapse mechanism of symmetric and skew barrel vaults. The effect of structural strengthening is examined as well. A static discrete model is developed for double curvature and polygonal domes, applying equilibrium at the blocks and strength criteria at interfaces. This allows to study a cracked masonry dome, evaluating the collapse multiplier and mechanism by considering the shell flexural response mechanism. This is used also to analyse the actual behaviour in membrane regime of a dome on reaching the maximum load before cracking. Finally, the polygonal dome supporting a tower of the Chiaravalle Abbey in Milan is analysed.

#### **Graphical Abstract**

**Keywords** Cultural heritage · Limit analysis · Upper bound · Lower bound · Vault · Dome · SDGs 11

M. C. Giangregorio (B)

e-mail<EMAIL_ADDRESS>
Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

#### **1 Protect and Safeguard the word's Cultural Masonry Heritage**

#### *1.1 Introduction*

Among the 17 Sustainable Development Goals (SDGs) this dissertation concerns the 11th goal: 'Make cities inclusive, safe, resilient and sustainable'. The focus is on the target 11.4 'Strengthen efforts to protect and safeguard the world's cultural and natural heritage'. Here the method of limit analysis is used for the study of historical masonry structures concerning cultural heritage such as domes and vaults. In order to do that, the first aim of the work is to develop simple discrete algorithms based on the two theorems of limit analysis (static and kinematic theorem). The models introduced are here shown and used for the structural study of barrel vaults, rotational domes, and polygonal domes. These algorithms use optimization of a load multiplier, to calculate the collapse multiplier and the collapse mechanism, but also the multiplier leading to crack initiation. The study of the actual state of the structure with the static method, that allows to find an equilibrated solution based on membrane behaviour, is one of the aims of the work. This is possible by considering the tensile strength at the block interfaces. To consider the three different states of the structure (un-cracked, cracked and collapse) allows a better understanding of the safety state of the structure. It must be underlined that the collapse of cultural heritage structures is strictly related to the cracked state. The focus on the geometry and its proportion reported in the work aims at understanding the role they play in the structural behaviour. Thanks to the simplicity of these models, it was possible to compare different geometries, load conditions and strength criteria, without any relevant computational effort. Two interesting typology of dome was investigated: hemispherical and polygonal domes. This allows to analyse the different behaviour of single and double curvature shells. This work is part of a research project that aims at developing an interdisciplinary methodology for structural analysis of historical masonry elements, to understand the causes of existing damage, verify the structural safety and study possible structural strengthening. This is pursued by using an integrated method of limit analysis with the survey and measurement of geometry, considering deformations, crack patterns and other damage. The multidisciplinary method includes the study of historical construction phases, the analysis of the actual configuration, with the survey of the building and the annotation of the damage, and the structural analysis, with the suggested method of limit analysis.

#### *1.2 The Geometry Considered*

In the ensemble of cultural masonry heritage, different shell shapes give different structural response. Since there is a close correlation between the geometry of a surface and its main failure mechanisms, the focus on geometry is a topic of interest. A vault can be obtained by translation of the arch, as in barrel vaults (Fig. 1.) or by revolution around a vertical axis, as in the hemispherical dome (Fig. 2). The different typologies of vaults can be subdivided into "simple vaults" and "composite vaults". The "simple vaults" are those where the surface does not have solutions of continuity because there is no point in which the curvature changes as: (i) Barrel vault, (ii) Hemispherical dome, (iii) Sail vault (deriving from the dome). The "composed vaults" are those realized through the intersection of two or more parts of a simple vault, so that the surface has several zones in which the curvature changes. In order to describe a composite vault, it is necessary to observe the elements obtained by sectioning a barrel vault along the two diagonals. There will be two "spindles" and two "nails". If four nails are combined a cross vault is obtained, while with four spindles a cloister vault is obtained. The typical typologies are: (i) Cross vaults/groin vault, (ii) Cloister vaults, (iii) Ribbed vaults (cross vault with ribs) (iv) Polygonal vaults, (v) Stellar vaults, (vi) Fan vaults. In this work the focus is on: (i) barrel vault, (ii) dome, (iii) polygonal dome.

#### *1.3 Barrel Vault*

The barrel vault (Fig. 3), is the simplest typology of vault and is the base for many vaults of more complicated shape. It is composed of the translation of an arch in its

**Fig. 3** Barrel vault, with square base and rounded arch

perpendicular direction. It is mostly used as coverage of monumental buildings of a civil and religious nature.

The barrel vault has a semi-cylindrical intrados surface, but the vertical section can be ogival section if it is based on a translation of a pointed arch, but also parabolic or any other curved shape. In plan it is possible to have different quadrilateral shapes, and two opposite parallel walls are the typical vertical supports. A barrel vault subjected to self-weight only has "arch behaviour", but with different load positions or in presence of soil settlements, it could have a different behaviour, such as torsion. If the limit stress is reached, cracks will appear in the direction of the tension, on the intrados or on the extrados, as in the hinged mechanism for the arch.

#### *1.4 Hemispherical Dome*

The geometry of a dome is a revolution membrane generated by an arch that rotates around its central axis. It is a convex rounded vault with a horizontal section that may be circular elliptical or polygonal. In vertical section the dome may be hemispherical (Fig. 4), circular, parabolic, or partly elliptical. If the horizontal section is a circle and the vertical section is a round arch, the dome assumes the form of a portion of a sphere and is called hemispherical dome. A dome may be smooth or coffered as in the famous case of the Pantheon in Rome, where the dome is supported upon walls of circular plan. One of the main characteristics of a dome with respect to vaults is that of minor thickness to the other dimensions of the structure. In membrane static solution only internal forces, such as the meridian and parallel, lying on the tangent plane are considered. In this behaviour the compression along the meridians grows from the crown to the base. The parallels are compressed in the key and in tension at near to the springer, in a hemispherical dome the change is at 51°50- ° if a dome subjected to self-weight is considered. For axial symmetrical load a hemispherical dome, along the same parallel, has constant stresses.

**Fig. 4** Hemispherical dome

The problem of the stability of a dome is an ancient topic, due to the tensional state that determines lack of stability over time; when the tensile strength is overcome, cracks will appear at the base of the dome along the meridians. In such cases there is no more membrane behaviour, but if a series of half arches is considered, by dividing the dome into slices cut along the meridian plane, and if it is possible to draw a thrust line inside every arch, the dome can be considered safe [14]. The simplification of the behaviour of a cracked dome by dividing it into a series of arches was firstly developed by Poleni for his study on the Vatican Dome [20], who made one of the first examples of a drawing of crack pattern on a dome was applied to the dome of San Pietro in Rome. Here an algorithm is formulated that allows to analyse domes in their actual state and in their collapse state, considering different configurations. These different configurations concern geometrical parameters such as span, thickness, number of slices, different load conditions, also considering the effect of strengthening.

#### *1.5 Polygonal Dome*

The polygonal domes (Fig. 5) are a very particular type of dome, divided into slices. Unlike simple domes, which have a double-curved structure, resembling the shape of a spherical surface, the slices of polygonal domes are single-curved and derive from the section of a cylindrical surface. They are called polygonal domes because if sectioned with a horizontal plane parallel to the floor, the resulting section has the shape of a regular polygon. This structure geometry is similar to a pavilion vault, but with more than four edges. As it was demonstrated in this work, these domes have the characteristic of concentrating the loads in the corners of the polygon, developing concentrated and pushing forces on pointed vertical supports, such as pillars. A support on the structural behaviour is given by the diagonal ribs, often present in the polygonal domes. These typologies of dome are little analysed, Flügge [10] proposed an infinitesimal equilibrium solution for a dome subjected to self-weight only. Here a discrete algorithm is formulated that allows to analyse polygonal domes in their actual

**Fig. 5** Polygonal dome

state considering different configurations. These different configurations concern geometrical parameters such as span, thickness, number of slices, different load conditions (Fig. 6).

**Fig. 6** Rotations and displacements considered in three-dimensional space

#### **2 The Limit Analysis Algorithms for Shell Structures**

#### *2.1 The Kinematic Algorithm Applied to Barrel Vaults*

With respect to the kinematic theorem of limit analysis applied to shell structures, the aim of this chapter is to study the behaviour of masonry shell structures in their collapse mechanism. The kinematic method of limit analysis is applied to a three-dimensional shell problem with a formulation inspired by 'discontinuity layout optimization' (DLO), that was formulated for plane plasticity problems [22]. The method was successfully used for geotechnical [22], plate and slab problems of arbitrary geometry [11], and on three dimensional problems [13]. Here the innovation is to use it to analyse shell structures, also considering the effect of structural strengthening. An application of the kinematic theorem of limit analysis to barrel vault problems is here addressed. The main results are related to: (i) identification of the collapse mechanism; (ii) identification of the ultimate load carrying capacity: analysis of the amount of live load that can be applied before structural collapse; (iii) analysing strengthened barrel vaults.

Different yield domains and different behaviour of the material are considered. A case with infinite compression strength, no tensile strength and no sliding as stated by Heyman [15]. Then tensile strength different from zero and even the non-symmetric behaviour of a reinforced vaults is contemplated, considering different values of tensile strength according to the different types of reinforcement used. The contribution of the friction angle, mostly in the case of a torsion mechanism is also considered. The plastic dissipation, investigated for reinforced vaults, is governed by three dimensional hinges coupled with normal displacements at the interfaces. Strength criteria formulated in terms of force are opportunely converted into a displacement flow rule to fulfil the formulation that characterizes the DLO method.

This kinematic algorithm, which involves the achievement of collapse, was validated thanks to experimental tests concerning masonry vaults collapse reported in articles that were found in the literature. Some experimental tests on collapse of masonry barrel vaults are considered the benchmark, in particular the barrel rectangular vault tested by Vermeltfoort [27] was considered, that was also used as benchmark for the numerical simulations of [19]. From these experimental tests even barrel vaults with skew arches were investigated, to validate the behaviour of collapse due to torsion. In addition, the experimental tests performed by Girardello [12] allow to validate the work on reinforced vaults, considering two different materials for strengthening.

#### *2.2 The Static Algorithm Applied to Rotational Domes*

A discrete model is formulated, based on the static theorem of limit analysis to analyse domes. The structure is divided into rigid blocks, with forces acting on the interfaces. The equilibrium is imposed at each block and a resistance criterion is imposed at each interface. Two different behaviours are considered, membrane behaviour to analyse the actual state and flexural behaviour to analyse the collapse state. The internal forces of redundant structure with crack initiation load multiplier and the collapse load multiplier with corresponding mechanism are obtained after a simplex algorithm imposed. It is possible to analyse the structural behaviour considering different variables, such as geometry, loads variations and the presence of a reinforcement. Two different typologies of shell are analysed: the rotational dome and the polygonal dome. The former has a double curvature and a circular base, while the latter has a single curvature, in zenith direction.

In the literature, regarding the hemispherical domes, the solutions of differential equilibrium equations based on membrane theory have been acquired for self-weight and a few other loading conditions [10]. Membrane theory considers the stresses acting on an infinitesimal element, considering meridian and hoop stresses, and shear forces tangent to the mid surface. In this work it is proven that it is possible to analyse these structures using a discrete model, applying the static limit analysis theorem. The focus here is on the interaction between the geometry of the dome and its structural behaviour. Double curvature domes, rotational domes with round arch and pointed arch shape, are analysed with the static model in their membrane behaviour (Fig. 7),

**Fig. 7** Scheme of a rotational dome block in membrane behaviour

focusing on the response related to the different geometries. Furthermore, with the same discrete algorithm configuration, and using a flexural approach (Fig. 8), rotational domes are analysed up to collapse, finding the corresponding load multiplier and the collapse mechanism.

#### *2.3 The Static Algorithm Applied to Polygonal Domes*

The analysis of polygonal domes is investigated, in their membrane behaviour, developing the static algorithm for polygonal domes that have straight line in the hoop force direction for their single curvature shell. Since the geometry of the surface between

double curvature and single curvature domes differs, consequently, the response of the structure to load is also different. With the aim of describing the membrane behaviour of polygonal domes some geometric characteristics have been modified in the static model. The focus here is on the interaction between the geometry of the dome and the structural behaviour (Fig. 9).

In the literature, Flügge [10] directly analyses the polygonal domes subjected to self-weight, solving the differential equations of the membrane state for the specific case. D'Ayala [9, 23] and Como [8] consider pavilion vaults, that have a similar structure with single curvature surface, starting from their geometric configuration as portions of cylinders that concentrate most of the part of the loads along the diagonal ribs. In the work of D'Ayala and Tomasoni [9], a theory was formulated, based on lower bound approach of limit analysis, for the structural analysis of pavilion vaults. The formulation includes an optimized solution that allows to find the optimal thrust surface of a vault by minimizing the distance between thrust surface and middle surface. A strength criterion with finite friction is considered among block interfaces considering 3D effects that develop in vaults of complex geometry such as pavilion vaults, in the angular parts where different surfaces are connected. In this dissertation, the membrane behaviour of a single curvature dome is analysed, in a structure divided into blocks, considering the thrust surface coincident with the middle surface, analysing the maximum load that could be reached before the

**Fig. 9** Reference systems for the dome section and the forces acting on a block of polygonal dome

structure begins to crack. At this point the discrete static algorithm is applicable to polygonal domes: (i) to evaluate the action of a dome on underlying structures for single curvature dome; (ii) to solve the problem of the equilibrium of the diagonal rib; (iii) to compare maximum forces with crack positions both for double curvature dome and for single curvature dome. In the existing case of Chiaravalle abbey in Milan described in [6] the work allowed to: (i) consider load different from the selfweight adding the load of a lantern tower; (ii) to analyse and compare the behaviour of a polygonal dome in membrane behaviour and in a cracked state, by the integration of the structural analysis and the crack pattern.

#### *2.4 Application to Real Case Studies*

Some analytical cases are considered in order to analyse the effect of the geometry on the structural response. Amongst the topics dealt with are: (i) different spans; (ii) dome based on a round arch or on a pointed arch; (iii) the difference derived from tapering i.e. a reduction of the section thickness of the dome; (iv) the effects of different load conditions, such as the presence of a lantern; (v) the effect of proper structural strengthening with circular tie rods. Some existing cases of rotational domes with a lantern are analysed: the churches of (i) Sant' Agnese in Agone in Rome [3, 17] (Fig. 10); (ii) San Nicolò l'Arena in Catania [17, 18] (Fig. 11); (iii) San Giorgio in Ragusa [16] (Fig. 12).

Then the polygonal dome of Chiaravalle abbey in Milan is analysed. In this case the weight of a lantern tower called Ciribiciaccola is analysed with surveys, drawings and 3D model, showing the importance of the integrated approach to understand the geometrical configuration. After the analysis of the crack pattern, it is possible to analyse the behaviour of this dome. The analysis of geometry and materials is used as input to be included in the discrete algorithm and the application to Chiaravalle abbey also shows the information deriving from the crack pattern for the structural

**Fig. 10** Sant'Agnese in Agone

**Fig. 11** San Nicolò L'Arena

**Fig. 12** San Giorgio

analysis. The analysis of the dome shells both cracked and un-cracked are analysed and compared in their different structural response. Finally, the equilibrium of the rib with radial wall is calculated to evaluate their contribution to the structural behaviour.

#### **3 Conclusions**

Two methods are used to analyse shell masonry elements for calculating the safety of the structure to ensure conservation, protect and safeguard of cultural heritage, to ensure the target 11.4 of the 11th goal of the 17 Sustainable Development Goals (SDGs).

The kinematic theorem of limit analysis is applied to a discrete model with simplex method of optimization that allows to calculate the collapse load and the mechanism for shell structures such as barrel vaults. It also allows to evaluate behaviour of a vault after an intervention of structural strengthening like reinforced with FRPM material. One advantage of the kinematic code is that only a few parameters are needed to obtain a response. Material properties considered as input parameter: (i) cohesion; (ii) friction angle; (iii) tensile strength. The innovation of this work with respect to the previous formulations of DLO are: (i) three-dimensional shell structure is studied; (ii) the effect of structural strengthening is considered. Different barrel vault shapes are considered: (i) round barrel vaults; (ii) ogive barrel vaults; (iii) lowered barrel vaults; (iv) skew barrel vaults. Dead and live loads in different positions are considered. Among the loads analysed: (i) uniformly distributed load; (ii) linear load; (iii) punctual force; (iv) inclined linear load. Regarding the boundary condition with four external boundaries, the available behaviour considered are: (i) rigid; (ii) symmetry plane; (iii) free.

In order to validate the formulation, the model is applied to experimental tests of vaults up to collapse. Close agreement with experimental examples Vermeltfoort [27] and homogenized limit analysis numerical solutions Milani [19] was obtained. Even in the case of reinforced vaults, a close agreement with Girardello [12] and Valluzzi [25, 26] was reached. Foreseen developments of the model are the design of optimal strengthening intervention for vaul ts, and the consideration of vertical movements at the supports of the vaults.

The static discrete algorithms for the membrane behaviour evaluate static regimes for masonry domes, of different typologies, considering the presence of a minimum tensile and shear strength before the structure begins to crack. Through the optimized solution, the static algorithms return the value of the forces acting on the structure, and the value of the multiplier for which the load for first cracking is reached. New possibilities arise to safeguard the artistic heritage. The first cracks do not lead to collapse, which to occur requires a load such as to trigger a mechanism, with an adequate number of cracks related to membrane forces and hinges related to the flexural regime.

The collapse, with load multiplier and collapse mechanism, is also considered with a model including flexural behaviour response. The analyses allow to consider the behaviour of a dome under different conditions, with and without cracks.

The fact that the algorithms consider the strength of the material allows us to comprehend the contribution of restoration interventions involving reinforcement on the dome. A typical example of reinforcement is represented by the traditional iron tie rods and by the more modern strips of composite material in which fibres with very high tensile strength are added to a mortar matrix that strengthen the structure. Moreover, the design of proper circumferential strengthening can be studied, to avoid cracking during intervention woks.

The model shows that with the same algorithm structure and some punctual modification different geometries can be analysed and compared. Considering single or double curvature domes, this feature modifies the response of the structure to loads and the positions of weight transfer. The role of geometry analysed shows the different response given by a double-curved dome, which distributes the load over the entire support surface, and a single-curved dome, which with to the development of shear forces concentrates the weight on the diagonal ribs.

The discrete algorithm allows: (i) to calculate the multiplier value, beyond which the structure cracks; (ii) to calculate collapse multiplier and mechanism in flexural regime; (ii) to consider different load conditions; (iv) to consider the performance of the structure in the presence of structural reinforcement; (v) to obtain, with limited input data, the forces acting on the boundaries of hyper-static structures, which often require very long and complex analyses; (vi) the discrete formulation allows to change the geometry of the structure quickly by the modification of only a few parameters, this allows to compare different geometries and configurations, thus considering the role of proportions in the design of ancient structures; (vii) the simple solution obtained can be used as benchmark for more complex analysis like Finite Element Model [2].

Amongst further future developments it will be possible to focus on non-axial symmetric conditions, such as effect of soil settlements or variable lateral loads, due to wind effect or seismic events.

**Acknowledgements** I would like sincerely to acknowledge my supervisor Professor Dario Coronelli and my co-supervisor Professor Giuliana Cardani for their help throughout this thesis and this research. I wish to extend my special thanks to Professor Matthew Gilbert from Sheffield University, Professor Thomas Boothby from Penn State University, and Professor Patrick Bamonte from Politecnico di Milano.

#### **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Displacement-Based Design of Geosynthetic-Reinforced Pile-Supported Embankments to Increase Sustainability**

#### **Viviana Mangraviti**

**Abstract** Although the construction of concrete piles has a relevant environmental footprint, they are commonly used to reduce settlements of embankments on soft soil strata. A more sustainable choice to further reduce settlements (and, consequently, the number of piles) is to place geosynthetics below the embankment. However, existing design methods cannot calculate settlements at the embankment top and cannot be used to optimise the number of piles in a displacement-based design. In this note, an innovative model for assessing settlements at the top of Geosynthetic-Reinforced and Pile-Supported embankments induced by the embankment construction process is presented and validated against finite difference numerical analyses. The model is used to optimise the design of both piles and geosynthetic, and applied to a practical example, where the mass of CO2 saved by designing geosynthetics to reduce the pile number.

#### **Graphical Abstract**

**Keywords** Geosynthetic-reinforced and Pile-Supported embankments · Displacement-based · SDG 9 · Sustainability · CO2

V. Mangraviti (B)

Chalmers University of Technology, 412 96 Gothenburg, Sweden e-mail<EMAIL_ADDRESS>
Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy © The Author(s) 2022

M. Antonelli and G. Della Vecchia (eds.), *Civil and Environmental Engineering for the Sustainable Development Goals*, PoliMI SpringerBriefs, https://doi.org/10.1007/978-3-030-99593-5\_7

#### **1 Introduction**

The expansion of urban areas featuring the last century resulted in the exploitation of increasingly large areas of territory, leading to deleterious impacts on the environment. Civil engineering is immensely contributing to the consumption of global energy reserves along with the severe exploitation of raw materials such as gravel, sand, and water [1]. Furthermore, the greenhouse gas emissions due to the production of concrete structures compared to both steel and wood structures is the highest [2]. For this reason, at least 2 of the 17 Sustainable Development Goals (SDGs) defined by United Nations (UN) in 2015 (i.e. both SDGs 9, "industry, innovation and infrastructures", and 11, "sustainable cities and communities", in Johnston [3]) can be linked to civil engineering.

In a context where all engineers can have a major influence towards a more sustainable development, geotechnical engineering has a crucial role in influencing the sustainability of a project. In fact, according to Abreu et al. [4], geotechnical engineering is one of the key contributing fields to sustainable development, since it faces a challenging dichotomy between delivering project goals (environmental, economic, and social) and maintaining sustainability. In fact, from a practical point of view, the exploitation of increasingly large areas of territory has led also to the construction of infrastructures under difficult geological and geotechnical conditions, requiring geotechnical engineers to find new and not always "environmentallly friendly" solutions. As an example, embankments for major infrastructures are more often realised in areas where soils are deformable, and to avoid unacceptable settlements, concrete piles are commonly employed as settlement reducers. Such "geo-structures", composed by embankment, foundation soil and concrete piles, are named Conventional Pile-Supported (CPS) embankments. The rigid inclusion induces the development of the "arching effect" within the embankment soil, reducing the portion of embankment load transferred to the soft soil, while stresses flow towards the piles, and consequently alleviating differential settlements. Depending on both the overall length of the infrastructure to be realised and the mechanical properties of the ground to improve, CPS embankments may require the installation of a huge number of concrete piles along different kilometres of infrastructure, leading to a huge outflow of both economic and environmental resources.

To further reduce settlements at the top (where infrastructures are placed) of CPS embankments, geosynthetic layers can be placed below the embankment. In the literature, Geosynthetic-Reinforced and Pile-Supported (GRPS) embankments were studied by several authors [5–11], and geosynthetics were found to effectively increase the transfer loads towards the piles, leading to several advantages: (i) a decreased number of inclusions (piles) needed; (ii) faster construction, and (iii) better control of differential settlements associated with soft soils. As a consequence, for equal admissible settlements at the embankment top, GRPS embankments need a fewer number of piles than CPS embankment, reducing the Embodied Carbon (EC, referring to carbon dioxide emitted during the manufacturing, transport, construction and the "end of life" of a material) due to the use of concrete.

Unfortunately, due to the lack of simplified methods, nowadays the design of GRPS embankments under a displacement-based perspective can only be done by using advanced numerical methods. In fact, the current design guidelines for GRPS embankments issued by several countries [12–15], adopt approaches based on the limit-equilibrium method that are not suitable neither to estimate settlements at the top of the embankment nor to ensure the serviceability of the geo-structure over its all lifetime [16]. In fact, these equilibrium arching models could possibly lead to an overestimation of the number of piles needed representing, from a sustainability perspective, a waste of both energy and resources. Nevertheless, to reach SDG 9, a more sustainable design perspective needs to be developed and spread in the next years.

With the aim of providing a more effective displacement-based design tool for GRPS embankments, Mangraviti et al. [11, 17] proposed an upscaled constitutive relationship to evaluate both differential and average settlements at the top of the central part of the embankment. The model was conceived as an extension of the one proposed by di Prisco et al. [18] for CPS embankments and derives from the interpretation of the results of a series of Finite Difference (FD) numerical analyses focusing on the construction process under drained conditions of the embankment.

In this chapter, the GRPS embankments capability to deform less than CPS embankments is firstly discussed by means of FD numerical results, expressed in terms of evolution of both average and differential settlements at the top of the embankment during construction. The upscaled constitutive relationship from Mangraviti et al. [17] is then shortly described and used as a tool to optimise the design of both piles and geosynthetic layer in a direct displacement-based perspective. Optimise the design means to employ the number of piles strictly necessary to undergo an admissible settlement at the top and, therefore, to achieve a more sustainable design, reducing EC.

The text is structured as it follows: in Sect. 1 the FD numerical model is presented and the results for both CPS and GPRS embankments are discussed. In Sect. 2 the constitutive relationship is briefly introduced and compared against numerical results. In Sect. 3 a non-dimensional chart to optimise the design of both piles and geosynthetics is provided and used to solve a practical example, where the EC for both CPS and GRPS embankments are calculated and compared.

#### **2 Numerical Model**

In the most general case, the design of both CPS and GRPS embankments is a three-dimensional problem. Nevertheless, when the embankment transversal width is significantly larger than its height, side effects may be disregarded and only one central axisymmetric cell can be considered as representative of the mechanical behaviour of the central part of system (Fig. 1a). The cell, whose diameter is equal to the spacing (s) between piles, includes: (*i*) the pile of length *l* and diameter *d*, (*ii*) the soft foundation soil, (*iii*) the embankment, whose height, *h*, evolves during

**Fig. 1 a** Problem geometry and representative axisymmetric cell; **b** numerical model

construction and (*iv*) the geosynthetic layer. The origin of both radial and vertical coordinates (*r* and *z* respectively) is in the centre of the pile top (Fig. 1a).

The problem has been numerically modelled by means of the finite difference numerical code FLAC3D [19]. Due to axisymmetry, only one quarter of the representative cell has been considered (Fig. 1b). The concrete end-bearing has been modelled as an elastic element. The mechanical behaviour of both the embankment and the foundation soil was modelled by means of an elastic-perfectly plastic constitutive relationship with a Mohr-Coulomb failure criterion and a non-associated flow rule. An elastic membrane element, characterised by axial stiffness *J*, has been used to model the reinforcement. When *J* = 0, the case of CPS embankment is obtained. Smooth interface elements were introduced between the pile and the foundation soil, whereas frictional interface elements were used between the geosynthetic and the soil. Normal displacements are not allowed on the lateral boundary and at the base of the domain.

To reproduce the construction process of the embankment, the numerical analysis has been subdivided in several stages. Each stage corresponds to the construction of 25 cm thick layer of the embankment under drained conditions. Therefore, the geometry of the spatial domain progressively evolves, adding at each stage a new layer of elements at the top of the model.

Even though a parametric study was conducted [11], for the sake of brevity, the results concerning only one reference geometry (*s* = 1.5 m, *d* = 0.5 m and *l* = 5 m) for different values of geosynthetic axial stiffness are hereafter illustrated in order to highlight the effectiveness of the geosynthetic layer in reducing settlements at the top of the embankment. The mechanical parameters used for the reference case are reported in Table 1. The dilatancy angle was found not to affect the mechanical processes of the system, although a slightly decrease in both average and differential settlements is observed within the embankment (the results are here omitted for the sake of brevity).

During the first step of construction, plastic strains develop in a narrow zone close to the top corner of the pile (defined as "process zone" in [18, 20], see Fig. 2). The evolution of this yielded zone is described by the process height *hp* and when *hp* = *h*\* the plastic zone stops evolving.

According to di Prisco et al. [18], the mechanical response of the geo-structure can be described by using the following non-dimensional variables:

**Table 1** Mechanical properties for the reference case

**Fig. 2** Evolution of shear plastic strain during the construction process

$$H = h/d\tag{1}$$

$$U\_{t,p} = \frac{u\_{t,p}}{d} \frac{E\_{\text{oed},f}/l}{\chi} \text{ and } U\_{t,f} = \frac{u\_{t,f}}{d} \frac{E\_{\text{oed},f}/l}{\chi} \tag{2}$$

$$U\_{t, \text{diff}} = U\_{t,f} - U\_{t,p} \text{ and } U\_{t, \text{av}} = \frac{U\_{t,f} \left(S^2 - 1\right) + U\_{t,c}}{S^2} \tag{3}$$

where *ut*, are the average displacement at the top of the embankment, being the subscripts - = *p* and *f* when referring to pile (i.e. settlements and stresses for 0 *<r<d*/2) and foundation soil (*d*/2 *<r<s*/2) respectively. *Ut*,diff and *Ut*,av are the non-dimensional differential and average settlements at the top; *S* = *s*/*d* is the non-dimensional spacing; *E*oed,*f* is the foundation soil oedometric modulus and the embankment unit weight.

The numerical results in Fig. 3 are plotted in non-dimensional planes where the system response was found to be uniquely defined if the non-dimensional geometrical ratios (*S* = *s/d*, *L* = *l/d*), the non-dimensional stiffness ratio (*E*oed*,e/E*oed*,f* , being *Eoed,e* the embankment soil oedometric modulus) and the embankment soil failure parameters (friction, φ- *e*, and dilatancy angle, ψ*e*, values) are kept constant. Due to the high difference in stiffness between piles and surrounding soil, differential settlements developing at the embankment base propagate to the top (*Ut*,diff > 0 in Fig. 3a). When *H* is sufficiently large (*H* = *H*\* = *h*\*/*d*, i.e. values highlighted with filled black rectangles in Fig. 3), differential settlements at the top of the embankment stop increasing, whereas average settlements continuously increase (Fig. 3b). As a consequence, any increase in load (e.g. the construction of the infrastructure above the embankment) for *H>H*\* will not induce any increment of differential settlement in the transversal direction (*r* in Fig. 1), meaning that *H*\* in *r* − *z* plane coincides with the height of the "plane of equal settlements", defined as the locus where the increment of differential displacements is negligible. On the contrary, *Ut*,av continues to increase even for *H>H*\*, meaning that differential settlements in the longitudinal (*y* in Fig. 1a) direction increase. Therefore, *H*\* is a fundamental value to define the mechanical behaviour of the system when further loaded.

Due to the definition of non-dimensional variables (Eq. 3), the dashed lines inclined 1:1 in Fig. 3a,b represent the case of pile stiffness coincident with the foundation soil one and of *J* = 0 (i.e. nor piles neither geosynthetic are placed). The distance between *Ut*,av and the 1:1 line is a measure of the effectiveness of both piles and geosynthetics as settlements reducers. The presence of the geosynthetic further reduce settlements with respect to the *J* = 0 case (Fig. 3a, b) meaning that, given a fixed value of settlement, less piles are needed when a geosynthetic layer with larger *J* is used. A direct connection between pile spacing (strictly related to the number of piles) and geosynthetic stiffness will be discussed in Sect. 3.

#### **3 Mathematical Model**

In di Prisco et al. and Mangraviti et al. [10, 11, 21] the critical interpretation of numerical results for GRPS embankments lead to the identification of 6 subdomains (Fig. 4a). All the subdomains are considered as elastic and behave in pseudo-

**Fig. 3** Numerical results during embankment construction in terms of non-dimensional, **a** differential and **b** average settlements at the top of the embankment for different values of the geosynthetic axial stiffness

**Fig. 4 a** Rheological model for CPS embankments; **b** stiffness of reinforced foundation soil versus embankment base displacement for different *J*

oedometric conditions, whereas the arching effect [11, 17] is modelled as localised at the interface between subdomains 3 and 4. The mechanical behaviour of each subdomain can be reproduced by means of elastic springs and the arching effect is considered as localised and represented by a frictional slider placed in *z* = *Hp* and *r* = *d*/2. In Fig. 4a, the non-dimensional compliances *C*1 and *C*2 represent the pile and the reinforced foundation soil respectively, whereas *C*3 and *C*4 are the compliances related to the portion of embankment *Hp* thick. Due to the evolution of *Hp* (Fig. 2) with the loading function *H*˙ , subdomains 3 and 4 evolves during construction. *C*5 = *C*6 is the compliance of the soil stratum (*H*–*H*p) thick. Due to the definition of nondimensional quantities, *C*2 = 1 when *J* = 0, whereas, when *J* = 0, *C*2 is a function of non-dimensional settlement at the embankment bottom, *Ub*,*f* (i.e. geosynthetic deformation). As a consequence, when *J* = 0, the model for GRPS embankments [11, 17] reduces to the one for CPS ones [18]. The equation describing the evolution of the non-dimensional stiffness 1/*C*2 with *Ub*,*f* was numerically calibrated and the curves for different values of *J* are reported in Fig. 4b.

To evaluate settlements at the top of both CPS and GRPS embankments, an incremental relationship between the generalised loading variable *H*˙ and the displacements at the top of the embankment *Ut*,diff and *Ut*,av was conceived:

$$
\begin{bmatrix}
\dot{U}\_{t, \text{diff}} \\
\dot{U}\_{t, \text{av}}
\end{bmatrix} = \begin{bmatrix}
\mathbf{C}\_{\text{diff}} \\
\mathbf{C}\_{\text{av}}
\end{bmatrix} \dot{H} \tag{4}
$$

*C*diff and *C*av represent the non-dimensional compliances of the overall system, analytically evaluated by (i) employing the rheological scheme illustrated in Fig. 4a; (ii) imposing the balance of momentum and compatibility conditions along the vertical direction; (iii) imposing the definition of plane of equal settlements (*U*˙*t*,diff = 0).

The obtained constitutive model in Eq. (4), describing the response of GRPS embankments depends on: (i) the mechanical parameters of piles, soil (Table 1) and geosynthetic (*J*); (ii) the geometrical variables (*s*, *d*, *l*) and (iii) the average ratio between horizontal and vertical stresses (*k*) in the portion of embankment in which irreversible strains accumulated. According to di Prisco et al. [18], *k* is the only parameter of the model which is not directly related on the system geometry/mechanical properties. *k* is not significantly affected by *J* [11] but only depends on the dilatancy angle.

A conservative value of the final height of the plane of equal settlements can be estimated as (di Prisco et al. [18]):

$$H^\* = \frac{1}{2} \sqrt{\left[\frac{E\_{\text{ced},\varepsilon}}{E\_{\text{ced},f}} \frac{L}{S^2} C\_2\right]^2 + \frac{(S^2 - 1)}{\overline{k} \tan \phi\_{\text{xs}}'} \left(\frac{E\_{\text{ced},\varepsilon}}{E\_{\text{ced},f}} \frac{L}{S^2}\right) C\_2 - \frac{1}{2} \left(\frac{E\_{\text{ced},\varepsilon}}{E\_{\text{ced},f}} \frac{L}{S^2}\right) C\_2 \tag{5}$$

As previously mentioned, for GRPS embankments *C*2 in Eq. (5) is a function of *Ub*,*f* and, according to the trend reported in Fig. 4b, the critical height *H*\* decreases for larger values of the geosynthetic axial stiffness *J* (i.e. *H*\* is maximum when *J* = 0). Eq. (5) will be used in the following section as a key ingredient to optimise the design of GRPS embankments.

The results obtained by integrating the mathematical model in Eq. (4) are compared with the numerical ones (see Fig. 3) in Fig. 5, where a good agree-

**Fig. 5** Comparison between non-dimensional numerical results and the mathematical model in Eq. (4) in terms of **a** differential and **b** average settlements at the top of the embankment

ment is obtained for each value of *J* in terms of both differential (Fig. 5a) and average (Fig. 5b) settlement. The comparison between the mathematical model and the numerical results from a parametric study showed a satisfactory agreement [11], but the results are here omitted for brevity.

#### **4 Optimisation of GRPS Embankments Design to Increase Sustainability and Practical Example**

From a practical point of view, geotechnical engineers should design both piles (i.e. *l*, *s* and *d*) and geosynthetic layer (i.e. *J*) in order to have an average settlement at the top of GRPS embankments lower than an admissible settlement (*u*amm *t*,av ). If endbearing piles are considered, *l* is known, as well as the mechanical properties of the soft soil (*E*oed,*f* ).

Settlements accumulated during embankment construction are generally levelled thanks to the rollers compacting the soil. However, it is important that, after the construction of the infrastructure (i.e. either road superstructure or ballast plus rail track, where the rollers cannot be used anymore), the embankment does not settle more than expected. In fact, that would lead to possibly dangerous consequences to people and expensive damages to the infrastructure. As previously shown in Sects. 1 and 2, when *H* > *H*\*, differential settlements in *r*-direction stop increase (Fig. 5a), whereas average settlements (i.e. differential settlements in *y*-direction) continuously increase (Fig. 5b). As a consequence, to design GPRS embankments with a displacement-based approach, it is important: (i) that the final height of the embankment is larger than *H*\*, in order to avoid an increase in *Ut*,diff and (ii) that the value of *Ut*,av is equal or lower than the admissible one.

In this perspective, the rheological model in Eq. (4) was integrated and used to solve an optimisation problem: the maximum value of *S* = *s*/*d* was evaluated, for several values of non-dimensional *J*\* = (*Jl*)/( *E*oed,*f d2*) and for fixed values of the following non-dimensional efficiency: 1 − *u*amm *t*,av /*u*∗, where:

$$
\mu^\* = \Delta q \left( l / E\_{\text{oed}, \text{f}} + 0.5 \Delta h / E\_{\text{oed}, \text{e}} \right) \tag{6}
$$

is the settlement at the embankment top induced by the load *q* = γ *h* when nor piles neither geosynthetic are installed. *q* is the distributed load representative for the infrastructure weight, being *h* the thickness of embankment equivalent to the construction of the infrastructure layer (*h* = γ*ihi*/γ being γ*i* and *hi* the unit weight and the thickness of the infrastructure respectively). Several curves were obtained (Fig. 6) for fixed φ- *e* and ψ*e*, and for *H* > *H*\*, where a safe side estimation of *H*\* can be determined by substituting *C*2 *r* = 1 in Eq. (5). For the sake of safety, the curves were obtained by considering *u*t,avamm equal to the maximum increment of average settlements at the top of the embankment (Eqs. 4, 3, 2) for *H* > *H*\*.

1 − *u*amm *t*,av /*u*∗ is a measure of the efficiency of the installation of both piles and geosynthetic: it will be equal to 0 when *u*amm *t*,av = *u*\*, whereas it is 1 for *u*amm *t*,av /*u*∗ → 0. As expected, by increasing the axial stiffness of the geosynthetic layer, a larger pile spacing can be chosen, possibly leading to a reduction of the concrete piles number and to a more sustainable design. However, it is worth noticing that, since the geosynthetic is more effective in transferring stresses to the piles when it deforms more (i.e. larger settlements), for large *u*amm *t*,av /*u*∗ values (i.e. low values of the efficiency in Fig. 6) the curves are more inclined and a small increase in *J*\* lead to choose piles with larger spacing (or smaller diameter). On the contrary, when very small settlements are admitted (i.e. larger efficiency is required), the increase in *J*\* induces small increase in *s*/*d*.

As an example, a GRPS embankment, with 25 m central part in *r*-direction, can be considered to be realised over a 5 m thick soft soil stratum (i.e. *l* = 5 m). The mechanical properties of the foundation soil, the concrete pile and the embankment soil are those reported in Table 1. A differential settlement of 6 mm at the top of the embankment is considered as admissible after a *hi* = 50 cm thick superstructure is constructed. For the sake of simplicity, in this case, the unit weight of the infrastructure is (conservatively) assumed to be equal to the one of the embankment soil (γ*i* = γ → *q* = γ*i hi* = 18 · 0.5 = 9 kPa).

As a first step, the isoline with *efficiency* = 1 − (0.006)/[(9) · (5/1346 + + 0.5 · 0.5/13462)] = *0.82* is individuated in Fig. 6. All the *s*/*d* − *Jl*/(*E*oed,*f d*2) couples on the 0.82 isoline can be chosen to have a settlement at the top of the embankment equal to the admissible settlement (6 mm). In order to optimise both environmental and economic resources, the designer should look for the maximum values of both *s* and *J* that better suits the project needs.

To estimate the increment in sustainability (i.e. the reduction in CO2 emissions) induced by considering a GRPS embankment instead of a CPS one, both *J* = 0 and *J*

**Table 2** Example of design optimization: piles number and tCO2 for CPS and GRPS embankment

= 1000 kN/m were considered. By assuming a first tentative value of pile diameter equal to 0.5 m,*s* is estimated from Fig. 6 and the corresponding number of piles to be placed in the central part (25 m in *r*-direction) of the embankment are evaluated and reported in Table 2. To evaluate the tons of CO2 saved by realizing 17 piles and the geosynthetic layer (instead of 23 piles), the EC for both concrete and geosynthetics is considered. EC is generally measured in mass of CO2 emitted per mass of material. In particular, an average value of EC = 1.08tCO2/t was chosen for the concrete (whose mass is 2500 kg/m3) [22] and EC = 2.36tCO2/t was considered for a woven geogrid (whose mass is 0.53 kg/m2) [23]. The reduced number of piles employed for the GRPS embankment led to a 24% reduction of CO2 emissions if compared to the CPS embankment. The same calculation may be repeated for a different value of *d*, in other to further optimise the sustainability of the project.

The charts in Fig. 6 represent a very effective and quick tool to design GRPS embankments in a displacement-based perspective and to optimise the number of piles for a more sustainable design. Several design charts were obtained for different φ- *e* and ψ*e* and are here omitted for the sake of brevity.

#### **5 Conclusion**

In this chapter a mathematical model capable of reproducing the mechanical response of GRPS embankments is presented. The model considers the embankment height as a generalised loading variable and allows to evaluate settlements at the top of the embankment during construction under drained conditions. The model is highly innovative since it represents an effective tool during the preliminary design of GRPS embankments, including a displacement-based approach. In order to move a step forward towards a more sustainable construction of infrastructures (SDG 9) and reduce as much as possible the CO2 emissions due to the construction of unnecessary concrete piles, one chart was provided to optimise the design of both piles and geosynthetic in a displacement-based perspective. The calculation of CO2 saved for the practical example considered confirmed that GRPS embankments are a more sustainable choice if compared to CPS embankments.

**Acknowledgements** All the numerical results have been obtained by using the commercial code FLAC3D within the framework of the Itasca Education Partnership (IEP) program. I am grateful to Itasca Consulting Group and Harpaceas for the use of the software license. The financial support from Nordforsk (project #98335 NordicLink) is greatly appreciated. I would like also to acknowledge Prof. Claudio di Prisco, Prof. Jelke Dijkstra and PhD Luca Flessati, for supporting me during this research.

#### **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Characterization and Monitoring of an Unstable Rock Face by Microseismic Methods**

**Zhiyong Zhang**

**Abstract** Unstable rock slopes are likely to cause rockfalls, threatening human lives and properties, industrial activities, and transportation infrastructures in mountain areas. There is an increasing demand to forecast and mitigate the potential damage of rockfalls by developing a reliable early warning system. In this thesis, an unstable mountain slope in northern Italy was selected as the research target. A microseismic monitoring network has been operating since 2013 as a field research laboratory to study the microseismic monitoring technique in the perspective of developing rockfall early warning systems. Locating microseismic events is a basic step of this technique to obtain the location of developing cracks as possible precursors of rockfalls. However, it is still a challenging task due to the heterogeneity of fractured rock slopes. The main purpose of this thesis is to address the issues related to event localization for microseismic monitoring strategy applied to the unstable rock face.

#### **Graphical Abstract**

**Keywords** Landslide disaster · Rockfall · SDG 11 · Microseismic monitoring · Early warning system · Event localization

Z. Zhang (B)

e-mail<EMAIL_ADDRESS>
Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

#### **1 Introduction**

Extension of human activities in mountain areas has given rise to worries about unstable rock slopes. Unstable rock slopes are likely to result in rockslides, causing serious threats to human safety and properties, industrial activities, and transportation infrastructures. Therefore, it is an increasingly significant issue to prevent and forecast dangerous incidents caused by unstable rock slopes. Management of rockslide hazards requires adequate information to better understand the mechanisms of rock slope failure. Monitoring an unstable rock slope as an early warning system to identify the danger of mass movement is the first step to assess the risk of rockslides. In this perspective, building an early warning system for rockslide hazards is consistent with the 11th sustainable development goals (SDGs) set by the United Nations, which is 'Goal 11: Make cities inclusive, safe, resilient and sustainable'. More specifically, research in this field exclusively serves for one specific objective (11.5) under Goal 11: 'By 2030, significantly reduce the number of deaths and the number of people affected and substantially decrease the direct economic losses relative to global gross domestic product caused by disasters, including water-related disasters, with a focus on protecting the poor and people in vulnerable situations.' In details, the early warning system plays an important role to mitigate or avoid the deaths and economic losses caused by rockslide-related disasters in mountain areas throughout the world.

Rockslides, or more specifically 'rock' landslides, are a group of landslides composed of rocks rather than soils. According to the commonly used classification of landslide types [1], rockslides can be divided into different subclasses based on the type of movements (fall, topple, slide, spread, flow and slope deformation). Different rockslides present different movement velocities at various scales and the mechanical behavior of the rockslides is best related to the rock material. Due to the complex geological and geomorphological conditions on unstable rock slopes, rock mass failure contains more than one class of rockslides. For fractured brittle rock mass, the stability of the rock slope is primarily controlled by the existence of discontinuities. Since the discontinuity pattern of rock mass distributes both on the surface and in the subsurface, the designed monitoring system should investigate on the rock face and within the rock mass.

To acquire detailed information about the distribution of brittle discontinuities within rock mass, many geological, geomorphological and geophysical methods can be adapted. Remote-sensing and aerial techniques are usually employed to map the surface area of the unstable rock slope to indicate the topography. However, mapping investigation techniques limit the observation on the rock surface. Geotechnical techniques mainly including boreholes and trenching can provide detailed geological information, indicating the vertical boundary of the slide and the properties necessary for the slope stability analysis. However, these techniques can only monitor a few critical points or lines and the difficulty of drilling the unstable and steep slopes usually limits their application [2]. On the other hand, geophysical methods (e.g., seismic, electrical, electromagnetic and gravimetric methods) can detect the petrophysical parameters under the rock surface. Changes of the geophysical parameters characterizing the rock mass are likely to be generated by the rock mass modifications due to its instability.

Geophysical methods that are commonly used to investigate landslides are summarized in several review papers [3–6]. For rockslides studies, passive seismic techniques are the most frequently used method. The reason may be that these techniques can be carried out to characterize and monitor the stability of the rock slope. The application fields of passive seismic techniques mainly include two areas. The first application field is seismic noise measurements which can analyze the seismic response of rock slopes by processing seismic noise that is not related to incipient fracturing (e.g. earthquakes, ambient seismic vibrations). The second application field is to detect and locate microseismic events generated by fracture propagation inside unstable rock masses.

The capability of passive seismic methods in detecting and locating microseismic events makes it an efficient option to be integrated into early warning alarm systems. By locating microseismic events generated within an unstable rock mass, we can locate the growing cracks and understand the slide kinematics and triggering mechanisms of future collapses [7]. Therefore, microseismic events can be the precursors before the occurrence of a macroscopic failure of rockfall or rockslide.

Concerning the applications of passive methods in rockslides, several studies were devoted to analyzing microseismic signals as possible precursors of rockfalls [8–11]. These studies show the usefulness of a microseismic monitoring network in the early warning alarm systems for rockfall risk on unstable rock slopes. For early warning purposes, more applications of this method are used in different sites [12– 17]. These studies showed that the larger amounts of recorded seismic signals require a classification procedure to distinguish microseismic events from the noise. More importantly, these classified microseismic events also need to be located, because the localization of microseismic events is necessary to understand which part of the rock mass is cracking in order to be able to recognize the rockfall risk. Location results will also help to select the microseismic events close to the target monitored area and exclude small rockfalls and the events that are far from the monitored area, generated by other sources.

Although hypocenter localization of seismic events (usually followed by data acquisition and event classification) has been a basic step in microseismic monitoring, it is still a challenging task. One main reason that causes difficulties for a reliable event location is that the seismic velocity distribution is highly heterogeneous within unstable slopes so that the waveforms experience strong scattering and high attenuation. Therefore, contrary to what is usually adopted in large scale studies for earthquake localization, it is impossible to use a homogeneous or layered model to characterize the fractured zone in the limited rock volumes monitored by small-scale microseismic networks. Moreover, short distances between sources and receivers make it difficult to distinguish P and S waves, and thus direct estimations of source distance are impeded.

In this thesis, the localization problem was addressed for a microseismic monitoring network installed on the unstable rock cliff of Mount San Martino for early warning purposes. Based on the event location, the classification of microseismic events was revisited to extract fracture events. Finally, a procedure for the design of an expanded network was proposed to improve location accuracy.

#### **2 Methods and Results**

The research target is the limestone rock face ofMount SanMartino that is threatening the town of Lecco (northern Italy) due to its historical rockfall events (Fig. 1). A microseismic monitoring system was installed on the mountain for early warning purposes in 2013 and has continuously recorded the data since then.

**Fig. 1** The study site in the southern part of Mount San Martino. **a** Front view of Mount San Martino from Lecco. The yellow rectangle indicates the monitored area where the monitoring network was deployed. **b** Rock face with the positions of the five three-component geophones and the acquisition board of the microseismic monitoring system. The red arrow indicates the partially detached pillar below geophone 4. **c** Photogrammetric model of the monitored area with the orientations of the five geophones

To construct the three-dimensional (3D) velocity model required for reliable hypocenter localization, a seismic tomographic survey was performed on the mountain surface above the rock face. Source test measurements were conducted to select a suitable source capable of triggering all geophones. Hammer emerged among the other tested options as the preferred source because it performed like the seismic gun in terms of signal energy and spectral content while demonstrating superiority in terms of portability and flexibility in the harsh environment of the study site. We used GeoTomCG software [18] which performs three-dimensional tomographic inversion. The results of seismic traveltime inversion showed high heterogeneity of the rock mass with significant contrasts in velocity distribution (Fig. 2). Low velocities were found at the shallow depth on top of the rock cliff and intermediate velocities were observed in the most critical area of the rock face corresponding to a partially detached pillar. Two sensitivity tests were implemented to evaluate the resolution and stability of the inversion [19].

After obtaining the 3D velocity model from the inversion, the global grid search location method [20] was selected for event localization and the misfit function was defined based on the Equal Differential Time (EDT) method [21]. Seismic shots with known positions were located to estimate the location accuracy on the upper part of the rock mass. The hypocenter misfits were around 15 m with the 5 geophones of the microseismic network and the error was significantly decreased compared to the results produced by a constant velocity model. Besides, the analysis of location accuracy was extended to the whole volume of the rock mass by using synthetic traveltimes affected by random errors consistent with the noise level observed on real data (Fig. 3). Although three geophones of the seismic network are installed

**Fig. 2** Velocity model obtained from 3D tomographic inversion using a 2 × 2 × 4 m grid. Colored blocks indicate the velocity field in the rock mass where at least one ray travels. The red arrow indicates the partially detached pillar on top of which geophone 4 is installed

**Fig. 3** Average location error on vertical slices cutting the 3D model at X = 18, 26, 34 m (**a**, **b**, **c**) and at Y = 10 m. **d** Red squares indicate the positions of the five geophones projected on each slice

near the critical area where the partially detached rock pillar was located, accuracy in this area is not better than the accuracy on the upper part of the rock face probably due to the high heterogeneity of rock mass and the higher velocities in this area [22].

The classification procedure for microseismic events was updated by the hypocenter location of a subset of microseismic events with high data quality, which is one of the novelties of this research work [23]. The microseismic events were preliminarily classified into two subclasses: suspected rockfall events with multiple signals in the recordings and suspected fracture events with a single signal in the recordings. The location results for the suspected rockfall events almost met our expectations (Table 1). Most of the signals in rockfall events were located on or near the rock face thus confirming the initial classification. The last column in Table 1 refers to the rockfall type, which is an additional information that we can derive from the analysis of the number of recorded signals combined with their time of occurrence and their location. Based on that, rockfall events can be sub-classified into four rockfall types:

For the suspected fracture events, Table 2 summarizes the location results for 20 selected fracture events. Based on the hypocenter locations, these fracture events could be reclassified into five groups: events that are located inside the rock mass (Fracture); events that are located on the rock surface at the summit of the rock face and are probably related to the movement of the debris covering the summit (Rockfall); events that are located on the vertical boundaries of the model (Far event); events that are located near the rock face so that they are likely generated by a fracture although we cannot exclude a probable single stone rockfall hitting the rock face only once and then disappearing without generating any other signal from a lower point below the monitored area (Suspected fracture); and events that are located at the lower boundary of the model near the rock face so that we suspect that they are fracture events occurring within the lower section of the unstable area of the rock mass, i.e., the lower part of the unstable rock pillar, although we cannot exclude the case of a single stone hitting the rock face only once at a point located below the

**Table 2** Summary of the location results for 20 fracture events

monitored area (Suspected fracture (outside the area)). Based on the results, only a few (4 out of 20) events were located inside the rock mass at such a distance from the rock face that they cannot be confused with rockfalls. Further improvements in location accuracy are necessary to distinguish suspected fracture events that were located close to the rock face from rockfalls. On the other hand, the hypocenter location helped to identify events generated outside the monitored area and rockfalls that were located on the rock surface at the summit of the rock face. This feasibility study shows that the hypocenter location is a promising method to improve the final classification of microseismic events.

Another original contribution of the thesis is to suggest a procedure for designing an expanded network in order to improve the localization accuracy in the most critical part of the rock mass [24]. Additional geophones were progressively added to the existing network, selecting their positions with special care to improve the azimuth coverage and source-receiver distance coverage. Three progressively expanded networks with 9, 13 and 15 geophones were studied to explore the improvement in location accuracy and it was observed that the location error was reduced from 12–24 m (5 geophones) to 4–6 m (15 geophones) (Fig. 4). The relatively low location errors in the critical part with 15 geophones would help to improve the classification of microseismic events. The method can be used in near future for expanding the

**Fig. 4** Average location error on the vertical slices at X = 18 m, **a** 26 m, **b** 34 m, **c** and the vertical slice at Y = 10 m **d** with a network of 15 geophones. Red squares and other colored squares indicate respectively the positions of the original five geophones and additional geophones projected on each slice (Colorbar: 0–40 m as in Fig. 3)

network transforming the current network with 15 channels using 5 three-component (3C) geophones into a network of 15 single-component (1C) geophones.

Summarizing, the main novelties of this research work are:

#### **3 Conclusions**

Microseismic monitoring, as one application of passive seismic techniques, has been increasingly used in the studies of unstable rock slopes to develop an early warning alarm system. This system would work for decreasing the damages caused by rockslide-related disasters, serving for the Goal 11 of SDGs. In order to recognize the areas with potential rockfall or rockslide risk triggered by unstable rock slopes, localization of seismic events is required to trace the propagation of fractures within the rock mass.

The first two goals of this thesis were to construct a 3D velocity model that is required for reliable hypocenter localization and to estimate the location accuracy based on the obtained 3D velocity model. To construct the 3D velocity model for the study area, a tomographic survey was carried out after performing source tests to select a suitable source. Then seismic traveltime inversion was implemented by using first-arrival picks to obtain the velocity distribution within the rock mass. Two sensitivity tests were performed to evaluate the resolution and stability of the inversion. To estimate the location accuracy, the global grid search method was first selected for event localization and the misfit function was defined based on the EDT method. Then, the location accuracy was estimated in two steps: 1-using the data of seismic shots with known positions (performed in the tomographic survey) to estimate the location accuracy in the upper part of the rock face; 2-assessing the expected location accuracy for the whole rock mass, particularly in the critical area, by using synthetic data affected by random errors.

However, the limitations of the present work must be noted for future improvements. Due to the harsh investigated area, the layout of the source positions for the tomographic survey was constrained on the rock surface at the summit of the rock face. This causes the inverted velocity model to only cover a limited volume of the rock mass, especially in the lower part of the monitoring area. Therefore, the localization results should be further improved, for example, by better extrapolating the velocity field to the neighboring areas of the current 3D model and by testing new misfit functions, also including a travel-time quality factor. Moreover, in order to enlarge the raypath coverage within the rock mass, some source positions can be designed on the rock face (if possible) for future tomographic investigation.

Although the location accuracy is not small enough to distinguish rockfalls from rock cracks occurring near the exposed face of the rock mass, the location algorithm can be used to improve the classification procedure by distinguishing the events occurring in the monitored area from rockfalls or other events occurring far from the monitored area. Moreover, the location accuracy can be improved by introducing more geophones to the current 5-geophone network. From these points of view, the location results implicate that the location algorithm based on the 3D velocity model can be applied to realize two other objectives of this thesis, which represent two original contributions of this research work: to explore the usefulness of hypocenter location in the classification of microseismic events and to design an expanded network to improve the location accuracy.

The results obtained in this thesis show the necessity of expanding the geophone network to improve the location accuracy and then improve the classification of the microseismic events. If event localization is accurate enough, its results can be used to distinguish rockfall events from fracture events because rockfalls only occur on the rock surface. Another future work would be exploring some efficient denoising methods to process the microseismic events with relatively lower SNRs to get reasonable arrival times for event localization. After this procedure, more fracture events can be extracted by the classification based on hypocenter location. This group of fracture events will be used to analyze the evolution of microseismic activities with time and space to indicate the most unstable area on the rock face. Moreover, the evolution of microseismic activities can be correlated with meteorological parameters to show the effects of temperature and rainfall on triggering the propagation of fractures probably leading to future collapse.

The take-home messages can be summarized as follows:

The perspective of the whole research is the implementation of an early warning methodology applicable to unstable rock slopes. Although this goal has not been achieved yet, the results of this work contribute to reduce the distance to the final objective and will provide valid support for scientists, technicians and decision makers to face future sustainability challenges related to rockslide hazards. Moreover, this work also contributes to fulfil the Goal 11 of SDGs, which is, in short, significantly reduce the loss in lives and property caused by disasters, including rockslide-related disasters mentioned in this research, with a focus on protecting the poor and people in vulnerable situations by 2030.

**Acknowledgements** I am grateful to my three supervisors Prof. Luigi Zanzi, Dr. Diego Arosio, Dr. Azadeh Hojat for their help throughout this thesis. This research was funded by China Scholarship Council (CSC), grant number<PHONE_NUMBER>51, to support me during my research activities in Italy.

#### **References**

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**4. Summary**

There are several surgical techniques to treat CP, recommended when medical treatment is ineffective or appear complications that can be surgically corrected. Success of these treatments depends on the natural history of the disease, on the appropriate selection of the technique and on the objectives and expected results. Surgeons must be aware of their surgical expertise and of the rate of pain control, morbi-mortality, quality of life and functional changes of the chosen technique.


**1. Introduction**

In accordance with modern concepts, noise and infrasound are classified as harmful and dangerous physical factors, the impact of which causes a decrease in efficiency and reliability of activity, and a long or short cumulative effect causes the development of a number of diseases [1–3].

To date, a large amount of data has been accumulated on the adverse effects of noise on humans. The nature of this influence depends on the sound level, the duration of exposure and the spectral composition of the noise [4–6]. The hearing organ is the critical organ of the body when exposed to noise. It is generally accepted that the most harmful effect on the organ of hearing is provided by noise, the spectrum of which is dominated by high frequencies of the sound range (from 1 to 8 kHz). In the clinical picture, along with hearing impairment, pathology of the cardiovascular and nervous systems is often found, which made it possible to form the concept of "noise disease" [7].

The physical characteristics of infrasound are well studied by acousticians, however, hygienists and occupational pathologists have long been limited in their research by the lack of reliable and affordable measuring equipment. Therefore, the history of the study of infrasound as a factor in the environment and production environment is relatively short. The first publications devoted to the action of infrasound appeared in the period 1970–1980. During this period, reports appeared in the scientific literature about the high biological efficiency of infrasound [1, 7, 8]. The first hygienic standards for infrasound in the USSR were adopted only in 1981, while the first noise standards for its limitation in workplaces were adopted in 1956. Subsequently, a large number of publications appeared, which reflect the point of view of hygienists on the problem of infrasound effects on humans [1, 7].

Since 2004, infrasound has been included in the list of harmful and hazardous production factors in Russia. The critical organs under the influence of infrasound include not only the organ of hearing, but also the vestibular analyzer, the central and autonomic nervous system, the circulatory and respiratory organs [9–12]. The presence of several organs and systems in the clinical picture allows us to speak about the separation of infrasound pathology into a separate nosological form [1].

There are reports that low-frequency noise can have a harmful effect not only on the organ of hearing, but also on other human organs and systems. Its biological effect has a certain similarity with the effect of infrasound on the human body. An analysis of industrial and transport noise shows that its spectrum is dominated by low frequencies of the audible and infrasound ranges. Close physical parameters and biological effects allowed a number of authors to introduce the terms "low-frequency acoustic oscillations", "infrasonic disease" and "vibroacoustic disease" [1, 7].