REVIEW OF THE RESEARCH ON STEEL STORAGE RACK STRUCTURES
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摘要: 随着物流和电商行业的飞速发展，钢货架结构从单纯提供货物存储功能的简单机械类产品逐步向高位立体库、库架合一式建筑发展，这对货架结构的安全性提出更高要求。与传统钢框架结构相比，钢货架结构的托盘货载远大于结构自重，竖向荷载活恒比值可达10∶1量级；主要竖向承重构件多采用连续开孔薄壁截面，其性能受到局部屈曲、畸变屈曲、整体屈曲以及各屈曲模式间相互作用的影响；梁柱节点和柱脚节点多为半刚性挂齿式机械连接，表现出强非线性和捏拢滑移滞回特征；竖向支撑体系对整体结构稳定性的影响机制和有效性。另外，在地震作用下，货架结构的破坏模式除了主要承重构件的破坏和整体结构的垮塌外，还存在托盘货载跌落导致的货物、结构破坏和人员伤害。在钢货架结构抗震分析中，托盘货物的滑动和跌落应属于一种极限状态加以考虑，托盘与横梁间的动力摩擦系数将成为评估结构性能的一个重要参数。结合国内外已有研究成果，该文基于钢货架结构的特点，评述了现有的研究方法，综述了各基本结构要素的力学行为、整体结构的稳定性态及抗震性能，探讨了研究中的关键问题。Abstract: With the rapid growth of logistics industry, steel storage racks are not just industrial products. They are commonly used in high-rise warehouses and clad racks. Therefore, the structural safety of storage racks is of vital importance. Steel storage racks are distinct from traditional moment resisting frames in the following aspects. Firstly, storage racks may carry extremely high live loads with comparatively light weight and reach up to 40 meters in height. Secondly, the uprights have open singly- or non-symmetric cross-sections and are continuously perforated along the length, the behavior of which is significantly influenced by local, distortional, global buckling and their interactions. Thirdly, the mechanical beam-to-upright connections and column bases are commonly utilized for their convenience in assembly and adjustment. Their nonlinear moment-rotation behavior and severely pinching characterization requires comprehensive investigations. Fourthly, the influences of the asymmetry configuration of the bracing system on the stability of the overall rack structure need to be carefully studied. Moreover, as for the aseismic behavior of rack structures, further investigations are required for the hysteretic behavior of beam-to-upright connections, the collapse mechanisms of the overall rack structures, and the sliding behavior between pallets and beams. It should be noted that besides usual local and global collapse mechanisms, the falling of pallets should also be considered as an additional serviceability limit state of rack structures. This paper reviews researches on the behavior of steel storage racks. A brief introduction of rack structures is provided, as well as the main research methodologies. The main research results on the static and dynamic behavior are then presented respectively. Finally, the key issues in studies of steel storage racks and the related research topics are proposed.
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常规砂土直剪试验的剪切面局限于上、下箱体之间的平面，但不一定沿土样的最薄弱面展开，其剪切带形成机制仍不十分明确。目前针对砂土剪切带的研究主要是从物理试验、数值模拟，以及基于二者的理论分析等方面入手，其中物理试验的研究手段包括平面应变试验、三轴试验和直剪试验，并利用数字图像技术进行观测和研究；理论分析方面主要基于连续体假定，对砂土本构模型进行改进；而数值模拟近年来则以离散元程序研究为主[1-10]。
近些年来，国内方面针对砂土的剪切带发展，进行了较为系统的试验研究。李福林等[11]根据饱和砂土排水平面应变压缩试验的应变场，分析了试样的应变局部化现象。研究发现，砂土材料的应变局部化发生在峰值应力状态附近，峰值应力后应变局部化更加明显并集中在一定区域，最终形成V型剪切带。郭莹等[12]对饱和细砂进行三轴固结排水剪切试验，通过对轴向应变场的分析发现，密砂和松砂的干样在应力峰值之后形成剪切带，而松砂湿样在峰值之前形成剪切带。孔亮等[13]基于数字图像相关法，对砂土试样进行了室内细观直剪试验，研究发现，随着剪切的进行，位移较大的颗粒逐渐集中在剪切面两侧、从左下到右上的一个斜带内。潘远阳等[14]对密砂直剪试验进行离散元数值模拟，通过对数值试验过程中的颗粒进行动态监测发现，剪切带的厚度受平均粒径和颗粒摩擦系数影响较大。
类似的研究工作近年来在国际上也比较多，Lai和Chen[15]利用X射线成像技术，采用离散元程序再现了不同形状的月壤数值颗粒，进行了二维直剪试验模拟，表明随着颗粒形状的不同，直剪试验的剪切带也具有不同的形式，但都没有严格按照剪切缝开展。Tang等[16]研发了新型土体平面应变试验装置，并结合图像分析技术对砂土剪切带进行研究，表明剪应变的分布在试验前期主要集中在试样中部，并向四周扩散，后期则会形成一条主要的剪切带，但是厚度比较大，也并不十分平直。Kawamoto等[17]同样利用X射线成像技术，采用LS-DEM的方法，再现了具有砂土形状的数值颗粒，并通过对三轴试验的模拟，发现剪切带上的力链发生了较大偏转，认为与应力主轴的旋转有关。Wiebicke等[18]通过在三轴试验中开设内、外2个视窗，结合X射线成像技术对剪切带进行联合观测，并采用统计的方法对剪切过程中细观组构的演化进行了分析，指出细观参量的变化是土体各向异性的主要原因。
以上研究大多关注于剪切过程中细观参数的改变对宏观现象的影响，对剪切带形成机制的分析尚不够系统；而剪切带的特征直接影响土体强度，现阶段由于三轴试验装置的局限性，难以对剪切带进行直观观测，可视化的直剪试验成为对剪切带进行深入研究的有效手段。因此，本文通过对传统直剪仪进行可视化改造，并结合数字图像变形量测技术探究了砂土试样在剪切过程中的演化规律，归纳出试样尺寸、法向应力等对剪切带形成机制和扩展过程的影响，同时对试验中发现的拱形副剪切带进行了强度分析，并与水平主剪切带进行了对比研究。
1 试验概况
1.1 试验装置
本试验所用主要仪器是ZJ-1A型应变控制式直剪仪，如图1(a)所示。原设备直剪盒为黄铜材质，很难直接观测到试样在剪切过程中的颗粒运动情况，对剪切带的研究受到限制。因此，为了进行可视化试验，采用厚度为10 mm的亚格力板设计制造了5种不同规格的透明直剪盒，以便于在直剪过程中利用数码相机对试样表面进行拍照分析，如图2所示。内径尺寸(长×宽×高，单位：cm)分别为10×10×10、10×10×5、10×10×2.5的直剪盒用于研究试样不同宽高比对砂土强度指标和剪切带形状的影响；而尺寸分别为10×10×5、10×5×5、10×2.5×5的直剪盒用于研究试样不同长宽比的影响。
原直剪仪加压框架分布在直剪盒两侧(图1(a))，不利于图像采集。因此设计了新型加压框架(图1(b))，能够在试验过程中完全展现试样侧面。新加压框架的使用需注意两点：① 新加压框架重量有所改变，加压前需重新调节平衡锤使杠杆水平；② 加压框架需作用在直剪盒中心，保持框架平面竖直防止偏心，并不能遮挡拍摄区域。结合图像采集设备能够保证全过程摄录的图像清晰(图3)。
1.2 试验材料及方法
试验土样选用天津地区工程中常用的海砂，经人工过筛剔除大颗粒，粒径范围0.075 mm~2 mm，级配曲线如图4所示。试验时保持含水率为1.2%，制样密度1.818 g/cm3，相对密度0.7，物理力学指标如表1所示。本文主要研究剪切过程中剪切带的形成机制，对于砂土试样的含水率、密实度等材料因素的影响留待进一步研究。
表 1 砂土试样的基本物理特性Table 1. Basic physical properties of sand samples粒径范围 含水率/(%) 不均匀系数Cu 曲率系数Cc 孔隙比 0.075~2 1.2 8.143 1.384 0.47 制样时先测定含水率，控制在预定数值上，再利用落砂法[19]进行装样，保证试样均匀，分5次将砂土填满剪切盒，静置24 h后进行试验。每组试样施加不同的法向压应力(50 kPa、100 kPa、150 kPa、200 kPa)，待试样稳定后施加切向拉力进行剪切。试验控制以0.8 mm/min的速率进行剪切，每隔15 s记录1次剪切力、剪切位移等试验数据，并摄录数码照片，用于图像分析。根据《土工试验方法标准》(GB/T 50123−2019)，当剪应力达到稳定或显著下降时减损完成，宜剪切至位移4 mm以上；若剪应力持续增加，应剪切至位移6 mm以上。本文各组试验都剪切至剪应力下降，即完全剪损时为止。
2 试验结果分析
2.1 剪应力-剪切位移关系曲线特征
5种尺寸规格砂土试样直剪试验的剪应力与剪切位移关系曲线如图5所示，不同尺寸试样曲线的变化规律基本相同，随着剪切位移的增加，剪应力先增加后减小，临近结束时的曲线较为平缓，且随着法向应力的增加剪应力下降的幅度有所增大。曲线都存在峰值，剪应力达到峰值点时所对应的剪切位移随着法向应力的增大而增大。取峰值时刻的剪应力作为试样的抗剪强度，5种规格试验的抗剪强度与法向应力拟合曲线如图6所示，其强度参数结果示于表2中。
表 2 砂土直剪试验结果及强度参数Table 2. Shearing test results and strength parameters of sand samples试样尺寸/cm 长宽比 宽高比 法向应力/kPa 峰值剪切位移/mm 抗剪强度/kPa 黏聚力/kPa 内摩擦角/(°) 拟合度 10×2.5×5 4∶1 1∶2 50 2.74 39.6 12.30 30.2 0.9945 100 2.83 73.8 150 3.50 98.4 200 3.68 128.4 10×5×5 2∶1 1∶1 50 3.70 44.8 5.52 38.2 0.9860 100 4.24 82.6 150 4.54 127.3 200 5.04 161.2 10×10×5 1∶1 2∶1 50 3.82 52.7 7.60 43.1 0.9841 100 4.93 103.0 150 5.86 150.2 200 6.51 193.2 10×10×2.5 1∶1 4∶1 50 3.76 70.8 16.50 46.4 0.9938 100 4.91 119.6 150 5.78 173.2 200 6.41 228.2 10×10×10 1∶1 1∶1 50 4.98 52.7 9.45 39.5 0.9987 100 5.76 89.9 150 6.59 131.6 200 7.53 176.4 2.2 剪切盒尺寸影响分析
各种规格砂土试样的强度参数如表2所示，同一尺寸规格试验，剪应力达到峰值点时所对应的剪切位移随着法向应力的增大而增大。各种规格砂土试样的黏聚力在5.52 kPa~16.50 kPa，大部分黏聚力值小于10 kPa；内摩擦角在30.2°~46.4°内变化，大部分内摩擦角在40°上下。其中10 cm×2.5 cm×5 cm、10 cm×10 cm×2.5 cm试样的黏聚力值分别为12.30 kPa和16.50 kPa，对于砂土明显偏大；而对应的内摩擦角分别为30.2°和46.4°，与平均值相差较大。可见，试样尺寸影响抗剪强度指标，当试样长边与短边之比大于2时，剪切行为将呈现出尺寸效应，导致测得的强度参数偏离平均值；而当比值大于4时，尺寸效应更为明显，将导致试验数据严重偏离真实值。本文中10 cm×10 cm×5 cm试样的黏聚力和内摩擦角较为接近平均值，最具代表性，可用于下文中剪切带形成机制分析。
3 砂土试样剪切带发展规律分析
3.1 不同剪切时刻剪切带扩展规律
采用数字图像变形量测软件Geodog，对砂土直剪试验过程中的位移场进行分析。Geodog是一款采用无标点法对数字图像进行变形量测的软件，由于无需提前在试样上进行点位标记，仅通过一系列照片就能进行位移场的量测，为岩土工程有关试验提供了简便且有效的技术手段[19]。通过定点连续拍摄一系列数字照片，并在原始照片上设定测量点位，利用每个像素点(pixel)颜色的RGB分量，采用像素块追踪算法(block tracking)进行图像变形场的测量；并利用有限单元法(FEM)中四边形等参单元的方法，还可以进行各类应变场的计算[20]。
对砂土直剪试验过程中摄录照片进行分析，得到砂土试样侧表面土体颗粒在剪切时的运动位移情况，探究砂土试样剪切带的形成过程和扩展机制。10 cm×10 cm×5 cm试样在法向应力150 kPa下不同剪切时刻的位移场云图如图7所示。横向和纵向数字为像素点的坐标(像素点的序号)，单位为pixel，图例中的数字代表相对位移，单位为‰，表示图像分析得出的位移值与图像长边尺寸的相对比值。累计应变为剪切位移与剪切方向试样长度的比值。
需要说明的是，目前图像分析技术在小变形的时候精确度较高，而大变形时会增大误差。Geodog采用的是定点拍摄，在剪切过程中下盒的两端有部分土体进出，导致像素块不能完全追踪，且误差随变形增加会逐渐增大。但是图像变形场分析的整体规律是正确的，并且上盒固定不动，其位移计算结果的准确度会更高。本文对位移值的大小不作重点分析，着眼于上盒拱形剪切带形成机制及变化规律的研究。图像算法本身具有相当的困难，但随着图像分析需求的大幅度提升，精确度会越来越高。
依据不同剪切时刻的位移场云图，可以将砂土试样剪切带扩展过程划分为5个阶段，可以总结为：
1)初始挤密阶段：剪切刚开始，上下直剪盒发生微小错动，全局变形水平较低且均匀，沿着剪切方向土体颗粒逐渐挤密。
2)局部屈服阶段：上下盒之间已形成了一条明显的水平主剪切带，此时上盒土体的破裂面具有多种发展趋势。
3)剪切带发展阶段：在上盒中下部逐渐形成一条向上凸起的弧形副剪切带，此时剪应力尚未达到峰值，但副剪切带已经基本形成。
4)峰值应力剪切带：剪应力峰值时主副剪切带间的拱形剪切破坏区域略有减小，但更加清晰。
5)软化阶段：剪应力达到峰值后，试样发生一定程度的软化，此后由于法向应力的约束，拱形剪切区域随剪切位移的增加继续减小，但变化幅度较慢，一直持续到试验结束。
有理由相信，若砂土试样能够不受剪切盒尺寸限制，无限剪切下去，副剪切带可能会最终完全消失。但考虑到土体强度主要是以峰值时刻的剪应力为参考标准，因此，土样中的剪切破坏可认为是沿着主、副两条剪切带而展开的。
3.2 峰值剪应力时刻剪切带变化规律
图8所示为10 cm×10 cm×5 cm试样在不同法向应力下剪应力达峰值时的位移云图。
图8中根据云图颜色分界线，人工勾勒出副剪切带的位置，同时采用绘图软件在人工标定的副剪切带上提取坐标点，便于对副剪切带进行分析。由图8可以看出随着剪切的进行，当剪应力达到峰值点时，各组试验的水平主剪切带和拱形副剪切带已完全形成；而随着法向应力的增大，主副剪切带间的拱形剪切破坏区域逐渐增大。
为了进一步研究副剪切带，对砂土试样在不同法向应力下，剪应力达峰值时的拱形副剪切带进行曲线拟合，得到副剪切带形状随法向应力变化的函数表达式，进而可以得出副剪切带上的正应力和剪应力，以获得副剪切带上的抗剪强度指标，与水平主剪切带上的强度指标进行对比，分析变化规律。
3.3 副剪切带曲线拟合及强度分析
利用数据处理软件Matlab对人工勾勒出的副剪切带进行曲线拟合。由于副剪切带的形状呈现较为常见的二次抛物线特点，通过二次多项式函数进行拟合，可以得到拟合度较高的函数表达式。尺寸为10 cm×10 cm×5 cm试样在不同法向应力下，剪应力达到峰值时刻的副剪切带拟合曲线如图8所示。图中定义坐标原点为剪切缝左侧端点，即上下盒间主剪切带的最左侧点处；采用实际尺寸作为坐标系统，单位为mm。
试样在不同法向应力下的副剪切带形状可用如下公式统一表示：
y=Ax2+Bx+C (1) 式中：y/mm代表曲线上一点的纵坐标；x/mm代表曲线上一点的横坐标，坐标原点为剪切缝左侧端点；A、B、C为拟合参数，如表3所示。不同法向应力下拟合参数A和B变化不大，因此可以近似取平均值，保留3位小数，确定参数A取为–0.012，参数B取为1.034。
表 3 副剪切带拟合结果Table 3. Fitting results for sub-shear bands试样尺寸/
cm3法向应力/
kPa拟合
参数A拟合
参数B拟合
参数C拟合度 10×10×5 50 −0.0110 0.9845 −12.2660 0.929 90 100 −0.0112 1.0094 −10.4261 0.943 10 150 −0.0117 1.0585 −9.2839 0.962 60 200 −0.0121 1.0818 −7.5962 0.941 80 由表3可知，参数C随法向应力的增加而线性增大，可以通过线性拟合获得参数C与法向应力K的关系式：
C=0.03K−13.681 (2) 结合式(1)和式(2)，可得10 cm×10 cm×5 cm试样在不同法向应力下副剪切带的函数表达式：
y=−0.012x2+1.034x−0.03K−13.681 (3) 在确定副剪切带的函数表达式之后，对主、副剪切带之间的拱形区域进行受力分析，可以进一步得出副剪切带所确定的强度指标c2和φ2。根据试验结果，由峰值时刻的正应力和剪应力可以得出水平主剪切带所确定的土体抗剪强度指标c1和φ1。通过对比主、副剪切带所确定参数的差异，进一步研究直剪试验中剪切带的形成机制。试验中上盒固定不动，下盒从右往左剪切进行试验，对主、副剪切带之间的拱形区域进行受力分析，如图9所示。
假定主、副剪切带上的正应力和剪应力均匀分布，定义水平主剪切带上的正应力为σ1、剪应力为τ1，据此确定土体的抗剪强度指标为c1、φ1；同理，拱形副剪切带上的正应力为σ2、剪应力为τ2，由其确定的抗剪强度指标为c2、φ2。
如图9所示，在拱形副剪切带上定义D、E、F三点，其对应的横坐标分别为x1、x2、x3，根据副剪切带的函数表达式可以确定：
x1,x3=(−B±√(B2−4AC))/(2A) (4) x2=−B/(2A) (5) 式中，A、B、C即为式(1)中的拟合参数。将副剪切带曲线上任意一点的切线与X轴的夹角设为θ，则θ=arctan(2Ax+B)，据此将拱形副剪切带上的正应力和剪应力沿水平方向和竖直方向分解，可分别列出拱形破坏区域(图9)在水平方向和竖直方向上的平衡方程：
水平方向：
∫x2x1τ2cosθdx+∫x3x2τ2cos(−θ)dx=τ1(x3−x1) (6) 竖直方向：
∫x2x1σ2cosθdx+∫x3x2σ2cos(−θ)dx−∫x2x1τ2sinθdx+∫x3x2τ2sin(−θ)dx=σ1(x3−x1) (7) 当法向应力K一定时，副剪切带的曲线方程就确定；同时根据试验结果，剪应力峰值时刻主剪切带上的正应力σ1和剪应力τ1也确定，由此根据式(4)~式(7)可以求解出副剪切带上的正应力σ2和剪应力τ2。根据不同的法向应力水平，可求出四组副剪切带上的σ2和τ2，如表4所示。通过对4组σ2、τ2值进行线性拟合，便可求出拱形副剪切带上的抗剪强度指标c2和φ2，如图10所示。
表 4 主/副剪切带强度参数对比Table 4. Comparison on strength parameters of primary and secondary shear bands试样尺寸/
cm3主剪切带
正应力σ1/kPa主剪切带
剪应力τ1/kPa主剪切带
抗剪强度指标副剪切带
正应力σ2/kPa副剪切带
剪应力τ2/kPa副剪切带
抗剪强度指标10×10×5 50 52.7 c1=7.6 kPa
φ1=43.1°53.659 56.557 c2=8.2 kPa
φ2=43.2°100 103.0 108.120 111.364 150 150.2 163.625 163.843 200 193.2 219.886 212.410 表4同时列出了主剪切带确定的强度指标c1和φ1，与副剪切带强度指标c2和φ2进行对比，可以看出，10 cm×10 cm×5 cm尺寸试样副剪切带上的正应力和剪应力均比主剪切带上的应力值大，且应力水平越高，主、副剪切带的应力差值越大。同时，由主、副剪切带所确定的内摩擦角基本相同，而副剪切带确定的黏聚力c2也仅比主剪切带确定的c1大7.89%，增加幅度较小。因此，基本可以认为主、副剪切带得出的抗剪强度指标是一致的，从而也间接证明了副剪切带存在的合理性，是符合土的抗剪强度理论的。
4 讨论
4.1 剪切带的形成机制及影响因素
本文砂土可视化直剪试验中发现了主、副两条剪切带，而且在剪应力形成峰值前就已经形成。黏土直剪试验中并没有发现该类现象，但碎石土的大型直剪试验中也发现了主、副两条剪切带[21]，笔者认为形成主、副两条剪切带的本质原因是剪胀；颗粒旋转、翻滚，甚至破碎都会引起土体剪胀，使得颗粒运动偏离水平面，一侧向斜上方运动，受到顶板的约束，另一侧被迫向斜下方运动。
砂土直剪试验和离散元模拟也发现了剪切带偏离水平剪切缝的现象，如文献[14, 16]，并指出颗粒形状是剪切带偏离的关键。虽然剪切带发生了倾斜以及不均匀性，但并未形成明显的拱形副剪切带；对比分析发现，二者试样的高度相对较小，拱形剪切带尚未充分拱起，就受到顶板抑制，因此剪切带只是偏离，未能形成拱形副剪切带。可见试样尺寸，尤其是高度和长度的比值，对剪切带形态影响严重，并且试样长边尺寸越大，剪切时推进的长度就越长，颗粒翻滚的距离就增加，造成剪胀和副剪切带更加明显。另外，文献[15, 17]也指出剪切带的厚度对强度指标和剪切带的形态也有较大影响。
由此可见，剪切带的影响因素包括：土体剪胀特性、颗粒形状、试样的高长比、试样剪切方向的尺寸、剪切缝的厚度等，不仅影响剪切带的形态，其测得的强度指标也相差较大。笔者认为，副剪切带的存在会造成土体的抗剪强度被高估，因为理想的直剪试验只考虑剪切面上的正应力σ和剪应力τ，而拱形副剪切带会带动更多的土体抵抗外荷载，相当于抗剪材料总量的增加，造成测得的强度偏高，当然该假设有待进一步试验验证。那么如何准确测量土体的强度指标呢？三轴试验测量的结果更准确吗，会不会也存在副剪切带？需要如何修正试验方法以测得更准确的土体强度参数来指导工程实践呢？这些问题值得国内外同行们探讨解决。
4.2 存在不足与未来努力方向
受限于研究手段，以及笔者本身的研究水平，尚存在一些考虑不全面之处，有待进一步改进：
1) 为了便于拍照观察，本文砂土可视化直剪试验所采用的是方形直剪盒；对于圆形直剪盒，以及土体的三轴试验过程中，如何对试样进行图像观测分析，研究剪切带的形成过程，值得进一步探索。
2) 本文通过直剪试验过程中对剪切盒侧表面进行观测，研究剪切带的形成机制和扩展过程。尽管采取了一定的润滑措施，减小砂土与剪切盒边界的摩擦，但仍难以完全消除。试样内部其他位置剪切带的变形规律是否和侧表面完全一致，需要研发土体内部变形量测技术手段进行验证。
3) 本文主要研究砂土直剪试验过程中剪切带，尤其是副剪切带的形成机制，所选用砂土含水率较低，不涉及固结问题，因此采用快剪的方式。对于砂土试样的含水率、固结问题以及密实度等材料因素的影响，留待后续研究。
5 结论
本文通过不同尺寸的砂土可视化直剪试验，对剪切带扩展过程进行了总结，研究了副剪切带的形成机制，同时开展了破坏区域的受力分析，对主/副剪切带强度参数进行了对比，主要结论如下:
(1) 通过5种尺寸规格砂土试样的直剪试验，对试验结果进行对比分析，发现试样尺寸对抗剪强度指标确有一定的影响，当试样太薄或者太扁，即边长尺寸差异较大时，测得的强度参数也会偏离平均值，造成较大误差；建议砂土直剪试验剪切盒的长边与短边之比不宜大于2，且不应大于4。
(2) 通过对典型尺寸的砂土可视化直剪试验进行图像分析，可以将剪切带的扩展过程划分为5个阶段，即初始挤密阶段、局部屈服阶段、剪切带发展阶段、峰值应力剪切带阶段和软化阶段。
(3) 对不同法向应力下剪应力峰值时的图像进行位移场分析，发现剪切破坏区域不是始终沿着水平剪切缝发展，而是在上盒中下部逐渐形成一条向上凸起的拱形副剪切带，剪切破坏区域是沿着主、副两条剪切带而展开的。随着剪切位移的增加，拱形剪切破坏区域逐渐减小；而随着法向应力的增大，剪应力峰值时刻的拱形破坏区域逐渐增大。
(4) 通过对剪应力峰值时的拱形破坏区域进行受力分析发现，拱形副剪切带上的正应力和剪应力均大于水平主剪切带；由副剪切带得出的内摩擦角和主剪切带近似，黏聚力比主剪切带大8%左右。主/副剪切带的强度指标基本一致，间接证明了副剪切带存在的合理性，符合土的抗剪强度理论。
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