(Đồ án hcmute) tan tao 1 apartmment building

PROJECT OVERVIEW

Project introduction

In today's era of national integration and economic growth, there is a rising demand for high-quality living spaces that offer a clean environment and convenient services to support residents' careers This trend has led to the development of numerous upscale apartment buildings by various companies, catering to the evolving living needs of the population.

As urban housing demand rises and available land in city centers dwindles, investing in high-rise apartment projects in suburban areas becomes increasingly sensible These developments not only address housing needs but also enhance the urban landscape when designed thoughtfully and harmoniously with their surroundings.

The investment in the Tan Tao 1 apartment complex aligns with Ho Chi Minh City's policy to encourage investment, addressing the pressing housing needs of residents while fostering economic growth and enhancing urban infrastructure.

Address: 9/11 Ton Duc Thang street, District 1, Ho Chi Minh City.

Scale of construction works

According to Appendix II - Circular No 06/2021/TT - BXD dated June 30, 2021 of the Minister of Construction: Civil construction - grade 2 (10.000 m 2 ≤ slab ≤ 30.000 m 2 or 8 floors ≤ number of floors ≤ 24 floors)

The building has a height of 61.2 m (from the height of 0.00 m, not including the basement)

The construction area of the project is: 1440.25 𝑚 2

1.2.4 Construction function: o Basement floor: Garage arrangement o 1 st floor: Commercial center, service, office o 2 nd – 16 th floors: Apartment layout

Architectural solutions

The plan is rectangular with the area of the land as above (1440.25 m 2 )

The basement, situated at a depth of -3.60 m, features two ramps with an 18% slope for easy access from the main road, ensuring a well-organized entrance and exit to minimize damage and clutter Primarily designed for apartment rentals, the basement is optimally utilized for parking, with strategically placed gain boxes to maximize open space Additionally, the stair and elevator systems are conveniently located at the basement entrance, providing immediate visibility and accessibility for users.

The first floor serves as a communal living area, featuring elegant stainless steel columns, a dedicated book display section, and a welcoming living room that fosters interaction among residents Notably, the building management office is strategically placed for visibility, ensuring guests can easily access assistance when needed Additionally, the internal layout includes a separate entrance, enhancing operational efficiency and management in line with the existing architectural design.

The floor plan for floors 2-16 clearly illustrates the building's functionality, highlighting its effective design and strategic location adjacent to the road at both ends.

1.3.2 Construction traffic solutions: o Vertical walkways: there are 6 elevator rooms, 2 stairs o Horizontal walkways: Corridor is the main walkway

STRUCTURAL OVERVIEW

Analysis and selection of structural

Vertical load bearing system and horizontal bearing system

The vertical structural system has the main load-bearing role in the structure of high- rise buildings:

Receiving loads from slabs, beams to the foundations, to the ground

Receiving horizontal loads acting on the construction (distributed between columns, wall and transmitted to the foundations)

Linked with slabs, beams to form a rigid frame system, keeping the overall stability of the building, limiting the vibration and displacement of the top of the building

A structural system comprises slabs and beams, along with vertical bearing elements like columns and walls, designed to support and transfer loads efficiently Slabs act as rigid horizontal plates, distributing these loads to the vertical structures, ensuring stability and strength in the overall framework.

The building features a design comprising two basement levels and 17 above-ground floors, reaching a total height of 61.2 meters The chosen wall system serves as the primary load-bearing structure, effectively managing vertical loads, while the diaphragm enhances structural rigidity by accommodating both vertical and horizontal forces, as well as additional impacts.

For this project, it is essential to select a beam and slab plan that effectively meets load-bearing requirements while minimizing deflection, especially given the relatively small column pitch Additionally, the design must prioritize usability to ensure optimal functionality.

The vertical structure of the building features an elevator rigid core system, complemented by a diaphragm surrounding the stairs This design enhances the building's ability to withstand lateral loads and improves its torsional resistance.

High-rise buildings require foundations designed to withstand significant compressive forces, while also addressing the substantial horizontal forces generated by earthquake loads Proposed solutions for these foundations must effectively accommodate both types of stress to ensure structural integrity and safety.

Deep foundations include various types such as bored pile foundations, barret pile foundations, reinforced concrete pile foundations, and prestressed centrifugal pile foundations In contrast, shallow foundations consist of one-way strip foundations, two-way strip foundations, and raft foundations When selecting a foundation type, it's essential to compare the benefits of pressed pile foundations against bored piles to determine the most suitable solution for your construction needs.

Materials used

Concrete used according to tables 7 section 6, TCVN 5574 - 2018

Concrete used for structure includes the following types:

Table 2.1 The compressive strength of concrete for the components

The work uses ribbed steel CB400-V (6 ≤ d ≤ 50 mm) and plain steel CB300-T 6 ≤ f ≤

CB400-V ribbed steel (6 ≤ d ≤ 50 mm) has the following parameters:

Table 2.2 Specifications of CB400-V and CB300-T

CB400-V CB300-T Calculated compressive strength 𝑅 𝑠𝑐 350 260 (MPa)

Elastic modulus of steel 𝐸 𝑠 2 × 10 5 2 × 10 5 (MPa)

Preliminary section

For structural design, the minimum moment capacity (ml) must be greater than or equal to the minimum required moment (h min) The depth (D) of the slab ranges from 0.8 to 1.4, depending on the load conditions For beam-type slabs, the moment coefficient (m) is between 30 and 35, while for four-sided slabs, it ranges from 40 to 45, based on the span (l) in the short direction The minimum height (h min) for flat roofs is set at 50 mm Additionally, for two-way working slabs, the largest short side (L1) used in calculations should be 3750 mm, which corresponds to the short edge of the largest slab.

We calculate preliminary the beam height according to the formula:

We calculate preliminary the beam width according to the formula:

Table 2.4 Beam cross-sectional dimentions of typical slab

Types of beams Beam span Preliminary dimension

To select the appropriate column section size, follow these steps: First, determine the vertical transmission area (As) Next, perform a preliminary calculation of the total slab load (q), which includes both dead and live loads, with a value of q = 12.5 kN/m² for initial cross-section estimation Then, assess the number of floors (ns) above the columns in question After that, calculate the force acting on the column Finally, consider the horizontal load effect, represented by coefficient k, which varies based on the column's position, to finalize the preliminary column cross-section.

Where: k is the influence coefficient of the moment, k = 1.1 ÷ 1.5, take k = 1.5 for the side column, k = 1.2 for the middle column, k = 1.1 for the corner column

N: compressive force is approximated as follows:

To enhance bearing capacity and optimize architectural space, the column cross-section will be reduced by approximately one-third for every three floors from the foundation to the roof It is essential to avoid abrupt changes in stiffness; the upper floor structure must maintain at least 70% of the stiffness of the adjacent lower layer Continuous reductions in stiffness across three floors should not exceed a total of 50% (TCXD 198:1997, section 2.5.4).

Table 2.5 Column section preliminary of 2,5 – axis Column 2,5 – axis (B,C,D,E – axis) N (kN/m 2 ) A tt (m 2 ) A choose

Table 2.6 Column section preliminary of remaining columns

Remaining columns N (kN/m 2 ) A tt (m 2 ) A choose

We begin by determining the dimensions of the rigid wall based on architectural drawings and active loads In accordance with Article 3.4.1 of TCXD 198 – 1997, the diaphragm thickness must be at least 150 mm or no less than 1/20th of the floor height.

𝐹 𝑣𝑙 = 𝑓 𝑣𝑙 × 𝐹 𝑠𝑡 = 0.015 × 1440.25 = 21.603 𝑚 2 Where: o 𝐹 𝑠𝑡 : Slab area of each floor o 𝑓 𝑣𝑙 = 0.015

In addition, the selection of diaphragm in the corner and rigid diaphragm at core sections depends on the beam width: o Diaphragm in the corner: 𝑏 = 300 𝑚𝑚 o Rigid diaphragm at core: 𝑏 = 300 𝑚𝑚

LOAD AND IMPACT

Load classification

Loads are classified according to the duration of the load, divided into regular loads and temporary loads (long-term, short-term and special)

The self-weight of the building parts includes the supporting and covering structures, the mass and the pressure of the soil

The long-term temporary loads include the weight and impact of equipment and machinery during use, impact due to temperature, humidity, etc

Short-term loads encompass the weight of individuals, materials, tools, and fixtures involved in equipment servicing and repair, as well as wind loads These loads also arise during the fabrication and erection of building structures.

Special loads arise from explosions, significant breaches of technological processes, equipment failures, and temporary damages Additionally, ground deformation impacts, such as landslides or wet settlement, contribute to these loads by altering soil structure.

Dead load

3.2.1 Self-weight of the structure:

The standard specified gravity of reinforced concrete is 25 kN/m³ with a coefficient of "n = 1.1." The weight of soil cover is 20 kN/m³, also with a coefficient of "n = 1.1," while the weight of water is 10 kN/m³, having an overload coefficient of "n = 1.0." The self-load of the building is determined by the geometrical dimensions of each structural member, and this calculation is automatically performed by the ETABS structural software.

3.2.2 Weight of retaining wall and fixed wall:

𝑔 𝑤 = 𝑛 × 𝛾 𝑡 × 𝑏 𝑡 × ℎ 𝑡 (𝑘𝑁/𝑚) Where: o 𝑛: The overall coefficient o 𝑏 𝑡 : Width of wall o “ℎ 𝑡 = ℎ − ℎ 𝑑 ”: Wall above the beam

The total weight of the partition wall is transformed into a uniformly distributed load on the slabs by considering the entire wall load on the slab This load is multiplied by a coefficient of 1.10 to account for the impact of concentrated loads in the wall array, and then divided by the slab area that supports the walls to determine the uniformly distributed load.

Where: o 𝑛: The overall coefficient o 𝛾 𝑡 = 18 𝑘𝑁/𝑚 2 : Specified gravity of wall 100 mm o 𝑏 𝑡 : Thickness of wall o 𝐿 𝑡 : Length of wall o 𝑆 𝑏 : Slab area

Table 3.1 Load acting on slab

200mm wall railing terrace 1.2m high placed on side beams:

Wall load acting on beams:

The load acting to construction:

Figure 3.1 Structural layers of ordinary slab Table 3.2 Dead loads on the slab bedroom, kitchen, dining room and living room

Specified gravity 𝒕 𝒍𝒂𝒚𝒐𝒖𝒕 Standard dead load 𝜸 𝒐𝒗𝒆𝒓𝒂𝒍𝒍 Calculated dead load kN/m 3 m kN/m 2 kN/m 2

4 Total finish dead load (not including the weight of the slab itself) 1.33 1.64

Table 3.3 Dead loads acting on the toilet slab

Ceramic tiles 10 mm Morta 20 mm Reinforcement concrete 150 mm Morta 15 mm

Table 3.4 Dead loads acting on the terrace slab

5 Total finish dead load (not including the weight of the slab itself) 1,7 2.122

Table 3.5 Dead loads acting on the roof slab

Table 3.6 Dead loads acting on the basement slab

Live load

The live load acting on the building is based on TCVN 2737 - 1995 and the function of each work area, the live load value for each functional area is as follows:

Table 3.7 Summary table of active loads Functions of the rooms

(kN/m 2 ) n Long - term live load (kN/m 2 )

Short - term live load (kN/m 2 )

Living room, dining room, bathroom

Lobby, corridor, apartment floor stairs

Analysis of building dynamics

In high-rise buildings, it is essential to account for both static and dynamic loads, as these loads vary over time Static loads include factors like live floor loads, while dynamic loads encompass influences such as wind and earthquakes Unlike static problems, dynamic issues involve changes in stress and strain states over time, necessitating the consideration of inertia forces and drag forces due to significant acceleration of the system.

The free oscillation patterns of a building are analyzed using a simplified finite mass concentration point structure diagram Each oscillation type is defined by the amplitude of mass concentration points and their individual frequencies This study treats the building as a cantilever bar anchored in the foundation, with mass concentration points aligned with each floor level The mass at these points includes the structure's own weight, the floor layers, wall volumes, and a portion of the live load, calculated from half the height of the lower floor to half the height of the upper floor.

In this analysis, we assume that the floor beam exhibits significant rigidity within its plane, that the total weight of each floor is concentrated at its level, and that the vertical displacement of the structure remains minimal in comparison to the horizontal displacement.

Dynamic problems involve load changes over time, affecting the internal forces within a structure, making texture analysis a time-dependent function In contrast, static problems assume constant conditions When a structure accelerates, it produces an inertial force (F = ma), which must be included in the static equilibrium equations to ensure accuracy.

For diagrams with more than 3 mass concentration points, determining the specific vibration pattern of the building requires a large number of calculations

Therefore, students use the help of ETABS software

3.4.2 The volume of participation fluctuates:

Standard volume value for each slab:

The mass of participating oscillations declared during oscillation analysis is 100% dead load and 50% live load for dynamic wind; 100% dead load and 24% live load when calculating earthquakes

Figure 3.2 Declare Mas Source Data in Etabs

Buildings that declare both dynamic wind and earthquake loads should choose the number of vibrations to be considered in accordance with the conditions under consideration:

According to wind dynamics, the first number of cycles need considered is satisfied:

3.4.4 Space frame model: o Select the model, declare the grid unit o Material declaration o Declare section o Model building o Assign cross-section of floor beams, columns and walls o Structural analysis o Check model and run

Figure 3.3 Model of building in Etabs

Table 3.8 Period and frequency table of oscillation Case Mode Period

Table 3.9 Frequency period and percentage of mass involved in fluctuating

Fluctuating modes: 1, 2, 3 có 𝑓 < 𝐹 𝐿 = 1.3 𝐻𝑧 o Mode 1 oscillate to Y-direction o Mode 2 oscillate to X-direction o Mode 3 oscillate to Z-direction

According to the experience formula, the period of Mode 1 is in the range (0.1 ÷ 0.14)𝑛

Where n is the number of floors (n = 17) We have: Mode 1 = 1.916 is in the range:

Figure 3.7 Mode 1 oscillate to Z-direction

Figure 3.5 Mode 2 oscillate to X-direction Figure 3.6 Mode 1 oscillate to Y-direction

Wind load

3.5.1 Static component of wind load:

Standard wind pressure (W0) is calculated using monitored wind velocity data at a height of 10 meters, reflecting an average speed that is exceeded once every 20 years over a 3-second interval, in accordance with the wind pressure zoning of the terrain.

The wind pressure value is determined for each wind pressure partition:

Table 3.10 Table of wind pressure according to the map of wind pressure zoning

With the location of the project located in District 1, Ho Chi Minh City, the wind pressure area is determined to be II-A:

Select the method of inputting the static component of the wind load as the force concentrated at the geometric center of the floor in two directions

The wind load on a building can be calculated using the formula \( W_j = \gamma \times W_0 \times k(z_j) \times c \times H_j \times B_j \) In this equation, the reliability coefficient \( \gamma \) is set to 1.2 for buildings older than 50 years The aerodynamic coefficient \( c \), which accounts for both intake and thrust winds, totals 1.4, derived from a windward side measurement of 0.8 plus 0.6 Additionally, \( H_j \) represents the wind height at the j-th floor of the building.

To calculate the static wind component for the j-th floor, the formula is given by Hj = Hi + Hj-1, where Hj represents the height of the floor Additionally, Bj denotes the windward width of the j-th floor.

37 o 𝐻 − Relative height of the upper floor compared to the lower floor o 𝑘 𝑡 − Coefficient taking into account the change of wind pressure with altitude apply formula A.23 in TXCD 229:1999

Table 3.11 Wind load according Y – direction STORY

Width catch the wind W j W j tc W j tt m (m) (m) kN/m 2 kN kN

Table 3.12 Wind load according X – direction

3.5.2 Dynamic component of wind load:

According to [TCVN 229-1999]: Instructions for calculating the dynamic component of wind loads according to the standard TCVN 2737 - 1995 The building has a height of

H = 60.6m > 40m, so the calculation must take into account the dynamic wind component for the building

Calculation basis: According to [TCVN 229 -1999: Instructions for calculating the dynamic component of wind loads according to the standard TCVN 2737-1995]

The standard value of the dynamic component of the wind acting on element j of the ith vibration pattern is determined by the formula:

The equation \( W P(j_i) = M_j \times \xi_j \times \psi_i \times y_{ji} \) describes the relationship between various parameters in a structural analysis context Here, \( M_j \) represents the concentrated mass of the j-th element, while \( \xi_j \) is the dynamic coefficient for the i-th vibration, determined from its corresponding graph In the case of reinforced concrete structures, a value of \( \delta = 0.3 \) is utilized for calculations.

Width catch the wind W j W j tc W t tt m m m kN/m 2 kN kN

39 o The 𝜀 𝑖 parameter is determined by the formula:

940 × 𝑓 𝑖 Where: o 𝛾 − Reliability coefficient of load o 𝑊 0 ( 𝑘𝑁

The specific frequency of oscillation, denoted as \( m_2 \), is influenced by the factor \( \psi_i \), which is calculated by segmenting the building into multiple sections This approach allows for the wind load on each section to be treated as constant, thereby facilitating more accurate assessments of structural performance.

𝜓 𝑖 is determined by the formula:

The dynamic component of wind load acting on the j-th part of a building is quantified by the formula ∑ 𝑛 𝑗=1 𝑦 𝑗𝑖 2 × 𝑀 𝑗 o 𝑊 𝐹𝑗 This standard value reflects various types of oscillations while considering the impact of wind velocity pulses, with its measurement expressed in units of force.

The wind pressure acting on the jth part of a building is represented by the equation \( W_{Fj} = W_j \times \xi_j \times S_j \times v \), where \( W_j \) denotes the standard value of the static wind pressure, \( \xi_j \) is the dynamic pressure coefficient at the specific height of the jth section, and \( S_j \) refers to the area of the windward surface of that section Additionally, the dynamic component of the wind load is calculated using this formula.

𝑊 𝑃(𝑗𝑖) 𝑡𝑡 = 𝑊 𝑃(𝑗𝑖) × 𝛾 × 𝛽 (𝑘𝑁) Where: o 𝛾 = 1.2 − Reliability coefficient of load o 𝛽 − Wind load adjustment coefficient according to the use time of the building, taking 𝛽 = 1

Table 3.14 Calculated wind load dynamics in the Y-direction

No Story M j (kg)  j   1X  1X W Fj (kN) y ji y ji W Fj y ji 2 M j W pjiX (kN) W pjiX tt

Table 3.16 Calculated wind load dynamics in the X-direction

No Story M j (kg)  j  1y  1y W Fj (kN) y ji y ji W Fj y ji 2 M j W pjiY (kN) W pjiY tt

Equivalent horizontal static force method:

This method of analysis is applicable to houses whose response is not significantly affected by vibrations of higher order than the fundamental in each principal direction

The requirements of this clause are considered satisfied if the building structure meets both of the following conditions:

There are fundamental oscillation periods T1 in two main directions less than the following values:

2,0𝑠(𝑇 𝑐 𝑡𝑎𝑘𝑒𝑛 𝑖𝑛 3.2.2.2 𝑇𝐶𝑉𝑁 9386: 2012) Satisfy the criteria for vertical regularity given in 4.2.3.3 TCVN 9386:2012

This method of analysis should be applied to buildings that do not satisfy the conditions stated in 4.3.3.2.1 TCVN 9386:2012 when applying the equivalent lateral static force analysis method

The response of all types of vibrations that contribute significantly to the overall response of the house must be considered

The requirements given in 4.3.3.3.1 TCVN 9386:2012 may be satisfied if one of the following two conditions is met:

The sum of the effective masses of the considered vibration patterns accounts for at least 90 % of the total mass of the structure;

All oscillations with an effective mass greater than 5 % of the total mass are taken into account

When using the spatial model, the above conditions need to be checked for each required direction

When the criteria outlined in section 4.3.3.3.1 of TCVN 9386:2012 are not met, particularly in structures where torsional vibrations play a significant role, the minimum number of vibration patterns (k) must be taken into account during the analysis This ensures that the spatial requirements fulfill both necessary conditions for accurate evaluation.

𝑘: the number of oscillations to be considered in the calculation

𝑛: the number of floors above the foundation or top of the underlying hardware

𝑇 𝑘 : period of oscillation of the k th form

→ Based on the construction characteristics, the method of vibration response spectrum is selected to calculate earthquakes

𝑎 𝑔 , 𝑆, 𝑇 𝐶 , 𝑇 𝐷 : has been defined in section 3.2.2.2 TCVN 9386:2012

𝛽 = 0.2: coefficient corresponding to the lower bound of the horizontal design spectrum

In which: (according to TCVN 9386:2012)

Direction: horizontal (without considering the vertical)

In Y-direction: according to article 4.3.3.5.2 TCXDVN 375 - 2006 if the 𝑎 𝑣𝑔 is greater than 0.25g, the vertical component of the seismic action should be taken into account.

Load combination

According to TCVN: 2737-1995, there are two types of load combinations: basic combinations and special combinations The basic combination 1, also known as the main combination, consists of a permanent load (DL) and a temporary load, with a combination factor set at 1 Basic combination 2, referred to as a sub-combination, involves two or more types of loads, where the calculated values of temporary loads or their corresponding internal forces must be multiplied by a uniform combination factor; specifically, short-term transient loads are multiplied by a factor of 0.9.

For special combinations, including earthquake loads, the combination of internal forces should comply with TCVN: 9386 – 2012

Table 3.17 Load combination by ultimate limit state ULTIMATE LIMIT STATE (ULS): THGH I

SW Finish WALL LIVE 1 LIVE 2 WIND X WIND Y EQX EQY

Table 3.18 Load combination by service limit state SERVICE LIMIT STATE (SLS): THGH II

SW Finish WALL LIVE 1 LIVE 2 WIND X WIND Y EQX EQY

In structural engineering, various loads are considered for safety and stability, including permanent loads like self-weight (SW), temporary loads such as finish layers, and wall loads (WALL) Additionally, live loads (LIVE 1, 2) account for variable usage, while wind loads are categorized by direction (WLX for X and WLY for Y) Special loads, including earthquake forces (EQX and EQY), are also critical in assessing structural integrity under dynamic conditions.

STAIRS

General concept

Stairs serve as the primary vertical transportation method within a building, consisting of a series of steps that create the ladder's structure These steps are linked by landings and projections, forming a cohesive staircase Beyond their functional role, stairs are significant in architecture and art, contributing to the overall aesthetic appeal of the building.

Structure of stair: Ladder (structural depth), landing, beam, handrail

Stair structure

4.2.1 Floor plan and section of stairs:

4.2.2 Choose the preliminary size of the stairs:

The height of typical floor: ℎ 𝑑 = 3600 𝑚𝑚

The stair has 18 steps, each skirtboard has 9 steps o Width of step: 𝑏 = 300 𝑚𝑚 o Height of step: ℎ = 190 𝑚𝑚

The landing is connected directly to the rigid wall, so there is no need to arrange the landing beam

According to “Kết cấu bê tông cốt thép Tập 3 – Võ Bá Tầm” book o Tilt angle of skirtboard: tan 𝛼 =ℎ

Preliminary selection of the section

→ 𝑆𝑝𝑎𝑛 𝑜𝑓 𝑠𝑘𝑖𝑟𝑡𝑏𝑜𝑎𝑟𝑑 𝐿 0 = 3700 𝑚𝑚 Preliminary selection of the skirtboard:

30) × 3700 = (123.3 ÷ 148)𝑚𝑚 → ℎ 𝑠 = 150 𝑚𝑚 Preliminary selection of the beam:

Note: According to “Kết cấu bê tông cốt thép Tập 3 – Võ Bá Tầm” book, at case 2: Skirtboard and beam are continuous

Figure 4.4 Detail structure of stairs layers

Active load

4.3.1 Load acting on the landing:

Self-weight of layers of skirtboard:

Table 4.1 Load acting on landing

Load Material Thickness 𝜸 n Calculated load m kN/m 3 kN/m 2

Table 1 TCVN 2737-1995 Reliability factor for loads due to the mass of the building material and soil

Material and soil Reliability factor

Concrete with a volumetric weight greater than 1600 kg/m 3 , reinforced concrete, reinforced stone bricks and wood 1.1 Concrete with a volumetric mass of not more than

1600 kg/m3, separating materials, plasters and finishes (plates, shells, roll materials, coatings, primers, etc.) depending on production conditions

4.3.2 Load acting on the skirtboard:

Self-weight of layers of skirtboard:

𝛾 𝑖 : 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑖 𝑡ℎ 𝑙𝑎𝑦𝑒𝑟; 𝛿 𝑡𝑑,𝑖 : 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑐𝑙𝑎𝑠𝑠 𝑖 For granite tiles with thickness 𝛿 𝑖 :

For concrete cement with thickness 𝛿 𝑖 :

For step floor have section ℎ 𝑏 × 𝑙 𝑏 :

Table 4.2 Load active on skirtboard

Load Material Thickness 𝜸 n Calculated load m kN/m 3 kN/m 2

Load the transmission skirtboard onto the beam:

Note: Load the transmission skirtboard onto the beam by reaction at the support with the value 52.12 kN/m as the figure 4.3.3

𝑔 𝑏 = 𝑏 𝑏 (ℎ 𝑏 − ℎ 𝑠 )𝑛𝛾 𝑏 = 0.2 × (0.4 − 0.15) × 1.1 × 25 = 1.375 𝑘𝑁𝑚 Weight of rigid wall acting on beam:

Table 4.3 Dead load acting on the slab Structural layer Thickness (m) Self-weight n Calculated load

Live load acting on the slab: 𝑝 𝑡𝑡 = 𝑝 𝑡𝑐 × 𝑛 = 0.3 × 1.2 = 0.36 𝑘𝑁𝑚

Load transmission slab onto the beam:

For simplicity and safety, we consider the load from the skirtboard to be evenly distributed throughout the beam:

Calculation diagram

With the support of Sap2000 software, solve internal forces for the two-headed linkage cases as follows:

Figure 4.6 Fixed connection moment diagram

Figure 4.7 Pin connection moment diagram

Figure 4.8 Pin and roller connection moment diagram

Figure 4.9 Fixed connection shear force diagram

Figure 4.10 Pin connection shear force diagram

Figure 4.11 Pin and roller connection shear force diagram

Figure 4.12 Beam of stair diagram

Figure 4.13 Moment diagram of beam

Figure 4.14 Shear force diagram of beam

Internal force of landing, skirtboard results:

Based on the above diagrams, as well as to satisfy the condition that the connection is not completely fixed or pin, redistribute the moment as follows:

Calculation of reinforcement

𝑅 𝑠 = 350(𝑀𝑃𝑎); 𝐸 𝑠 = 200000(𝑀𝑃𝑎); 𝜉 𝑅 = 0.533; 𝛼 𝑅 = 0.39 Calculate reinforcement according to TCVN 5574-2018

𝑎 = 25𝑚𝑚 → ℎ 0 = ℎ − 𝑎 = 150 − 25 = 125𝑚𝑚 With the condition in work: 𝛾 𝑏 = 0.9; 𝛾 𝑠 = 1

Table 4.4 Calculating reinforcement for skirtboard Location Moment

4.5.2 Check the shear resistance of the skirtboard:

According to Article 8.1.3 of TCVN 5574-2018, the calculation of the strength of reinforced concrete members subjected to shear force must adhere to two key conditions First, it is essential to assess the strength of flexural members along the concrete strip between inclined sections If the cross-section does not meet the required standards, it may be necessary to increase either the strength level or the size of the section.

The skirtboard slab is designed to resist shear forces based on the strength calculations of the concrete strip between inclined sections According to Article 8.1.3.3.1 of TCVN 5574-2018, the shear force that the unreinforced skirtboard slab can withstand must meet specific criteria.

Calculated according to flexural structure, rectangular cross-section

Calculate reinforcement according to TCVN 5574-2018:

Table 4.5 Calculating reinforcement for beam Moment

Extra reinforcement 1𝜙16 at bottom beam

Shear force of concrete resistance:

𝑄 𝑚𝑎𝑥 = 131.15 𝑘𝑁 > 43.125 𝑘𝑁 → 𝑁𝑒𝑒𝑑 𝑡𝑜 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑠𝑡𝑖𝑟𝑟𝑢𝑝 Calculated according to flexural structure, rectangular cross-section

Distance between stirrups at support: 𝑠 = 150 𝑚𝑚 Distance between stirrups at span: 𝑠 = 250 𝑚𝑚

𝜙8𝑎150: at beam support (L/4) 𝜙8𝑎250: at beam center (L/2) Check the conditions (according to TCVN 9386-2012 and TCVN 5574-2018):

TYPICAL FLOOR DESIGN

General concept

A floor is a crucial structural element that directly supports internal loads perpendicular to its surface In multi-storey buildings, it plays a vital role in providing horizontal rigidity, enabling the transmission of horizontal loads, such as those from wind and earthquakes, to the frame structure.

The floor is also subject to internal forces due to uneven settlement, internal forces arising from temperature changes

The floor maintains complete rigidity in its horizontal plane, disregarding any curvilinear strain affecting the elements Additionally, the influence of this floor's stiffness on adjacent floors is not considered.

Computational hypothesis

The floor maintains a completely rigid horizontal plane, disregarding any curvilinear strain on its elements Additionally, the stiffness of this floor does not affect the adjacent floors.

All load bearing system components on each floor have the same horizontal displacement

When a horizontal load is applied to a building, it distributes forces across the floors, which then transfer these forces to the columns and walls.

The axial deformation of the floor, beam is considered negligible.

Dead loads acting on the floor

Dead loads acting on the floor are shown in Chapter 3, Section 3.2.

Live load acting on the floor

Live load acting on the floor are shown in Chapter 3, Section 3.3

Set up calculation scheme

The 3rd floor model is exported from ETABS to SAFE including the force on the floor

Figure 5.1 3D model of the 3rd floor floor in SAFE

Figure 5.2 Floor plan of the 3 rd floor in SAFE

Load cases are exported from ETABS:

Figure 5.3 Finish load acting on 3 rd floor

Figure 5.4 Live load (LL2) acting on floor

Figure 5.6 Wall load acting on floor

Figure 5.8 Draw trip sequences in the y direction with the width of 1m to get the internal force

Figure 5.9 Draw trip sequences in the x direction with the width of 1m to get the internal force

Floor test by limit state I

5.6.1 Sequence of calculation of reinforcement for floor:

The calculation is done as follows:

The selected floor reinforcement content must satisfy the following requirements: (according to section 10.3.3.1 TCVN 5574:2018)

5.6.2 Calculation and arregement rebar for floor:

From the long strips of the floor Take internal force and cross-section, calculate steel as a beam Calculate steel for floor 3 with moment value at span M1=7.139 kN/m

Table 5.1 Spreadsheet of floor steel in X direction Slab Section M

𝜶 𝒎 𝝃 𝑨 𝒔 Steel 𝝁 kN/m 𝒎𝒎 𝟐 Φ (mm) a As (mm 2 ) %

Table 5.2 Spreadsheet of floor steel in Y direction Slab Section M

𝜶 𝒎 𝝃 𝑨 𝒔 Steel 𝝁 kN/m 𝒎𝒎 𝟐 Φ (mm) a As (mm 2 ) %

FRAME DESIGN

Shape and size

Tan Tao apartment according to architectural drawings include:

𝐿 𝑥 = 39.5 𝑚 𝐿 𝑦 = 39.5 𝑚 The structural system used is the frame structure system - hard wall (hard core).

Section size

Dimensions of space frame members have been preliminarily selected in Chapter 2

Evaluation of frame internal force results

Figure 6.1 Name of frame element

Figure 6.2 Force chart along the column, the wall (kN)

Figure 6.3 Diagram of the moment of beams, columns and frames (kN/m)

Figure 6.4 Diagram of shearing force of beams and columns (kN)

Figure 6.5 Wall shear force diagram frame B

Figure 6.6 Diagram of wall moment axis frame (kN/m)

Figure 6.7 Diagram of wall axial force

6.3.2 Displacement of the top of the building:

As per TCVN 5574:2018, specifically in table M.4 of Appendix M, it is essential to maintain a specific ratio between the horizontal displacement (D) at the top of a building due to wind load and its height (H) measured from the foundation surface.

H: is the height of the building from the top of the foundation

𝑓: is the horizontal displacement at the top of the structure

The reactions in the two modes of vibration are considered to be independent of each other

𝑓 𝑦 𝑚𝑎𝑥 , 𝑓 𝑡𝑢 𝑥 Check 4 combination SLS2, SLS3, SLS4 and SLS5:

Story Diagram Combo Load UX UY mm mm mm mm

→ The displacement at thep top is sastified

6.3.3 Check the relative horizontal displacement between floors:

Relative horizontal displacement between floors due to wind:

Appendix M.4.4 of TCVN5574:2018 specifies in table M4 that buildings must exhibit limited horizontal displacement and deflection, particularly in response to wind loads, foundation inclination, and the influences of temperature and climate.

Relative horizontal displacement of a floor in a multi-storey house with “walls, partitions made of bricks, gypsum concrete, reinforced concrete panels” with limited displacement:

In a multi-storey building, the height of the floors, denoted as ℎ𝑠, is defined differently for lower and upper levels For the lower floors, it is measured from the foundation surface to the axis of the roof floor beams In contrast, for the remaining floors, the height is determined by the distance between the axes of the beams on each floor, starting from the top of the foundation to the axis of the roof support beams.

Table 6.2 Horizontal limit displacement f u according to structural requirements

Houses, walls and partitions Connection between wall and frame

2 One floor of a multi-storey house: Soft ℎ 𝑠 /300 a Walls and partitions made of bricks, gypsum concrete, reinforced concrete panels

Hard ℎ 𝑠 /500 b Walls (natural stone cladding) made of bricks ceramic Hard ℎ 𝑠 /700

(with self-loading walls) floor height, m

Take SLS2 (x-axis), SLS4 (y-axis) Combo to check condition:

Table 6.3 Combination table for checking floor displacement due to wind X, Y Story Height

𝒉 𝒔 /𝟓𝟎𝟎 Check mm mm mm mm

Relative horizontal displacement between floors due to earthquake

According to section 4.4.3.2 TCVN 9386:2012, Limit the relative horizontal displacement between floors

For buildings with non-structural members of brittle material attached to the structure:

𝑑𝑟 𝜗 ≤ 0.005ℎ For buildings with non-structural parts of flexible materials:

For buildings with non-structural parts fixed so as not to affect structural deformation or buildings without non-structural parts

𝑑𝑟 𝜗 ≤ 0.01ℎ Where: dr: relative design horizontal displacement between floors, determined as the difference of mean horizontal displacements “ds” at the ceiling and floor of the floors under consideration

𝑑 𝑟 = 𝑑 𝑠 = 𝑞 𝑑 × 𝑑 𝑐 (𝑎𝑐𝑐𝑜𝑟𝑑𝑖𝑛𝑔 𝑡𝑜 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 4.3.4.1 𝑇𝐶𝑉𝑁 9386: 2012) ds: displacement of a point of the structural system caused by the design seismic action

The displacement behavior coefficient, denoted as \( q_d = 3.9 \), is typically assumed to be "q" unless stated otherwise The displacement at a specific point within the structural system is calculated through linear analysis, utilizing the design response spectrum.

The reduction factor considers the diminished periodicity of seismic actions in relation to damage limitation requirements, which vary based on seismic hazards and the importance of the structure (Appendix E).

According to section 4.4.3.2 of TCVN 9386:2012, recommended values for the coefficient v vary based on seismic hazards and the importance of the building Specifically, a value of 𝜗 = 0.4 is suggested for buildings with importance levels I and II, while a value of 𝜗 = 0.5 is recommended for buildings categorized as importance levels III and IV, with h representing the height of the story.

𝜗 × 𝑞 𝑑 = 0.0032 × ℎ dc: is the dislocation displacement from the Etab model

Table 6.4 Combination table checking floor displacement due to earthquake X, Y Story Height

Limit value h Check mm mm mm mm

In order for the structure not to overturn when subjected to earthquakes, the following conditions must be satisfied: (according to section 2.6.3 TCVN 198:1997)

𝑀 𝐶𝐿 : is moment resist overturn 𝑀 𝐿 : is moment overturn

According to section 3.2 of TCVN 198 - 1997, high-rise reinforced concrete buildings with a height-to-width ratio exceeding 5 must undergo testing for anti-rollover stability against dynamic impacts from earthquakes and wind loads In the calculation of the anti-rolling moment, the live load of the floors is considered at 50%, while the final load is factored at 90%.

GEOGRAPHY OF CONSTRUCTIONS

Introduction to engineering geology

A new development project is set to be constructed at the intersection of Ton Duc Thang and Le Thanh Tong streets in District 1, Ho Chi Minh City, covering an area of approximately 900 square meters.

The survey area features relatively flat topography with minimal elevation differences, making it suitable for construction Additionally, the presence of solid construction works nearby enhances the area's viability for development.

Students chose borehole BH3 from the geological survey of the Tan Tao Apartment Building in District 1, Ho Chi Minh City, to perform calculations for the project's foundation design This selection was made due to borehole HK3's passage through various layers and its significant sandy soil layer length.

The soil profile consists of four distinct layers extending from the surface to a depth of approximately 35 meters Layer 1 is filled soil (fs) reaching depths of 1.4m to 1.8m Layer 2 comprises very plastic clay mixed with organic fine sand (OH), spanning from 1.4m/1.8m to 4.7m/5.3m Layer 3 features medium-density fine sand and poorly mixed powder (SP-SM) found between 6.5m/7.5m and 11.2m/13.2m, along with thin lenses (3a and 3b) Finally, Layer 4 consists of medium-density fine sand mixed with clay and powder (SC-SM), extending from 9.0m/13.2m to depths of 33.5m/36.5m, also containing thin lenses (4a and 4b).

The primary components of this section consist of fine-grained sand mixed with clay and powder, while layers 1 and 2 exhibit poor and unstable composition due to their thin thickness The fine sandy soil layer demonstrates medium density, offering moderately favorable geotechnical conditions for foundation design and construction.

Soil layer 2 is characterized by soft soil, which requires careful consideration during foundation design and construction Additionally, the non-cohesive properties of the fine-grained sandy soil layers located near the surface must be addressed during excavation and basement construction.

The second part consists of three layers of hard clay located between depths of 35m and 50m Layer 5 features flexible clay mixed with fine sand (CL) in a semi-hard to hard state, extending from depths of 33.5m/36.5m to 39.0m/41.0m Layer 6 comprises very plastic clay (CH) in a hard state, found from 39.0m to 45.0m Lastly, Layer 7 consists of plastic clay mixed with fine-grained sand (CL) in a hard state, distributed between depths of 45m and 48.7m/51.4m.

The soil layers in this area exhibit a consistent depth and thickness, characterized by a clay composition that ranges from semi-hard to hard powder With a thickness between 12m and 16m, these layers provide favorable geological conditions for construction, facilitating the design and implementation of deep pile foundations.

The final section of the drilling profile reveals dense to very dense sandy soil layers, extending from approximately 50m to the maximum drilling depth of 100m This includes Layer 8, characterized by medium-density fine sand mixed with fine clay (SC-SM), found between depths of 49.3m to 61.3m, along with lens 8a (SC) Additionally, Layer 9 consists of very dense fine-grained sand combined with clay (SC-SM), spanning depths from 57.0m to 89.0m.

112 o Layer 10: Fine sand mixed with clay, powder (SC-SM) with very tight density, distributed from a depth of 89.0m to more than 100m

The soil layers in this area exhibit a consistent thickness and depth, primarily composed of fine-grained sand with high density These favorable engineering geological conditions facilitate the design and construction of deep pile foundations.

Groundwater depth was recorded after the completion of drilling 24 h and 1 week thereafter The results are presented in the following table:

The existing underground water level is about 3-4m

Theoretical basis of geological data statistics

7.2.1 Processing and statistics to calculate the foundation:

Geological surveys for foundation design involve numerous boreholes and soil samples across extensive soil layers A key challenge is selecting appropriate criteria that accurately represent the foundation Initially, drilling and sampling were guided by observable changes in soil color and the classification of soil grains within each layer.

According to TCVN 9362 - 2012, an engineering geology class is defined by a set of values exhibiting mechanical and physical characteristics with a low coefficient of variation Consequently, samples that deviate significantly from the average value of a geological unit must be excluded.

Statistics is a very important job in the calculation of the foundation, requiring high accuracy

7.2.2 Determine the standard value, the calculated value of the physical and mechanical properties of the soil:

Division of geological units (engineering geological classes)

Where: σ - the mean square error of the feature

Ai - eigenvalue a characteristic of sample i from a particular experiment n - the number of experiments is determined, where n is the number of samples in the same class

In a soil layer sample set, a coefficient of variation (𝑣) less than or equal to the allowable limit ([𝑣]) indicates that the geological unit condition is met Conversely, if 𝑣 exceeds this threshold, it is essential to exclude data that exhibit significant errors, with [𝑣] varying based on the specific characteristics being analyzed.

Table 7.2 Coeficient of variation Characteristic of soil Coefficient of variation

Raw error exclusion: exclude the Ai error from the set when:

, 𝑛 ≤ 25 v - Statistical criteria determined depends on the number of experimental samples, look up from the following table:

If there is an error, remove the Ai error and recalculate the above values

7.2.3 Determination of standard characteristics and calculated values:

Determine the standard values of 𝑐 𝑡𝑐 and 𝜑 𝑡𝑐 by the method of least squares of direct shear tests for all experimental values of τ in a engineering geology unit

The relationship between τ and σ is determined by the Coulomb equation (soil strength condition):

𝑐 − 𝐶𝑜ℎ𝑒𝑠𝑖𝑜𝑛 Use the least squares method to find c and φ:

Taking the partial derivative of both sides with respect to c and tgφ, respectively, we get:

𝜕𝑐∑(𝜏 1 − 𝜎 𝑖 𝑡𝑔𝜑 − 𝑐) 2 = ∑[−2(𝜏 1 − 𝜎 𝑖 𝑡𝑔𝜑 − 𝑐)] = 0 From here we deduce the equation of two unknowns c and tgφ:

Solving the equation we get:

𝐴 𝑡𝑡 = 𝐴 𝑡𝑐 (1 ± 𝜌) Where: 𝜌 − is the accuracy index, calculated by the following formula:

√𝑛For c and φ: 𝜌 = 𝑡 𝛼 × 𝑣 Where: 𝑡 𝛼 − coefficient depends on the confidence probability α

When calculating the ground by intensity (TTGH1), then α = 0.95 When calculating the ground according to deformation (TTGH2), then α = 0.85

The coefficient 𝒕 𝜶 corresponds to the confidence probability α α = 0.85 α = 0.95

In statistical analysis, the minimum sample size for limit state statistics is n ≥ 6 For sample sizes less than 6 (n < 6), statistical tests are conducted with ν < [ν], using standard values such as mean density (γ) and humidity (W) In the case of the fast undrained shear test, when there is only one sample (n=1), which corresponds to three pairs of values (σ, τ), only standard values are calculated However, when the sample size is n ≥ 6, corresponding to six pairs of values (σ, τ), limit state statistics can be applied.

When looking up the table tα note n-1, n-2 Using the LINEST function in EXCEL to support statistics of the stick force c and the friction angle in φ

When making statistics for the criteria c, φ, we must initially check the statistics for each pressure level to know if there is any type of sample or not.

BORED PILE FOUNDATION PLAN DESIGN

Introduce about bored piled foundation

Bored piles are a type of foundation support created by drilling holes into the soil, which are subsequently filled with concrete The hole-making process can involve various techniques, including drilling and excavation Currently, the standard diameters for bored piles range from 600 mm to 1200 mm.

Understanding ground conditions and construction technology is essential for designing and constructing quality piles that meet regulatory standards.

8.1.1 Advantages : o During construction, there is no impact on the surrounding environment o The bearing capacity of the pile is very large o The amount of steel in bored piles is small, mainly to support horizontal loads o Capable of constructing piles when passing through interspersed hard soil layers

8.1.2 Disadvantages: o High cost due to complicated construction techniques, although the design of reinforcement in piles is very economical o The method to check the quality of bored pile concrete is very complicated by ultrasonic method or pile static load test o The side friction of the pile body can be significantly reduced compared to the driven pile and the pressed pile due to the hole drilling technology

Bored piles are typically constructed using ordinary concrete, which must meet specific requirements for both strength and workability The concrete grade for bored piles should generally be no less than 20 MPa, and it is essential to achieve a large slump to ensure the continuity of the pile Refer to Table 8.1.3 for detailed slump specifications.

Table 8.1 Punching concrete bored piles

Pouring freely in water, the reinforcement has a large gap that allows the concrete to move easily

The reinforcement spacing is not large enough to allow the concrete to move easily, when the pile head is in the temporary bulkhead area

When the pile diameter is 15 Normally, the concrete of bored piles has a cement content of not less than 350kg/m3

To avoid segregation due to high slump concrete or dehydration in high temperature conditions, appropriate admixtures should be used

The reinforcement of bored piles is determined according to the calculation, and at the same time, the structural requirements must be satisfied:

For tension piles, it is essential to distribute the longitudinal reinforcement evenly along the entire length of the pile Proper welding of the longitudinal reinforcement is crucial to meet the bearing requirements When the pulling force is minimal, the reinforcement should be placed to the necessary depth to ensure that the pulling force is fully countered by the friction between the pile and the surrounding soil.

For axially compressed piles, the reinforcement content is not less than 0.2-0.4%

The diameter of reinforcement is not less than 10mm and is arranged evenly around the pile circumference

For piles exposed to horizontal loads, the reinforcement content should be maintained between 0.4% and 0.65% Typically, bolts ranging from Φ6 to Φ10 are used, with a spacing of 200 to 300 mm A single ring belt or a discontinuous spiral belt can be implemented for reinforcement When the length of the steel cage exceeds 4 meters, it is essential to enhance the stiffness of the entire structure by adding Φ12 steel belts spaced 2 meters apart, which also serve to secure the rollers and provide an additional layer of reinforcement protection.

The thickness of the longitudinal reinforcement protection layer of bored piles is not less than 50mm

Bored piles are constructed by drilling holes from the ground level and removing the soil within them During construction, soil stretching can create tensile stress on the piles, which continues until the piles are sufficiently loaded to withstand this tensile force, ultimately alleviating the stress through the transfer of the applied load.

In tall buildings, the horizontal forces are minimal, allowing for the steel cage to be staggered or entirely disconnected to mitigate earthquake effects, based on the moment diagram and shear force analysis of piles subjected to horizontal loads.

8.1.5 Contents of foundation and pile foundation design:

Pile foundations are designed based on limit state criteria, which include Limit State I (TTGH I) focusing on bearing capacity, material strength, and stability of both piles and foundations, and Limit State II (TTGH II) addressing deformation aspects such as settlement and horizontal displacement of piles.

Structure and size

Student choose height for all cap: 2.2m

Choose height of pile cap: Hd = 2.2 m

Elevation of the bottom of the pile cap: 𝐷 𝑓 = −7.2 − 2.2 = −9.4𝑚

The pile is attached to the cap: 0.1 m

Pile head smashing section: 0.7 m (the reinforcement section anchored to the cap approximately 40d)

The total section of the pile head and the pile attached to the cap: 0.7 + 0.1 = 0.8 m Pile length from the bottom of the cap: 𝐿 = 53 − 9.4 = 43.6 𝑚

The depth of the pile tip is set at -53 meters, ensuring it does not penetrate the eighth soil layer, which consists of a dense mixture of fine sand and clay powder, exhibiting a Standard Penetration Test (SPT) value ranging from 32 to 47.

Choose protective concrete layer: 30mm

The reinforcement content in piles should range from 0.4% to 0.65% based on structural requirements, but it must not fall below the minimum threshold of 0.2% to 0.4% when exposed to horizontal loads For this application, select 14𝜙20 reinforcement, which corresponds to an area of 4398 mm².

Figure 8.1 Detail of bored pile

Figure 8.2 Geological cross-section and piling depth -53m

Calculating the bearing capacity of a single pile

8.3.1 Piles bearing capacity by material:

The bearing capacity of pile according to material is determines as follow:

𝛾 𝑐𝑏 = 0.85: is the working condition coefficient of concrete

𝛾′ 𝑐𝑏 = 0.7: is the effect coefficient of pouring concrete in the narrow space of the pit and the wall pipe when pouring concrete into the borehole cage under the drilling fluid

𝐴 𝑠 = 0.0044𝑚 2 : is cross-sectional area of longitudinal reinforcement

4 − 0.0044 = 0.781 𝑚𝑚 2 : is cross-section area of concrete

𝜑: coefficient of reduction of bearing capacity due to longitudinal bending effect according to TCVN 5574:2012 for concrete and reinforced concrete structures according to design standards

Because the pile is plugged into the mud layer, it is necessary to consider the longitudinal bending coefficient calculated as follows:

𝐸 𝑏 = 3.25 × 10 7 𝑀𝑃𝑎: Elastic modulus of the pile material

Moment of inertia of horizontal piles:

𝑏 𝑝 : is the conventional width of the pile in (m), for piles with a minimum pile diameter of 1m take 𝑏 𝑝 = 𝑑 + 1 = 1 + 1 = 2 𝑚

Radius of inertia of pile cross section:

In material strength calculations, a pile can be considered a rigid fix within the soil at a cross-section located approximately l1 from the station's base, as determined by the relevant formula.

𝛼 𝜀 : Deformation coefficient determined according to the instructions in Appendix A

𝑙 0 = 0.2: the length of the pile from the bottom of the cap to the leveling height

𝑘 (𝑘𝑁/𝑚 4 ): Proportional coefficient, taken depending on the type of soil surrounding the pile according to Table A.1, TCVN 10304: 2014

Figure 8.3 Coefficient K according to table A1 TCVN 10304:2014

Table 8.2 Coefficient K in each soil layer around the pile

8.3.2 Piles bearing capacity according to ground criteria:

Pile bearing capacity according to soil and mechanical indicators:

For bored piles, the bearing capacity according to the physico-mechanical properties of the ground soil is determined according to Section 7.2.3 TCVN 10304 – 2014

𝛾 𝑐 = 1: is the working condition coefficient of the pile

𝛾 𝑐𝑞 : is the coefficient of working condition of the soil under the pile tip, 𝛾 𝑐𝑞 = 0.9 for the case of using the method of pouring concrete under water, 𝛾 𝑐𝑞 = 1 for other cases

𝐴 𝑏 : is the cross-sectional area of the pile tip

𝑢: is the circumference of the cross-section of the pile body

𝛾 𝑐𝑓 : is the coefficient of working conditions of the soil on the pile body, depending on the method of creating holes and concrete pouring conditions, look up table 5, page 29, TCVN 10304-2014

𝑓 𝑖 : is the average resistance strength of the soil layer “i” on the pile body, look up table

𝑙 𝑖 : is the length of the pile in the "i" soil layer

𝑞 𝑏 : is the resistance strength of the soil under the pile tip, determined as follows:

4 Poorly graded fine sand with silt (SP-SM), yellow-brown, brown-gray, medium dense 0.43 12000 27.5 330000

5 Lean clay with fine sand (CL), yellow-gray, green-gray, very stiff to hard 0.27 14280 4.5 64260

6 Fat clay (CH), yellow-gray, red-brown, green-gray, hard

7 Fine sandy lean clay (CL), yellow-gray, green-gray, hard 0.08 17040 3.7 63048

8A Very clayey fine sand (SC), yellow-gray, green-gray, medium dense to dense -0.07 12000 2.3 27600

8 Silty, clayey fine sand (SC-SM), yellow- gray, grayish, dense -0.15 12000 2 24000

𝛼 1 , 𝛼 2 , 𝛼 3 , 𝛼 4 : are dimensionless coefficients that depend on the value of friction angle in the calculation 𝜑 1 of the ground and are taken according to Table 6 (page 30, TCVN 10304-2014)

𝛾′ 1 : is the calculated density of the soil under the pile tip (taking into account the buoyancy effect in the water-saturated soil)

𝛾 1 : is the average calculated density (in layers) of the soil above the pile tip (taking into account buoyancy in water-saturated soils)

The diameter (d) refers to the size of closed or pressed piles, bored piles, and pipe piles It also includes the diameter of extensions for piles with fore extensions and the borehole diameter for piles or pillars that are bonded to the soil using a cement-sand mixture.

The pile lowering depth refers to the measurement from the natural ground level or the design ground level, in cases of excavation design, down to the tip of the pile or the bottom of the fore extension.

The tip of the pile plugged into the 8 th layer of soil is tight sand:

Table 8.3 Resistance coefficient of loose soil under the pile tip (M1)

Layer 4 Layer 5 Layer 6 Layer 7 Layer 8a

Table 8.4 Soil resistance according to physico-mechanical criteria

Type of soil Layer Depth Average depth 𝑳 𝒊 𝑰 𝑳 𝜸 𝒄𝒓 𝒇 𝒊 𝒇 𝒊 𝟑𝟎% 𝜸 𝒄𝒓 𝒇 𝒊 𝑳 𝒊 m m m 𝒌𝑵/𝒎 𝟐 𝒌𝑵/𝒎 𝟐 kN/m

Poorly graded fine sand with silt

(SP-SM), yellow-brown, brown- gray, medium dense 4

Lean clay with fine sand (CL), yellow-gray, green-gray, very stiff to hard

Fat clay (CH), yellow-gray, red- brown, green-gray, hard 6 41 43 42 2 -0.07 1 109.8 109.8 219.6

Fine sandy lean clay (CL), yellow- gray, green-gray, hard 7 45 47 46 2 -0.15 1 115.4 115.4 230.8

Very clayey fine sand (SC), yellow-gray, green-gray, medium dense to dense

Silty, clayey fine sand (SC-SM), yellow-gray, grayish, dense 8 51 53 52 2 0.32 0.8 60.2 78.26 125.216

Table 8.5 Summary table of calculation parameters

→Load bearing capacity according to the physical-mechanical norms of the ground:

Extreme bearing capacity of piles according to ground strength

According to Appendix G.2 TCVN 10304-2014, the ultimate bearing capacity of piles according to the criterion of ground strength is as follows:

𝐴 𝑏 : is the cross-sectional area of the pile tip

𝑢: is the perimeter of the pile cross-section

𝑙 𝑖 : is the length of the pile in the "i" soil layer

𝑓 𝑖 : is the shear strength (due to unit friction) of the “i” soil layer on the pile body

𝑞 𝑏 : is the resistance strength of the soil under the pile tip determined by the formula

𝑁′ 𝑐 , 𝑁′ 𝑞 : are the bearing capacity coefficients of the soil under the pile tip (looked up in Appendix B TCXD 205: 1998 "Figure B3")

Parameters in the formula Value Unit

According to figure 8.3.2.a (Figure B3, TCXD 205:1998), we have formula:

Bored pile: 𝜑 = 𝜑 1 ′ − 3 0 where 𝜑 1 ′ is internal friction angle of the soil beforce lowering the pile

𝑞′ 𝛾,𝑝 : is the effective mantle pressure at the pile tip level (with a value equal to the effective vertical soil stress at the pile tip level)

For adhesive soils the strength of non-drained shear resistance under the tip of the pile:

𝑞 𝑏 = 𝑐 𝑢 𝑁′ 𝑐 𝑁′ 𝑐 = 6: for large diameter bored piles

For loose soil (c = 0), the shear strength below the pile tip:

When the pile tip depth is less than 𝑍 𝐿, the mantle pressure at that depth is represented by 𝑞′ 𝛾,𝑝 Conversely, if the pile tip depth exceeds 𝑍 𝐿, the mantle pressure is defined by the value of 𝑞′ 𝛾,𝑝 at depth 𝑍 𝐿 To accurately determine these values, refer to Table G.1 in TCVN 10304-2014 for the coefficients k and 𝑞′ 𝛾,𝑝.

Shear resistance due to friction on pile body 𝒇 𝒊

For cohesive soils, the undrained shear strength on the pile body in the ith layer is determined by method 𝛼

𝑐 𝑢,𝑖 : Undrained resistance strength of the “i” soil layer

The coefficient is influenced by the properties of the soil layer situated above the cohesive soil, the type of pile used, the technique employed for pile installation, the soil consolidation during construction, and the method used to determine the undrained shear strength (cu), as detailed in graph G1 in Appendix G.

For loose soil (c = 0) the average shear strength on the pile body in the “i” th layer determined by method 𝛽:

𝑘 𝑖 : The coefficient of horizontal pressure of the soil on the pile body

𝜎̅ 𝑣,𝑧 ′ : Mean vertical effective stress in the “i” th layer

𝛿 𝑖 : is the friction angle between the soil and the pile, normally the concrete pile is taken

𝛿 𝑖 equal to the internal friction angle of the soil 𝜑 𝑖 , for steel piles taken as 2𝜑 𝑖 ⁄3

The shear strength of a pile body increases with depth, reaching a maximum at a limit depth (ZL) of approximately 15 to 20 times the pile diameter (d), beyond which it does not increase further In loose soil conditions, the shear resistance on the pile body can be calculated accordingly.

On piles with depth less than ZL:

On piles with depth equal to and greater than ZL:

Strength of undrained shear strength below pile tip:

Table 8.7 Table of coefficients for calculating shear resistance under pile tip

Table 8.8 Table of C u parameters from the UU experiment in the summary table

Table 8.9 Calculation table of hip resistance of cohesive soil layer

Table 8.10 Table of hip resistance of loose soil layers

→ Total hip resistance around the pile:

→ Bearing capacity according to ground strength criteria:

Pile bearing capacity according to standard penetration test SPT Calculation formula

Formula of the Japanese Institute of Architecture (1988):

𝑙 𝑠,𝑖 : Length of pile in loose soil layer “i”

𝑙 𝑐,𝑖 : The length of the pile in the cohesive soil layer "i"

𝑞 𝑏 : The resistance strength of the soil under the pile tip is determined as follows:

When the pile tip is in loose soil, 𝑞 𝑏 = 300𝑁 𝑝 for driven piles and 𝑞 𝑏 = 150𝑁 𝑝 for bored piles

When the pile tip is in the cohesive soil 𝑞 𝑏 = 9𝑐 𝑢 for driven piles and 𝑞 𝑏 = 6𝑐 𝑢 for bored piles

𝑁 𝑝 : Average SPT is in the range of 1d below and 4d above the pile tip

𝑓 𝑠,𝑖 : Average resistance strength on piles in loose soil layer “i”:

𝑓 𝑐,𝑖 : Resistance strength on the pile segment located in the “i”th cohesive soil layer:

𝑐 𝑢,𝑖 : The undrained shear strength of cohesive soil can be determined from the SPT index in cohesive soil 𝑐 𝑢,𝑖 = 6.25𝑁 𝑐,𝑖

𝑁 𝑐,𝑖 : Average SPT index in loose soil layer “i”

The correction factor for driven piles, denoted as 𝛼 𝑝, is influenced by the ratio of undrained shear strength (𝑐 𝑢) to the average effective normal vertical stress This relationship is illustrated in the accompanying figure.

𝑓 𝐿 = 1: Coefficient of adjustment according to thinness h/d of driven piles, bored piles

The tip of the pile is forbidden to enter the soil layer 7 so we have the resistance calculated as follows:

𝑁 𝑝 = 33.5 → 𝑞 𝑝 = 150 × 33.5 = 5025 𝑘𝑁/𝑚 2 With 𝑁 𝑐 is SPT index in the cohesive soil layer under the pile tip

According to TCVN 10304 - 2014, the undrained shear strength of cohesive soil, denoted as 𝑐 𝑢, is a critical factor in calculating the bearing capacity of piles using the Japanese formula, and it can be determined from the SPT index.

Table 8.11 Resistance strength on the pile segment in the cohesive soil layer “i” Class Depth Thickness

Table 8.12 Resistance strength on the pile segment in the loose soil layer “i”

→ The ultimate bearing capacity of piles according to the Japanese formula:

Computational bearing capacity of compressive pile

𝑁 𝑐,𝑑 : calculated value of the compressive load acting on the pile (the value of the load transmitted to the pile when the pile is working)

The coefficient of working condition, denoted as 𝛾 0, is essential for evaluating the homogeneity of the ground when utilizing pile foundations For a single pile, this coefficient is set at 1, while for multi-pile foundations, it is increased to 1.15 to account for enhanced ground uniformity.

𝛾 𝑛 : reliability coefficient on the importance of the works, taken as 1.2, 1.15, 1.1 corresponding to the importance of the works of grade I, II, III (Appendix E)

𝑅 𝑐,𝑑 : calculated value of the compressive bearing capacity of the pile

𝛾 𝑘 : The confidence coefficient is taken as follows:

When designing foundations with piles subjected to compressive loads, the value of 𝛾 𝑘 is determined based on the number of piles used, particularly when the base rests on a highly deformed soil layer, regardless of whether it is a high or low calyx foundation.

𝛾 𝑘 = 1.4: Foundation with at least 21 piles

𝑅 𝑐,𝑘 : The standard value of the pile beaing capacity is determined from the eigenvalues of the ultimate compressive bearing capacity (minimum value)

Table 8.13 Summary table of extreme bearing capacity Calculated bearing capacity Extreme bearing capacity

According to the intensity criterion 9747.448528

According to Japanese SPT experiment 13292.04554

Table 8.14 Summary table of design bearing capacity of piles in pile group

Figure 8.6 The layout of bored piles

Foundation design F1

The foundation is located at the boundary position, subject to the reaction from the foot at the intersection between the 2 axes 6 and B

Table 8.15 F1 foundation calculation load combination

𝑵 𝒎𝒂𝒙 𝒕𝒕 𝑴 𝟐−𝟐 𝒕𝒕 𝑴 𝟑−𝟑 𝒕𝒕 𝑸 𝟐−𝟐 𝒕𝒕 𝑸 𝟑−𝟑 𝒕𝒕 kN kN/m kN/m kN kN

8.4.3 Calculate and arrange the number of piles in the work:

Calculate the number of piles in the cap

Design foundation with bored piles with diameter 𝑑 = 1𝑚 with pile length 𝐿 = 43.6 Calculated bearing capacity: 𝑁 𝑐,𝑑 = 4997 211 𝑘𝑁 (1-5 piles)

Maximum calculated compressive force value: 𝑁 𝑡𝑡 = 10943.10 𝑘𝑁

Number of pile in the cap:

Arrangement of piles in the cap

Distance between two piles from 3𝑑 ÷ 6𝑑

Distance from the center of the pile to the edge of the platform is 1𝑑

With the number of piles as above, students choose the distance of the piles, arrange the piles from which to calculate the size of the cap

Table 8.16 Parameter table of pile layout

Distance from center of piles 3 m

Distance from the center of the pile to the edge of the platform 1 m

The elevation of the bottom of the tower 9.4 m

Thickness of lining concrete layer 0.1 m

Arrange piles and cap foundations as shown:

Figure 8.7 Pile and foundation layout plan M1

Length of foundation cap in X direction: 𝐵 𝑐 = 5 𝑚

Length of foundation cap in Y direction: 𝐿 𝑐 = 5 𝑚

Utilize ETABS 2018 software to determine the forces acting on the pile head, where the base station is modeled as a slab element with a thickness of 2.2 meters The piles supporting the foundation are represented as column supports, configured with spring constants at their ends, and the spring stiffness is calculated accordingly.

The single pile settlement, denoted as S, refers to the elastic settlement that aligns with the design bearing capacity This includes the axial deformation caused by the longitudinal force on the pile, the elastic settlement of the surrounding ground, and the elastic settlement at the pile tip.

According to Appendix B of TCVN 10304:2014, the settlement of a single pile is influenced by the load size and pile diameter When a foundation is designed with adequate bearing capacity, the settlement in sandy soil tends to be minimal In such scenarios, the settlement of a single pile can be empirically calculated using Vesic's expression from 1977.

𝑄 = 𝑁 𝑐𝑑 = 4997.211 𝑘𝑁: load acting on the pile

𝐴: Cross-sectional area of the pile

𝐸 = 3.25 × 10 7 𝑘𝑃𝑎: Elastic modulus of the pile material

Figure 8.8 Max pile head reaction (ULS8)

Figure 8.9 Min pile head reaction (ULS13)

The values obtained from the pile head reaction are consistently lower than the calculated allowable bearing capacity, indicating that the pile is not under excessive load and is effectively meeting the necessary bearing conditions.

Check the bearing capacity of pile group

Bearing capacity of pile group:

𝑄 𝑔𝑟𝑜𝑢𝑝 = 𝜂 × 𝑛 × 𝑁 𝑐,𝑑 = 0.9964 × 4 × 4997.211 = 19917.38 𝑘𝑁 Self-weight of foundation cap:

→ The bearing capacity of pile group is sastified

8.4.4 Stress test under conventional foundation block:

Define conventional block foundation according to Section 7.4.4 and Appendix C TCVN 10304-2014

Length of pile in soil: 𝐿 = 43.6 𝑚

Table 8.17 Table for determination of average friction angle 𝝋 𝒊

4 = 5 0 56 Conventional block foundation width in X direction:

𝐿𝑐𝑜𝑛𝑣𝑒𝑛𝑡𝑖𝑜𝑛𝑎𝑙 = 𝐿 𝑏 + 2 × 𝐿 𝑖 × tan 𝛼 = (5 − 1) + 2 × 44 × tan(5 0 56) = 13.145 𝑚 Conventional block foundation length in Y direction:

𝐵𝑐𝑜𝑛𝑣𝑒𝑛𝑡𝑖𝑜𝑛𝑎𝑙 = 𝐵 𝑏 + 2 × 𝐿 𝑖 × tan 𝛼 = (5 − 1) + 2 × 44 × tan(5 0 56) = 13.145 𝑚 Conventional foundation block bending moment:

Table 8.18 Calculation of soil volume in conventional foundation blocks

3b-cap Lean clay with fine sand (CL), red-brown, green-gray, stiff 2.2 9.5 20.9

4 Poorly graded fine sand with silt (SP-SM), yellow- brown, brown-gray, medium dense 27.5 10 275

5 Lean clay with fine sand (CL), yellow-gray, green- gray, very stiff to hard 4.5 10.4 46.8

6 Fat clay (CH), yellow-gray, red-brown, green-gray, hard 4 10.5 42

7 Fine sandy lean clay (CL), yellow-gray, green-gray, hard 3.7 11 40.7

8A Very clayey fine sand (SC), yellow-gray, green-gray, medium dense to dense 2.3 10.6 24.38

8 Silty, clayey fine sand (SC-SM), yellow-gray, grayish, dense 2 10.1 20.2

Total mass in the conventional foundation block:

Table 8.19 Table of loads to the bottom of the conventional foundation

Stress at the bottom of conventional block foundation:

Table 8.20 Stress table at the bottom of the conventional foundation block

Bearing capacity of the ground:

𝑚 1 = 1.3: Coefficient of working conditions of the ground

𝑚 2 = 1.3: Coefficient of working conditions of the work interacting with the ground

𝑘 𝑡𝑐 : Reliability coefficient, 𝑘 𝑡𝑐 = 1 when the computed features are taken directly from the experiments

Table 8.21 Average stress of pile foundation, 𝝈 𝒗𝒑 ′ Layer 𝑳 𝒊 (𝒎) 𝜸 ′ (𝒌𝑵/𝒎 𝟑 ) 𝜸 ′ 𝑳 𝒊 (𝒌𝑵/𝒎 𝟑 )

Total from layer 4 to layer 8 488.72

At the tip of the pile in class 8 we have: (Check table 14 TCVN 9362-2012 for parameters A, B, D)

Table 8.22 Coefficients calculating the bearing capacity of the foundation (ULS II)

8.4.5 Checking for settlement of conventional foundation blocks:

The average stress at the base of the conventional foundation:

172.791 = 545.005 𝑘𝑁/𝑚 2 Stress due to self-weight at the foundation bottom:

Void ration e, according to applied pressure kG/cm 2

8.4.6 Checking for shear condition for cap:

Take the maximum shear force in the strips with a width of 1 m in the x direction and in the y direction to check the shear strength of the foundation concrete

According to TCVN 5574:2018, Section 8.1.3.3, it is essential to calculate the most critical oblique cracks in reinforced concrete members lacking shear force reinforcement to ensure durability against these cracks.

𝑄 𝑏 , 𝑄 𝑏1 , 𝑄 𝑏2 : are the existing shear resistance, the shear resistance, respectively maximum and maximum of the non-reinforced cross-section;

C is the vertical projection length of the most dangerous oblique crack;

𝜑 𝑏2 = 1.5: is the coefficient taking into account the influence of longitudinal reinforcement, cohesion force and stress state characteristics of the compressive concrete lying on the oblique crack

𝑎 = 0.04: Thickness of protective concrete layer

Shear strength of concrete on a strip of width b = 1m

Figure 8.11 MAX shear force diagram in the X direction Detect:

𝑄 𝑥𝑚𝑎𝑥 = 1851.661 𝑘𝑁 < 𝑄 𝑏 = 3726 𝑘𝑁 Satisfying shear conditions, the foundation does not need to arrange the reinforcement

Figure 8.12 MAX shear force diagram in the Y direction Detect:

Based on the book "Kết cấu bê tông cốt thép 2" (Võ Bá Tầm), we have the following formulas and conditions:

𝐹 ≤ 𝛼𝛾 𝑏 𝑅 𝑏𝑡 𝑢 𝑚 ℎ 0 For square foundation, we have:

Average perforation circumference of an obelisk:

𝛾 𝑏 = 0.85: coefficient of working condition of concrete

𝐹 = 9685.49 𝑘𝑁: Maximum axial force of column C22

Penetration test due to the reaction from the pile to the cap:

Step 1: Determine the penetration resistance zone

Figure 8.13 An obelisk penetration of foundation F1

Step 2: Determination of penetration resistance force:

Any group of piles located in the penetration resistance zone will not cause penetration, only those piles located outside the penetration zone will be counted

There are some other cases like this F1 foundation, the penetration resistance zone is located in the center of the 4 piles, so the penetration force is still different from 0

8.4.8 Calculation of reinforcement for the foundation cap:

The internal force calculation for reinforcement is done with the help of ETABS 2018 software Calculation of reinforcement for the envelope combination

Figure 8.14 MAX moment diagram of foundation base F1 in X direction

Figure 8.15 MIN moment diagram of foundation base F1 in X direction

Table 8.25 Steel calculation in the X direction of foundation base F1

Figure 8.16 MAX moment diagram of foundation base F1 in Y direction

Figure 8.17 MIN moment diagram of foundation base F1 in Y direction

Table 8.26 Steel calculation in the Y direction of foundation base F1

8.4.9 Calculation of piles with horizontal load:

We analyze the scenario involving the maximum total shear force at the base of the cap Given the minimal internal force, we utilize the designated computational load rather than the standard load for our assessment.

Table 8.27 Table of the maximum shear force at the base of F1

Case 𝑴 𝟐−𝟐 𝒕𝒄 𝑴 𝟑−𝟑 𝒕𝒄 𝑸 𝟐−𝟐 𝒕𝒄 𝑸 𝟑−𝟑 𝒕𝒄 kN/m kN/m kN kN

Model pile into bar element, surrounding ground is converted into springs with stiffness 𝑘 𝑙𝑥

The horizontal ground coefficient of a soil layer according to TCVN 10304:2014 is:

𝐾: The scale factor is taken depending on the type of soil surrounding the piles according to table A1 (TCVN 10304:2014)

The depth of the pile cross-section in the soil, denoted as 𝑧, varies depending on the type of pile foundation; for high pile foundations, it is measured from the ground level, while for low pile foundations, it is measured from the bottom of the casing.

Table 8.28 Table for determining spring stiffness (F1)

Figure 8.18 Horizontal displacement of pile head (F1)

Figure 8.19 Horizontal pressure chart from Sap2000 (F1)

Figure 8.20 Shear force chart from Sap2000 (F1)

Figure 8.21 Moment chart from Sap2000 (F1)

Horizontal displacement of pile head (m)

8.4.10 Checking pile horizontal displacement and ground stability around the pile:

Using the calculation results of piles bearing horizontal load from SAP2000 model with the foundation coefficient changing according to the depth of each soil layer for testing

As the depth increases, the spring stiffness escalates, resulting in minimal moment, shear force, and spring reaction Consequently, I focused my explanation on the upper third of the pile.

Maximum stress in the ground at depth Z = -1m from the bottom of the cap (maximum spring reaction)

𝐴 𝑎𝑟𝑜𝑢𝑛𝑑 : cylindrical area (According to TCVN 205-1998, The calculated pressure is on the soil on the side of the pile, so the value is halved)

Check the horizontal displacement and rotation angle of the pile head:

Horizontal displacement, according to TCVN 10304:2014, section 11.12: Δ 𝑛 = 𝑦 0 = 8.01 × 10 −5 𝑚 < [𝑦 0 ] = 0.02 𝑚

Swivel angle, according to TCVN 10304:2014, appendix A3 and TCVN 205:1998, appendix G1:

Check the stability of the ground around the pile:

According to section A.7, Appendix A, TCVN 10304 - 2014, the ground stabilization conditions around the piles when there is lateral pressure exerted by the pile takes the form:

The largest 𝜎 𝑧 position is z = -1m compared to the base of the base (soil layer 3a) with

𝜂 2 : The factor that takes into account the part of the permanent load in the total load is calculated as follows:

From the results of histology and analysis in Sap2000, we have:

Foundation design F2

Located in the middle position, bearing the force from the foot of the column at the intersection between axis B and axis 5

Table 8.29 Summary table of internal force calculation for foundation F2

𝑵 𝒎𝒂𝒙 𝒕𝒕 𝑴 𝟐−𝟐 𝒕𝒕 𝑴 𝟑−𝟑 𝒕𝒕 𝑸 𝟐−𝟐 𝒕𝒕 𝑸 𝟑−𝟑 𝒕𝒕 kN kN/m kN/m kN kN

8.5.3 Calculate and arrange the number of piles:

Calculate the number of piles in the cap

Design foundation with bored piles with diameter 𝑑 = 1𝑚 with pile length 𝐿 = 43.6 𝑚 Calculated bearing capacity: 𝑁 𝑐,𝑑 = 4997.211 𝑘𝑁 (1-5 piles)

Maximum calculated compressive force value: 𝑁 𝑡𝑡 = 15884.9 𝑘𝑁

Number of pile in the cap:

Arrangement of piles in the cap

Distance between two piles from 3𝑑 ÷ 6𝑑

Distance from the center of the pile to the edge of the platform is 1𝑑

With the number of piles as above, students choose the distance of the piles, arrange the piles from which to calculate the size of the cap

Table 8.30 Parameter table of pile layout

Distance from center of piles 3 m

Distance from the center of the pile to the edge of the platform 1 m

The elevation of the bottom of the tower 9.4 m

Thickness of lining concrete layer 0.1 m

Arrange piles and cap foundations as shown:

Figure 8.22 Pile and foundation layout plan F2

Length of foundation cap in X direction: 𝐵 𝑑 = 5 𝑚

Length of foundation cap in Y direction: 𝐿 𝑑 = 5 𝑚

Utilize ETABS 2018 software to determine the forces exerted on the pile head, with the base station modeled as a slab element measuring 2.2 m in thickness The foundation's force is derived from the de-framing results obtained through ETABS 2018 Additionally, the piles supporting the foundation are represented as column supports, employing spring constants at the pile ends, with the spring stiffness calculated accordingly.

The single pile settlement, denoted as S, reflects the elastic settlement associated with the design bearing capacity This settlement encompasses the axial deformation caused by longitudinal forces on the pile, the elastic settlement of the surrounding ground, and the elastic settlement at the pile tip.

According to TCVN 10304:2014, the settlement of a single pile is influenced by the load size and pile diameter When foundations are designed with adequate bearing capacity, pile settlement in sandy soil tends to be minimal The settlement can be empirically calculated using Vesic's formula from 1977.

𝑄 = 𝑁 𝑐𝑑 = 4997.211 𝑘𝑁: load acting on the pile

𝐴: cross-sectional area of the pile

𝐸 = 3.25 × 10 7 𝑘𝑃𝑎: elastic modulus of the pile material

Figure 8.23 Max result of pile head reaction (ULS16)

Figure 8.24 Min result of pile head reaction (ULS19)

The pile head reaction values consistently fall below the calculated allowable bearing capacity, indicating that the pile is not overloaded and effectively meets the required bearing conditions.

Check the bearing capacity of pile group

Bearing capacity of pile group:

𝑄 𝑔𝑟𝑜𝑢𝑝 = 𝜂 × 𝑛 × 𝑁 𝑐,𝑑 = 0.9964 × 4 × 4997.211 = 19917.38 𝑘𝑁 Self weight of foundation cap:

→ The bearing capacity of pile group is sastified

8.5.4 Stress test under conventional foundation block:

Define conventional block foundation according to Section 7.4.4 and Appendix C TCVN 10304-2014

Length of pile in soil: 𝐿 = 43.6 𝑚

Table 8.31 Table for determination of average friction angle 𝝋 𝒊

4 = 5 0 56 Conventional block foudation width in X direction:

𝐿𝑐𝑜𝑛𝑣𝑒𝑛𝑡𝑖𝑜𝑛𝑎𝑙 = 𝐿 𝑏 + 2 × 𝐿 𝑖 × tan 𝛼 = (5 − 1) + 2 × 44 × tan(5 0 56) = 13.145 𝑚 Conventional block foundation length in Y direction:

𝐵𝑐𝑜𝑛𝑣𝑒𝑛𝑡𝑖𝑜𝑛𝑎𝑙 = 𝐵 𝑏 + 2 × 𝐿 𝑖 × tan 𝛼 = (5 − 1) + 2 × 44 × tan(5 0 56) = 13.145 𝑚 Conventional foundation block bending moment:

Table 8.32 Calculation of soil volume in conventional foundation blocks

3b-cap Lean clay with fine sand (CL), red-brown, green-gray, stiff 2.2 9.5 20.9

4 Poorly graded fine sand with silt (SP-SM), yellow- brown, brown-gray, medium dense 27.5 10 275

5 Lean clay with fine sand (CL), yellow-gray, green- gray, very stiff to hard 4.5 10.4 46.8

6 Fat clay (CH), yellow-gray, red-brown, green-gray, hard 4 10.5 42

7 Fine sandy lean clay (CL), yellow-gray, green-gray, hard 3.7 11 40.7

8A Very clayey fine sand (SC), yellow-gray, green-gray, medium dense to dense 2.3 10.6 24.38

8 Silty, clayey fine sand (SC-SM), yellow-gray, grayish, dense 2 10.1 20.2

Total mass in the conventional foundation block:

Table 8.33 able of loads to the bottom of the conventional foundation

Stress at the bottom of conventional block foundation

Table 8.34 Stress table at the bottom of the conventional foundation block

𝑚 1 = 1.3: coefficient of working conditions of the ground

𝑚 2 = 1.3: coefficient of working conditions of the work interacting with the ground

𝑘 𝑡𝑐 : reliability coefficient, 𝑘 𝑡𝑐 = 1 when the computed features are taken directly from the experiments

Table 8.35 Average stress of pile foundation, 𝝈 𝒗𝒑 ′ Layer 𝑳 𝒊 (𝒎) 𝜸 ′ (𝒌𝑵/𝒎 𝟑 ) 𝜸 ′ 𝑳 𝒊 (𝒌𝑵/𝒎 𝟑 )

Total from layer 4 to layer 8 488.72

At the tip of the pile in class 7 we have: (Check table 14 TCVN 9362-2012 for parameters A, B, D)

Table 8.36 Coefficients calculating the bearing capacity of the foundation (ULS II)

8.5.5 Checking for settlement of conventional foundation blocks:

The average stress at the base of the conventional foundation:

172.791 = 569.779 𝑘𝑁/𝑚 2 Stress due to self-weight at the foundation bottom:

Figure 8.25 Compression result chart Table 8.38 Check settlement condition

Void ration e, according to applied pressure kG/cm 2

8.5.6 Checking for shear condition for cap:

Take the maximum shear force in the strips with a width of 1 m in the x direction and in the y direction to check the shear strength of the foundation concrete

According to Section 8.1.3.3 of TCVN 5574:2018, it is essential to assess the most critical oblique cracks in reinforced concrete members without shear reinforcement to ensure durability.

𝑄 𝑏 , 𝑄 𝑏1 , 𝑄 𝑏2 : are the existing shear resistance, the shear resistance, respectively maximum and maximum of the non-reinforced cross-section;

C is the vertical projection length of the most dangerous oblique crack;

𝜑 𝑏2 = 1.5: is the coefficient taking into account the influence of longitudinal reinforcement, cohesion force and stress state characteristics of the compressive concrete lying on the oblique crack

𝑎 = 0.04: thickness of protective concrete layer

Shear strength of concrete on a strip of width b = 1m

Figure 8.26 MAX shear force diagram in the X direction

Figure 8.27 MAX shear force diagram in the Y direction Detect:

Satisfying shear conditions, the foundation does not need to arrange the reinforcement

Based on the book "Kết cấu bê tông cốt thép 2" (Võ Bá Tầm), we have the following formulas and conditions:

𝐹 ≤ 𝛼𝛾 𝑏 𝑅 𝑏𝑡 𝑢 𝑚 ℎ 0 For square foundation, we have:

Average perforation circumference of an obelisk:

𝛾 𝑏 = 0.85: coefficient of working condition of concrete

𝐹 = 13966.227 𝑘𝑁: Maximum axial force of column C22

Penetration test due to the reaction from the pile to the cap:

Step 1: Determine the penetration resistance zone

Figure 8.28 An obelisk penetration of foundation F2

Step 2: Determination of penetration resistance force:

Any group of piles located in the penetration resistance zone will not cause penetration, only those piles located outside the penetration zone will be counted

There are some other cases like this F1 foundation, the penetration resistance zone is located in the center of the 4 piles, so the penetration force is still different from 0

8.5.8 Calculation of reinforcement for the foundation cap:

The internal force calculation for reinforcement is done with the help of SAFE 16 software Calculation of reinforcement for the envelope combination

Figure 8.29 MAX moment diagram of foundation base F2 in X direction

Figure 8.30 MIN moment diagram of foundation base F2 in X direction

Table 8.39 Steel calculation in the X direction of foundation base F2

Figure 8.31 MAX moment diagram of foundation base F2 in Y direction

Figure 8.32 MIN moment diagram of foundation base F2 in Y direction

Table 8.40 Steel calculation in the Y direction of foundation base F2

8.5.9 Calculation of piles with horizontal load:

We analyze the maximum total shear force at the base of the cap, opting for the assigned computational load in place of the standard load due to the minimal internal force.

Table 8.41 Table of the maximum shear force at the base of F2

Case 𝑴 𝟐−𝟐 𝒕𝒄 𝑴 𝟑−𝟑 𝒕𝒄 𝑸 𝟐−𝟐 𝒕𝒄 𝑸 𝟑−𝟑 𝒕𝒄 kN/m kN/m kN kN

Model pile into bar element, surrounding ground is converted into springs with stiffness 𝑘 𝑙𝑥

The horizontal ground coefficient of a soil layer according to TCVN 10304:2014 is:

𝐾: The scale factor is taken depending on the type of soil surrounding the piles according to table A1 (TCVN 10304:2014)

The depth of the pile cross-section in the soil is denoted as 𝑧, which measures from the ground level for high pile foundations or from the bottom of the cassock for low pile foundations.

Table 8.42 Table for determining spring stiffness (F2)

Figure 8.33 Horizontal displacement of pile head (F2)

Figure 8.34 Horizontal pressure chart from Sap2000 (F2)

Figure 8.35 Shear force chart from Sap2000 (F2)

Figure 8.36 Moment chart from Sap2000 (F2)

Horizontal displacement of pile head (m)

8.5.10 Check pile horizontal displacement and ground stability around the pile:

Using the calculation results of piles bearing horizontal load from SAP2000 model with the foundation coefficient changing according to the depth of each soil layer for testing

As the depth increases, the spring stiffness also rises, resulting in minimal moment, shear force, and spring reaction Consequently, I focused my explanation on the upper third of the pile.

Maximum stress in the ground at depth Z = -1m from the bottom of the cap (maximum spring reaction)

𝐴 𝑎𝑟𝑜𝑢𝑛𝑑 : cylindrical area (According to TCVN 205-1998, The calculated pressure is on the soil on the side of the pile, so the value is halved)

Check the horizontal displacement and rotation angle of the pile head

Check the stability of the ground around the pile

According to section A.7, Appendix A, TCVN 10304 - 2014, the ground stabilization conditions around the piles when there is lateral pressure exerted by the pile takes the form:

The largest 𝜎 𝑧 position is z = -1m compared to the base of the base (soil layer 3a) with

𝜎 𝑧 = 0 … (kN/m2) Students test with values of c,𝜑 in the instantaneous state (most dangerous)

𝜂 2 : The factor that takes into account the part of the permanent load in the total load is calculated as follows:

From the results of histology and analysis in Sap200, we have:

Elevator foundation (F4)

Figure 8.59 Horizontal displacement of pile head (F4) 227Figure 8.60 Horizontal pressure chart from Sap2000(F4) 228Figure 8.61 Shear force chart from Sap2000 (F4) 228Figure 8.62 Moment chart from Sap2000 (F4) 229

WATER TANK

Tiêu đề	Tan Tao 1 Apartment Building
Tác giả	Tran Xuan Phong
Người hướng dẫn	Assoc. Prof. Dr. Le Anh Thang
Trường học	Ho Chi Minh City University of Technology and Education
Chuyên ngành	Civil Engineering Technology
Thể loại	Đồ án
Năm xuất bản	2022
Thành phố	Ho Chi Minh City

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Số trang	265
Dung lượng	10,78 MB