CC BY
0ARCHITECTURE AND CONSTRUCTION
THE REACTIVE CAPACITY OF THE SOIL BASES OF GRAVITY-TYPE QUAY WALL
Assistant professor Natela Khoneliia Assistant professor Svetlana Bugaeva
Ukraine, Odessa, Odessa National Maritime University
DOI: https://doi.org/10.31435/rsglobal_ws/30092019/6696
ARTICLE INFO ABSTRACT
Received: 20 July 2019 The results of studies of the reactive capacity of the soil base of a gravity-
Accepted: 13 September 2019 type quay-wall on the basis of the method developed for calculating the
PubHshed: 30 September 2019 "structure - soil base" system are considered. The method proposed allows
- determining the reactive capacity of the soil base in conditions of mixed
KEYWORDS stress state model (limit and sublimit stress state of the soil base) under and
the reactive capacity, gravity-type f^ of the base of if foundation structure in a wide range of loads of quay wall numerical modeling limit lateral earth pressure. The transformation of limit and sublimit stress state
qnd sublinrit stress-strain states' lateral zones of the soil base on the basis of numerical modeling is presented
earth pressure, the soil base. which shows an increase of the sizes of limit stress state and a decrease of
the sizes of sublimit stress state.
Citation: Natela Khoneliia, Svetlana Bugaeva. (2019) The Reactive Capacity of the Soil Bases of Gravity-Type Quay Wall. World Science. 9(49), Vol.1. doi: 10.31435/rsglobal_ws/30092019/6696
Copyright: © 2019 Natela Khoneliia, Svetlana Bugaeva. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
Introduction. Gravity-type quay-walls are the most common type of walls used for harbor berths. Reliability of the soil bases is one of the main factors in the design and the reconstruction of gravity-type quay-walls. Maritime transport development considerate the task of cargo complexes modernization and change their specialization including change of their operating condition. Thus, the studies of the reactive capacity of the soil base of a gravity-type quay-wall are importance and up-to-date.
The limit loads produced an effect on gravity-type quay-walls are of interest in the design or reconstruction of mentioned structures. It should be noted that the increase limit loads cause the loss of the reactive capacity of the soil base under the base of the foundation structure. Most often disturbance of stability of the soil base leads to a large settlement, to the rise from under the foundation and to the displacement of the structure. Significant displacement is dangerous for most of the aforementioned structures. Therefore, it is important to determine the maximum possible load on the soil base that won't disturb its stability.
Purpose of the study: to present the study's results of the reactive capacity of the soil base of gravity-type quay-wall on the basis of developed calculation method "structure - soil base" system [1] taking into consideration features work of the structure and soil backfill. The method proposed determines the reactive capacity of the soil base in the conditions of mixed stress state model. The model considers limit and sublimit stress state of the soil base under and around the foundation structure.
Research results. Calculation model of the "structure - soil base" system has been developed and numerical modeling has been performed in a wide range of loads of soil backfill pressure for studying of the system considered.
Occurrence issues of limit state zones of the soil base, determination of limit load causing their formation under the base of the foundation structure and influence of considered factors on the work
of the "structure - soil base" system have been discussed earlier by authors: M.V. Malyshev [2], P.I. Yakovlev [3], S.G. Kushner [4].
Currently, methods of calculation of the soil bases which are used in the design of berth structures don't take into consideration the presence and the transformation of the limit and sublimit stress state zones. Experimental studies conducted by Y.K. Zaretsky [5] have shown that the reactive capacity of the soil base depends not only on the strength properties of the soil base but also on the parameters which describe its behavior in sublimit stress state.
The calculation method of the reactive capacity of the soil base has been developed. It is based on the theory of the limit stress state. The method is different from other methods by the presence of two zones of soil stress state (limit and sublimit) in the soil base of the structure and by considering of the friction on the contact of rigid foundation structure and the soil base. The scheme of calculation of the reactive capacity of the soil base is shown in Fig. 1.
The model proposed of the interaction of a gravity-type quay wall with the soil base is based on the following presupposition:
1. The soil base interacting with the base of the foundation structure includes zones of limit and sublimit stress state.
2. The boundary of limit and sublimit stress state zones of the soil base (the width be of the contact zone of the soil base which is in limit stress state) is determined according to recommendations [1] and can be got from the expression
E - 0.5 • B •(/ + fT)
= - - -v + / / (1)
e 2-(/„J - f)
be - the width of the contact zone of the soil base interacting with the base of the foundation
structure in limit stress state;
B - the width of the base of the foundation structure interacting with the soil base;
rmp
J„p - the intensity of the friction forces on the contact of the base of the foundation structure and the soil base within the width of limit stress state zone;
f - the intensity of the friction forces on the contact of the base of the structure and the soil
base within the width of the sublimit stress state zone;
E - the resultant of lateral earth pressure (depends on an uniformly distributed load of intensity q). It is defined as the vector sum of two components: limit Ee and sublimit E', according to the recommendations [6] and may be expressed as
E = \e2 + E'2 + 2-Ee -Ecos(5e -5 ')J/2 (2)
3. Limit component of the reactive capacity of the soil base Ne. It conforms to the force acting within the width be of limit stress state zone. Sublimit component of the reactive capacity N'. It
conforms to the force acting within the width B-be of sublimit stress state zone (see fig. 1).
Fig. 1. The sliding surface and the outlines of limit and sublimit stress state zones of the soil base
4. The components' deflection angles Ne and N' and the resultants of reactive pressure of the soil base along the sliding surface from the normal to the boundary of this surface are accepted for limit stress state zone 8e, pe and for sublimit stress state zone accordantly 8 , p . It should be noted that the angle p is determined according to the recommendations [6] and may be expressed in form
P' = Po + n(P-Po ) .
Based on the design scheme (see Fig. 1) it can be obtained followed characteristics:
- the angels 8 and 8e, determine as tg8 = El G and tg8e = Ee / Ge where Ee, Ge and
E , G horizontal and vertical components of the resultants Ne and N' accordingly in the range of
limit and sublimit stress state zones;
- the parameter n is depended on the sizes of limit and sublimit stress states zones of the soil base and is determined by the ratio n = V l V where Ve - the volume of the area of the soil base
being in limit stress state; V - volume of whole soil mass interacting with the base of the foundation structure. Ve and V can be determined from geometrical consideration of the design scheme;
- the angle pa conforms to the earth pressure at rest and can be taken according to the recommendations [7].
5. The resultant of the reactive capacity of the soil base N can be determined for each current deformed state of the structure as the vector sum of two components: limit Ne acting within the wide
be and sublimit N' acting within the wide B- be. In this case, the resultant of the reactive capacity of
the soil base N can be expressed by the equation
N = N + N2 + 2 • Ne • N • cos(8e - 8 )} 2 (3)
6. The cohesive soil characterized by specific cohesion c can be taken into consideration by loading of an uniformly distributed load acting downward on the top surface of the sol backfill. The intensity of the load within limit stress state ne = c l tgp and the intensity of the load within sublimit stress state n' = cltgp as shown in fig. 1.
The resultants of uniformly distributed loads in the first case Gce and in the second case Gc . It should considerate the increment of the cohesive pressure An on the boundary of limit and sublimit stress state zones which can be calculated as follows: An = c • ctg(p-pe) .
The balance conditions of limit and sublimit strain stress zones of the soil base are considered consistently for determination of limit Ne and sublimit N' reactive capacity of the soil base. In this
case, it considers force interaction of the aforementioned zones.
Some results of numerical modeling of the "structure - soil base" system are considered. It should be emphasized that there are two phases of the interaction of gravity-type quay wall and the soil backfill: the phase of structure construction which includes the process of formation of the soil backfill; the phase of operation when an uniformly distributed load q effects on the structure. The paper studies the second phase of the interaction of gravity-type quay wall and the soil backfill. In this case, soil backfill lateral pressure will increase depending on the loading and the increase of an uniformly distributed load q.
The increase load q leads to the growth of the reactive capacity of the soil base (due to the appearance and development of limit stress zones in the soil base). This process can be continued while limit reactive capacity in the soil base won't be reached. Further increase of the external load may lead to loss of the structure stability due to the exhaustion of the bearing capacity of soil base.
The growth of an uniformly distributed load q leads to the increase of active earth pressure of the soil backfill and to the transformation of the areas of limit and sublimit stress states of the soil base. The transformation leads to the increase of the area of limit stress state and to the decrease of the area of sublimit stress state. An example of the transformation of considered zones as a result of the increase of the load q is given in fig. 2.
Fig. 2. The transformation of limit and sublimit stress state zones of the soil base: 1' - the boundary of sublimit strain stress zone in the case of the achievements of active pressure which leads to formation of limit strain stress zone 1; 2, 2'; 3, 3'; 4, 4' - the boundaries of limit and sublimit stress state zone of the soil base as a result of
the increase of the load q; 5 - the boundary of the soil mass in case of achievements of limit reactive capacity of the soil base
At the time of the transformation of the boundaries of limit stress state of the soil base 1, 2, 3 and 4 falls down remaining parallel due to the constancy of the angle Ve. The boundaries pointed pass through the points of the contact surface of the base of the foundation structure within the width bi, b2, b3 and b4. The boundaries of limit stress state of the soil base 1, 2, 3 and 4 in the area located b ehind the foundation structure fall down remaining parallel due to the constancy of the angle 45 фJ2.
The boundaries of limit stress state of the soil base 1, 2, 3 and 4 in the intermediate area (Prandtl zone) fall down due to the constancy of the angle бе (бе is the angle of the logarithmic spiral of considered area). At the same time the boundaries of sublimit stress state 1 ', 2', 3 'and 4' under the base of the foundation structure change the slope to the horizon from angle V{ to V-2 , V3 and V4 as a result of the increase of active pressure in the range from Еа to ЕПр.
The boundaries of sublimit stress state 1', 2', 3' and 4' in the area located behind the foundation structure change the slope to the horizon from angle 45°- ф1'/2 to 45°- ф2'/2; 45°- фз'/2; 45°- ф4'/2 in accordance with considered range of active pressure. The boundaries of sublimit stress state 1', 2', 3' and 4' in the intermediate area change the angle from 01 to 02 , 03 , 04. Pointed boundaries are drowned by a logarithmic spiral as shown in fig. 2.
It should be noted that the growth of an uniformly distributed load q at the time of the formation of sublimit stress state zones reduces the sizes of sublimit stress state and changes the boundaries outline of the sliding surfaces. This process continues until the width of limit stress state zone won't reach of the value B.
Conclusions. The most important factor affecting on the assessment of the reactive capacity of the soil bases of gravity-type quay walls and on the determination of work of the "structure- soil base" system is lateral soil pressure. Thus, the study of the reactive capacity of the soil base on the basis of the calculation model proposed of the "structure-soil base" system is an important task. The findings of studies can be used in the design and the construction of considered structures and so for the analysis of the technical condition of the operation structures including rigid retaining walls.
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